cherry-pick BN254::constraints & Grumpkin to be able to use them with compatibility at v0.4.0

* update

* use r1cs std

* fix

* rem

* Apply suggestions from code review

Co-authored-by: onewayfunc <onewayfunc@gmail.com>

.github/ISSUE_TEMPLATE/bug_report.md

@@ -0,0 +1,25 @@
+---
+name: Bug Report 
+about: Create a report to help us squash bugs!
+
+---
+
+<!-- < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < ☺ 
+v                            ✰  Thanks for opening an issue! ✰    
+v    Before smashing the submit button please review the template.
+v    Please also ensure that this is not a duplicate issue :)  
+☺ > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  -->∂
+
+## Summary of Bug
+
+<!-- Concisely describe the issue -->
+
+## Version
+
+<!-- git commit hash or tagged version -->
+
+## Steps to Reproduce
+
+<!-- Also please note what feature flags the library was compiled with? -->
+<!-- If this is a build issue, also indicate your OS and compiler versions (clang --version) -->
+

.github/ISSUE_TEMPLATE/feature_request.md

@@ -0,0 +1,35 @@
+---
+name: Feature Request
+about: Create a proposal to request a feature
+
+---
+
+<!-- < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < ☺ 
+v                            ✰  Thanks for opening an issue! ✰    
+v    Before smashing the submit button please review the template.
+v    Word of caution: poorly thought-out proposals may be rejected 
+v                     without deliberation 
+☺ > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  -->
+
+## Summary
+
+<!-- Short, concise description of the proposed feature -->
+
+## Problem Definition
+
+<!-- Why do we need this feature? 
+What problems may be addressed by introducing this feature?
+Are there any disadvantages of including this feature? -->
+
+## Proposal
+
+<!-- Detailed description of requirements of implementation -->
+
+____
+
+#### For Admin Use
+
+- [ ] Not duplicate issue
+- [ ] Appropriate labels applied
+- [ ] Appropriate contributors tagged
+- [ ] Contributor assigned/self-assigned

.github/PULL_REQUEST_TEMPLATE.md

@@ -0,0 +1,26 @@
+<!-- < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < < ☺
+v                               ✰  Thanks for creating a PR! ✰
+v    Before hitting that submit button please review the checkboxes.
+v    If a checkbox is n/a - please still include it but + a little note why
+☺ > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >  -->
+
+## Description
+
+<!-- Add a description of the changes that this PR introduces and the files that
+are the most critical to review.
+-->
+
+closes: #XXXX
+
+---
+
+Before we can merge this PR, please make sure that all the following items have been
+checked off. If any of the checklist items are not applicable, please leave them but
+write a little note why.
+
+- [ ] Targeted PR against correct branch (master)
+- [ ] Linked to Github issue with discussion and accepted design OR have an explanation in the PR that describes this work.
+- [ ] Wrote unit tests
+- [ ] Updated relevant documentation in the code
+- [ ] Added a relevant changelog entry to the `Pending` section in `CHANGELOG.md`
+- [ ] Re-reviewed `Files changed` in the Github PR explorer

.github/workflows/ci.yml

@@ -14,7 +14,7 @@ jobs:
     steps:
 
     - name: Checkout
-      uses: actions/checkout@v1
+      uses: actions/checkout@v3
     - name: Install Rust
       uses: actions-rs/toolchain@v1
       with:
@@ -29,8 +29,8 @@ jobs:
         command: fmt
         args: --all -- --check
 
-  test:
-    name: Test
+  check:
+    name: Check
     runs-on: ubuntu-latest
     env:
       RUSTFLAGS: -Dwarnings
@@ -41,7 +41,7 @@ jobs:
           - nightly
     steps:
       - name: Checkout
-        uses: actions/checkout@v2
+        uses: actions/checkout@v3
 
       - name: Install Rust (${{ matrix.rust }})
         uses: actions-rs/toolchain@v1
@@ -78,29 +78,93 @@ jobs:
             args: --all-features --examples --workspace --benches
         if: matrix.rust == 'nightly'
 
-      - name: Test
-        uses: actions-rs/cargo@v1
-        with:
-            command: test
-            args: "--workspace \
-                   --all-features \
-                   --exclude curve-benches"
+
+  directories: # Job that list subdirectories
+    name: List directories for parallelizing tests
+    runs-on: ubuntu-latest
+    outputs:
+      dir: ${{ steps.set-dirs.outputs.dir }} # generate output name dir by using inner step output
+    steps:
+      - uses: actions/checkout@v3
+      - id: set-dirs # Give it an id to handle to get step outputs in the outputs key above
+        run: echo "::set-output name=dir::$(ls -d */ | jq -R -s -c 'split("\n")[:-1]')"
+        # Define step output named dir base on ls command transformed to JSON thanks to jq
+  test:
+    name: Test
+    runs-on: ubuntu-latest
+    needs: [directories] # Depends on previous job
+    strategy:
+      matrix:
+        dir: ${{fromJson(needs.directories.outputs.dir)}} # List matrix strategy from directories dynamically
+        # rust:
+        #   - stable
+        #   - nightly
+        exclude:
+          - dir: scripts/
+          - dir: curve-constraint-tests/
+          - dir: mnt4_753/
+          - dir: mnt6_753/
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+      - name: Run tests
+        run: |
+          cd ${{matrix.dir}}
+          cargo test --all-features
+
+  test-mnt4-753:
+    name: Test (mnt4_753/)
+    runs-on: macos-latest
+    needs: [directories] # Waits for the directory listing job
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+      - name: Run tests
+        run: |
+          cd mnt4_753/
+          cargo test --all-features
+
+  test-mnt6-753:
+    name: Test (mnt6_753/)
+    runs-on: macos-latest
+    needs: [directories] # Waits for the directory listing job
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+      - name: Run tests
+        run: |
+          cd mnt6_753/
+          cargo test --all-features
+
+  docs:
+    name: Check Documentation
+    runs-on: ubuntu-latest
+    steps:
+
+    - name: Checkout
+      uses: actions/checkout@v3
+    - name: Install Rust
+      uses: actions-rs/toolchain@v1
+      with:
+        profile: minimal
+        toolchain: stable
+        override: true
+        components: rustfmt
+
+    - name: cargo doc --all --no-deps --document-private-items --all-features
+      uses: actions-rs/cargo@v1
+      with:
+        command: doc
+        args: --all --no-deps --document-private-items --all-features
 
   check_no_std:
     name: Check no_std
     runs-on: ubuntu-latest
     steps:
       - name: Checkout
-        uses: actions/checkout@v2
+        uses: actions/checkout@v3
 
       - name: Install Rust (${{ matrix.rust }})
-        uses: actions-rs/toolchain@v1
-        with:
-          toolchain: stable
-          target: thumbv6m-none-eabi
-          override: true
-
-      - name: Install Rust ARM64 (${{ matrix.rust }})
         uses: actions-rs/toolchain@v1
         with:
           toolchain: stable
@@ -119,10 +183,10 @@ jobs:
         uses: actions-rs/cargo@v1
         with:
             command: check
-            args: --examples --workspace --exclude ark-curve-tests --exclude ark-curve-benches --target thumbv6m-none-eabi
+            args: --examples --workspace --exclude ark-curve-constraint-tests --target aarch64-unknown-none
 
       - name: build
         uses: actions-rs/cargo@v1
         with:
             command: build
-            args: --workspace --exclude ark-curve-tests --exclude ark-curve-benches --target thumbv6m-none-eabi
+            args: --workspace --exclude ark-curve-constraint-tests --target aarch64-unknown-none

.github/workflows/linkify_changelog.yml

@@ -0,0 +1,20 @@
+name: Linkify Changelog
+
+on:
+  workflow_dispatch
+
+jobs:
+  linkify:
+    runs-on: ubuntu-latest
+    steps:
+    - name: Checkout
+      uses: actions/checkout@v2
+    - name: Add links
+      run: python3 scripts/linkify_changelog.py CHANGELOG.md
+    - name: Commit
+      run: |
+          git config user.name github-actions
+          git config user.email github-actions@github.com
+          git add .
+          git commit -m "Linkify Changelog"
+          git push

CHANGELOG.md

@@ -0,0 +1,81 @@
+# CHANGELOG
+
+## Pending
+
+- [\#76](https://github.com/arkworks-rs/curves/pull/76) twisted Edwards parameters for bls12-377
+- Fixed curve benches
+
+### Breaking changes
+
+- [\#104](https://github.com/arkworks-rs/curves/pull/104) Remove `QUADRATIC_NONRESIDUE` parameter from implementors of `Fp2Config`.
+- [\#129](https://github.com/arkworks-rs/curves/pull/129) Implement custom serialization for BLS12-381 for compatibility with the [Zcash lib](https://github.com/zkcrypto/bls12_381).
+ 
+### Features
+
+- [\#121](https://github.com/arkworks-rs/curves/pull/121) Add the ed25519 curve.
+- [\#122](https://github.com/arkworks-rs/curves/pull/122) Add the secp256k1 and secq256k1 curves.
+- [\#124](https://github.com/arkworks-rs/curves/pull/124) Add the curve25519 curve.
+
+### Improvements
+
+- [\#70](https://github.com/arkworks-rs/curves/pull/70) Add prepared G2 pairing consistency test. 
+- [\#74](https://github.com/arkworks-rs/curves/pull/74) Use Scott's subgroup membership tests for `G1` and `G2` of BLS12-381.
+- [\#103](https://github.com/arkworks-rs/curves/pull/103) Faster cofactor clearing for BLS12-381.
+- [\#107](https://github.com/arkworks-rs/curves/pull/107/) Use 2-NAF of `ATE_LOOP_COUNT` to speed up the Miller loop in MNT curves.
+
+
+### Bug fixes
+
+## v0.3.0 
+
+### Breaking changes
+
+- [\#60](https://github.com/arkworks-rs/curves/pull/60) Change the scalar group generator of `Fr` of `bls12_377` Fr from `11` to `22`.
+- [\#61](https://github.com/arkworks-rs/curves/pull/61) Remove `ATE_LOOP_COUNT_IS_NEGATIVE` from BN254 curve parameter.
+
+### Features
+
+- [\#64](https://github.com/arkworks-rs/curves/pull/64) Implement the Bandersnatch curve, another twisted Edwards curve for BLS12-381.
+
+### Improvements
+
+### Bug fixes
+
+## v0.2.0
+
+### Breaking changes
+
+- Requires all crates from `arkworks-rs/algebra` to have version `v0.2.0` or greater.
+
+### Features
+
+- [\#3](https://github.com/arkworks-rs/curves/pull/3) Add constraints for
+        `ark-bls12-377`,
+        `ark-ed-on-bls12-377`,
+        `ark-ed-on-bls12-381`,
+        `ark-ed-on-bn254`,
+        `ark-ed-on-cp6-782`,
+        `ark-ed-on-bw6-761`,
+        `ark-ed-on-mnt4-298`,
+        `ark-ed-on-mnt4-753`,
+        `ark-mnt4-298`,
+        `ark-mnt6-298`,
+        `ark-mnt4-753`,
+        `ark-mnt6-753`.
+- [\#7](https://github.com/arkworks-rs/curves/pull/7) Add benchmarks for Edwards curves.
+- [\#19](https://github.com/arkworks-rs/curves/pull/19) Change field constants to be provided as normal strings, instead of in Montgomery form.
+- [\#53](https://github.com/arkworks-rs/curves/pull/53) Add benchmarks for Pallas and Vesta curves.
+
+### Improvements
+
+- [\#42](https://github.com/arkworks-rs/curves/pull/42) Remove the dependency of `rand_xorshift`.
+
+### Bug fixes
+
+- [\#28](https://github.com/arkworks-rs/curves/pull/28), [\#49](https://github.com/arkworks-rs/curves/pull/49) Fix broken documentation links.
+- [\#38](https://github.com/arkworks-rs/curves/pull/38) Compile with `panic='abort'` in release mode, for safety of the library across FFI boundaries.
+- [\#45](https://github.com/arkworks-rs/curves/pull/45) Fix `ark-ed-on-mnt4-753`.
+
+## v0.1.0
+
+Initial Release

CONTRIBUTING.md

@@ -0,0 +1,65 @@
+# Contributing
+
+Thank you for considering making contributions to `curves`!
+
+Contributing to this repo can be done in several forms, such as participating in discussion or proposing code changes. 
+To ensure a smooth workflow for all contributors, the following general procedure for contributing has been established:
+
+1) Either open or find an issue you'd like to help with
+2) Participate in thoughtful discussion on that issue
+3) If you would like to contribute:
+    * If the issue is a feature proposal, ensure that the proposal has been accepted
+    * Ensure that nobody else has already begun working on this issue. 
+    If they have, please try to contact them to collaborate
+    * If nobody has been assigned for the issue and you would like to work on it, make a comment on the issue to inform the community of your intentions to begin work. (So we can avoid duplication of efforts)
+    * We suggest using standard Github best practices for contributing: fork the repo, branch from the HEAD of `master`, make some commits on your branch, and submit a PR from the branch to `master`.
+    More detail on this is below
+    * Be sure to include a relevant change log entry in the Pending section of CHANGELOG.md (see file for log format)
+        * If the change is breaking, we may add migration instructions.
+
+Note that for very small or clear problems (such as typos), or well isolated improvements, it is not required to an open issue to submit a PR.
+But be aware that for more complex problems/features touching multiple parts of the codebase, if a PR is opened before an adequate design discussion has taken place in a github issue, that PR runs a larger likelihood of being rejected.
+
+Looking for a good place to start contributing? How about checking out some good first issues
+
+## Branch Structure
+
+`curves` has its default branch as `master`, which is where PRs are merged into. Releases will be periodically made, on no set schedule.
+All other branches should be assumed to be miscellaneous feature development branches.
+
+All downstream users of the library should be using tagged versions of the library pulled from cargo.
+
+## How to work on a fork
+Please skip this section if you're familiar with contributing to opensource github projects.
+
+First fork the repo from the github UI, and clone it locally.
+Then in the repo, you want to add the repo you forked from as a new remote. You do this as:
+```bash
+git remote add upstream git@github.com:arkworks-rs/curves.git
+```
+
+Then the way you make code contributions is to first think of a branch name that describes your change.
+Then do the following:
+```bash
+git checkout master
+git pull upstream master
+git checkout -b $NEW_BRANCH_NAME
+```
+and then work as normal on that branch, and pull request to upstream master when you're done =)
+
+## Updating documentation
+
+All PRs should aim to leave the code more documented than it started with.
+Please don't assume that its easy to infer what the code is doing,
+as that is usually not the case for these complex protocols.
+(Even when you already understand the paper!)
+
+Its often very useful to describe what is the high level view of what a code block is doing,
+and either refer to the relevant section of a paper or include a short proof/argument for why it makes sense before the actual logic.
+
+## Performance improvements
+
+All performance improvements should be accompanied with benchmarks improving, or otherwise have it be clear that things have improved.
+For some areas of the codebase, performance roughly follows the number of field multiplications, but there are also many areas where
+hard to predict low level system effects such as cache locality and superscalar operations become important for performance.
+Thus performance can often become very non-intuitive / diverge from minimizing the number of arithmetic operations.

Cargo.lock

@@ -1,458 +0,0 @@
-# This file is automatically @generated by Cargo.
-# It is not intended for manual editing.
-[[package]]
-name = "ark-bls12-377"
-version = "0.1.0"
-dependencies = [
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-bls12-381"
-version = "0.1.0"
-dependencies = [
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-bn254"
-version = "0.1.0"
-dependencies = [
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-bw6-761"
-version = "0.1.0"
-dependencies = [
- "ark-bls12-377",
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-cp6-782"
-version = "0.1.0"
-dependencies = [
- "ark-bls12-377",
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-curve-benches"
-version = "0.1.1-alpha.0"
-dependencies = [
- "ark-bls12-377",
- "ark-bls12-381",
- "ark-bn254",
- "ark-bw6-761",
- "ark-cp6-782",
- "ark-ec",
- "ark-ff",
- "ark-mnt4-298",
- "ark-mnt4-753",
- "ark-mnt6-298",
- "ark-mnt6-753",
- "ark-serialize",
- "paste",
- "rand",
- "rand_xorshift",
- "rustc_version",
-]
-
-[[package]]
-name = "ark-curve-tests"
-version = "0.1.0"
-dependencies = [
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-ec"
-version = "0.1.0"
-source = "git+https://github.com/arkworks-rs/algebra#d5202f896ca9700c5c22d7a1266ada600f913dc4"
-dependencies = [
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "derivative",
- "num-traits",
- "rand",
-]
-
-[[package]]
-name = "ark-ed-on-bls12-377"
-version = "0.1.0"
-dependencies = [
- "ark-bls12-377",
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-ed-on-bls12-381"
-version = "0.1.0"
-dependencies = [
- "ark-bls12-381",
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-ed-on-bn254"
-version = "0.1.0"
-dependencies = [
- "ark-bn254",
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-ed-on-bw6-761"
-version = "0.1.0"
-dependencies = [
- "ark-ed-on-cp6-782",
-]
-
-[[package]]
-name = "ark-ed-on-cp6-782"
-version = "0.1.0"
-dependencies = [
- "ark-bls12-377",
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-ed-on-mnt4-298"
-version = "0.1.0"
-dependencies = [
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-mnt4-298",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-ff"
-version = "0.1.0"
-source = "git+https://github.com/arkworks-rs/algebra#d5202f896ca9700c5c22d7a1266ada600f913dc4"
-dependencies = [
- "ark-ff-asm",
- "ark-serialize",
- "ark-std",
- "derivative",
- "num-traits",
- "rand",
- "rustc_version",
-]
-
-[[package]]
-name = "ark-ff-asm"
-version = "0.1.0"
-source = "git+https://github.com/arkworks-rs/algebra#d5202f896ca9700c5c22d7a1266ada600f913dc4"
-dependencies = [
- "quote",
- "syn",
-]
-
-[[package]]
-name = "ark-mnt4-298"
-version = "0.1.0"
-dependencies = [
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-mnt4-753"
-version = "0.1.0"
-dependencies = [
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-mnt6-298"
-version = "0.1.0"
-dependencies = [
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-mnt4-298",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-mnt6-753"
-version = "0.1.0"
-dependencies = [
- "ark-curve-tests",
- "ark-ec",
- "ark-ff",
- "ark-mnt4-753",
- "ark-serialize",
- "ark-std",
- "rand",
- "rand_xorshift",
-]
-
-[[package]]
-name = "ark-serialize"
-version = "0.1.0"
-source = "git+https://github.com/arkworks-rs/algebra#d5202f896ca9700c5c22d7a1266ada600f913dc4"
-dependencies = [
- "ark-std",
-]
-
-[[package]]
-name = "ark-std"
-version = "0.1.0"
-source = "git+https://github.com/arkworks-rs/utils#7bde3ab01799da8429b8fa9c3f152201415cdfe7"
-
-[[package]]
-name = "autocfg"
-version = "1.0.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "cdb031dd78e28731d87d56cc8ffef4a8f36ca26c38fe2de700543e627f8a464a"
-
-[[package]]
-name = "cfg-if"
-version = "0.1.10"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4785bdd1c96b2a846b2bd7cc02e86b6b3dbf14e7e53446c4f54c92a361040822"
-
-[[package]]
-name = "derivative"
-version = "2.1.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "cb582b60359da160a9477ee80f15c8d784c477e69c217ef2cdd4169c24ea380f"
-dependencies = [
- "proc-macro2",
- "quote",
- "syn",
-]
-
-[[package]]
-name = "getrandom"
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Cargo.toml

@@ -1,8 +1,7 @@
 [workspace]
 
 members = [
-    "curve-benches",
-    "curve-tests",
+    "curve-constraint-tests",
 
     "bls12_377",
     "ed_on_bls12_377",
@@ -15,9 +14,11 @@ members = [
 
     "bls12_381",
     "ed_on_bls12_381",
+    "ed_on_bls12_381_bandersnatch",
 
     "bn254",
     "ed_on_bn254",
+    "grumpkin",
 
     "mnt4_298",
     "mnt6_298",
@@ -25,13 +26,24 @@ members = [
 
     "mnt4_753",
     "mnt6_753",
-    "ed_on_mnt4_298",
+    "ed_on_mnt4_753",
+
+    "pallas",
+    "vesta",
+
+    "secp256k1",
+    "secq256k1",
+    
+    "curve25519",
+    "ed25519",
 ]
+resolver = "2"
 
 [profile.release]
 opt-level = 3
 lto = "thin"
 incremental = true
+panic = 'abort'
 
 [profile.bench]
 opt-level = 3
@@ -43,6 +55,7 @@ debug-assertions = false
 
 [profile.dev]
 opt-level = 0
+panic = 'abort'
 
 [profile.test]
 opt-level = 3
@@ -50,3 +63,11 @@ lto = "thin"
 incremental = true
 debug-assertions = true
 debug = true
+
+# The following patch is to use a version of ark-r1cs-std compatible with
+# v0.4.0 but that includes a cherry-picked commit from after v0.4.0 which fixes
+# the in-circuit scalar multiplication of the zero point. The commit is from
+# https://github.com/arkworks-rs/r1cs-std/pull/124, without including other
+# changes done between v0.4.0 and this fix which would break compatibility.
+[patch.crates-io]
+ark-r1cs-std = { git = "https://github.com/arnaucube/ark-r1cs-std-cherry-picked/" }

README.md

@@ -1,31 +1,36 @@
 # Curve implementations
 
-This directory contains implementations of some popular elliptic curves.
+This repository contains implementations of some popular elliptic curves. The curve API implemented here matches the curve traits defined [here](https://github.com/arkworks-rs/algebra/blob/master/ec/src/lib.rs) in the [arkworks-rs/algebra](https://github.com/arkworks-rs/algebra) repository.
 
 ### BLS12-381 and embedded curves
-* [`ark-bls12-381`](bls12-381): Implements the BLS12-381 pairing-friendly curve
-* [`ark-ed-on-bls12-381`](ed-on-bls12-381): Implements a Twisted Edwards curve atop the scalar field of BLS12-381
+* [`ark-bls12-381`](bls12_381): Implements the BLS12-381 pairing-friendly curve
+* [`ark-ed-on-bls12-381`](ed_on_bls12_381): Implements a Twisted Edwards curve atop the scalar field of BLS12-381
+* [`ark-ed-on-bls12-381-bandersnatch`](ed_on_bls12_381_bandersnatch): Implements Bandersnatch, another Twisted Edwards curve atop the scalar field of BLS12-381
 
 ### BLS12-377 and related curves
-* [`ark-bls12-377`](bls12-377): Implements the BLS12-377 pairing-friendly curve
-* [`ark-ed-on-bls12-377`](ed-on-bls12-377): Implements a Twisted Edwards curve atop the scalar field of BLS12-377
+* [`ark-bls12-377`](bls12_377): Implements the BLS12-377 pairing-friendly curve
+* [`ark-ed-on-bls12-377`](ed_on_bls12_377): Implements a Twisted Edwards curve atop the scalar field of BLS12-377
 
-* [`ark-bw6-761`](bw6-761): Implements the BW6-761 pairing-friendly curve, which is a curve whose scalar field equals the base field of BLS12-377
-* [`ark-ed-on-bw6-761`](ed-on-bw6-761): Implements a Twisted Edwards curve atop the scalar field of BW6-761
+* [`ark-bw6-761`](bw6_761): Implements the BW6-761 pairing-friendly curve, which is a curve whose scalar field equals the base field of BLS12-377
+* [`ark-ed-on-bw6-761`](ed_on_bw6_761): Implements a Twisted Edwards curve atop the scalar field of BW6-761
 
-* [`ark-cp6-782`](cp6-782): Implements the CP6-782 pairing-friendly curve, which is a curve whose scalar field equals the base field of BLS12-377
-* [`ark-ed-on-cp6-782`](ed-on-cp6-782): Implements a Twisted Edwards curve atop the scalar field of CP6-782. This is the same curve as in `ark-ed-on-bw6-761`
+* [`ark-cp6-782`](cp6_782): Implements the CP6-782 pairing-friendly curve, which is a curve whose scalar field equals the base field of BLS12-377
+* [`ark-ed-on-cp6-782`](ed_on_cp6_782): Implements a Twisted Edwards curve atop the scalar field of CP6-782. This is the same curve as in `ark-ed-on-bw6-761`
 
 ### BN254 and related curves
 * [`ark-bn254`](bn254): Implements the BN254 pairing-friendly curve
-* [`ark-ed-on-bn254`](ed-on-bn254): Implements a Twisted Edwards curve atop the scalar field of BN254
+* [`ark-ed-on-bn254`](ed_on_bn254): Implements a Twisted Edwards curve atop the scalar field of BN254
 
 ### MNT-298 cycle of curves and related curves
-* [`ark-mnt4-298`](mnt4-298): Implements the MNT4-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-298
-* [`ark-mnt6-298`](mnt6-298): Implements the MNT6-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT4-298
-* [`ark-ed-on-mnt4-298`](ed-on-mnt4-298): Implements a Twisted Edwards curve atop the scalar field of MNT4-298
+* [`ark-mnt4-298`](mnt4_298): Implements the MNT4-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-298
+* [`ark-mnt6-298`](mnt6_298): Implements the MNT6-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT4-298
+* [`ark-ed-on-mnt4-298`](ed_on_mnt4_298): Implements a Twisted Edwards curve atop the scalar field of MNT4-298
 
 ### MNT-753 cycle of curves and related curves
-* [`ark-mnt4-753`](mnt4-753): Implements the MNT4-753 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-753
-* [`ark-mnt6-753`](mnt6-753): Implements the MNT6-753 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT4-753
-* [`ark-ed-on-mnt4-753`](ed-on-mnt4-753): Implements a Twisted Edwards curve atop the scalar field of MNT4-753
+* [`ark-mnt4-753`](mnt4_753): Implements the MNT4-753 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-753
+* [`ark-mnt6-753`](mnt6_753): Implements the MNT6-753 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT4-753
+* [`ark-ed-on-mnt4-753`](ed_on_mnt4_753): Implements a Twisted Edwards curve atop the scalar field of MNT4-753
+
+### [Pasta](https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/) cycle of curves
+* [`ark-pallas`](pallas): Implements Pallas, a prime-order curve that forms an amicable pair with Vesta
+* [`ark-vesta`](vesta): Implements Vesta, a prime-order curve that forms an amicable pair with Pallas

bls12_377/Cargo.toml

@@ -1,27 +1,29 @@
 [package]
 name = "ark-bls12-377"
-version = "0.1.0"
+version = "0.4.0-alpha.2"
 authors = [ "arkworks contributors" ]
 description = "The BLS12-377 pairing-friendly elliptic curve"
-homepage = "https://arworks.rs"
-repository = "https://github.com/arkworks/algebra"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
 documentation = "https://docs.rs/ark-bls12-377/"
-keywords = ["cryptography", "finite fields", "elliptic curves" ]
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"
 
 [dependencies]
-ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-ff = { version="0.4.0-alpha", default-features = false }
+ark-ec = { version="0.4.0-alpha", default-features = false }
+ark-r1cs-std = { version="0.4.0-alpha", default-features = false, optional = true }
+ark-std = { version = "0.4.0-alpha", default-features = false }
 
 [dev-dependencies]
-ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-curve-tests = { path = "../curve-tests", default-features = false }
-rand = { version = "0.7", default-features = false }
-rand_xorshift = "0.2"
+ark-relations = { version="0.4.0-alpha", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }
+ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }
 
 [features]
 default = [ "curve" ]
@@ -30,3 +32,9 @@ std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
 curve = [ "scalar_field", "base_field" ]
 scalar_field = []
 base_field = []
+r1cs = [ "base_field", "ark-r1cs-std" ]
+
+[[bench]]
+name = "bls12_377"
+path = "benches/bls12_377.rs"
+harness = false

bls12_377/benches/bls12_377.rs

@@ -0,0 +1,16 @@
+use ark_algebra_bench_templates::*;
+
+use ark_bls12_377::{
+    fq::Fq, fq2::Fq2, fr::Fr, Bls12_377, Fq12, G1Projective as G1, G2Projective as G2,
+};
+
+bench!(
+    Name = "Bls12_377",
+    Pairing = Bls12_377,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq2,
+    TargetField = Fq12,
+);

bls12_377/scripts/base_field.sage

@@ -0,0 +1,28 @@
+modulus = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

bls12_377/scripts/scalar_field.sage

@@ -0,0 +1,28 @@
+modulus = 8444461749428370424248824938781546531375899335154063827935233455917409239041
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 30):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

bls12_377/src/constraints/curves.rs

@@ -0,0 +1,39 @@
+use ark_ec::{bls12::Bls12Config, CurveConfig};
+use ark_r1cs_std::{
+    fields::fp::FpVar,
+    groups::{bls12, curves::twisted_edwards::AffineVar as TEAffineVar},
+};
+
+use crate::Config;
+
+/// An element of G1 in the BLS12-377 bilinear group.
+pub type G1Var = bls12::G1Var<Config>;
+/// An element of G2 in the BLS12-377 bilinear group.
+pub type G2Var = bls12::G2Var<Config>;
+
+/// An element of G1 (in TE Affine form) in the BLS12-377 bilinear group.
+pub type G1TEAffineVar = TEAffineVar<
+    <Config as Bls12Config>::G1Config,
+    FpVar<<<Config as Bls12Config>::G1Config as CurveConfig>::BaseField>,
+>;
+
+/// Represents the cached precomputation that can be performed on a G1 element
+/// which enables speeding up pairing computation.
+pub type G1PreparedVar = bls12::G1PreparedVar<Config>;
+/// Represents the cached precomputation that can be performed on a G2 element
+/// which enables speeding up pairing computation.
+pub type G2PreparedVar = bls12::G2PreparedVar<Config>;
+
+#[test]
+fn test() {
+    use ark_ec::models::bls12::Bls12Config;
+    ark_curve_constraint_tests::curves::sw_test::<<Config as Bls12Config>::G1Config, G1Var>()
+        .unwrap();
+    ark_curve_constraint_tests::curves::te_test::<
+        <Config as Bls12Config>::G1Config,
+        G1TEAffineVar,
+    >()
+    .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<<Config as Bls12Config>::G2Config, G2Var>()
+        .unwrap();
+}

bls12_377/src/constraints/fields.rs

@@ -0,0 +1,32 @@
+use ark_r1cs_std::fields::{fp::FpVar, fp12::Fp12Var, fp2::Fp2Var, fp6_3over2::Fp6Var};
+
+use crate::{Fq, Fq12Config, Fq2Config, Fq6Config};
+
+/// A variable that is the R1CS equivalent of `crate::Fq`.
+pub type FqVar = FpVar<Fq>;
+
+/// A variable that is the R1CS equivalent of `crate::Fq2`.
+pub type Fq2Var = Fp2Var<Fq2Config>;
+/// A variable that is the R1CS equivalent of `crate::Fq6`.
+pub type Fq6Var = Fp6Var<Fq6Config>;
+/// A variable that is the R1CS equivalent of `crate::Fq12`.
+pub type Fq12Var = Fp12Var<Fq12Config>;
+
+#[test]
+fn bls12_377_field_test() {
+    use super::*;
+    use crate::{Fq, Fq12, Fq2, Fq6};
+    use ark_curve_constraint_tests::fields::*;
+
+    field_test::<_, _, FqVar>().unwrap();
+    frobenius_tests::<Fq, _, FqVar>(13).unwrap();
+
+    field_test::<_, _, Fq2Var>().unwrap();
+    frobenius_tests::<Fq2, _, Fq2Var>(13).unwrap();
+
+    field_test::<_, _, Fq6Var>().unwrap();
+    frobenius_tests::<Fq6, _, Fq6Var>(13).unwrap();
+
+    field_test::<_, _, Fq12Var>().unwrap();
+    frobenius_tests::<Fq12, _, Fq12Var>(13).unwrap();
+}

bls12_377/src/constraints/mod.rs

@@ -0,0 +1,163 @@
+//! This module implements the R1CS equivalent of `crate`.
+//!
+//! It implements field variables for `crate::{Fq, Fq2, Fq6, Fq12}`,
+//! group variables for `crate::{G1, G2}`, and implements constraint
+//! generation for computing `Bls12_377::pairing`.
+//!
+//! The field underlying these constraints is `crate::Fq`.
+//!
+//! # Examples
+//!
+//! One can perform standard algebraic operations on `FqVar`:
+//!
+//! ```
+//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+//! use ark_std::UniformRand;
+//! use ark_relations::r1cs::*;
+//! use ark_r1cs_std::prelude::*;
+//! use ark_bls12_377::{*, constraints::*};
+//!
+//! let cs = ConstraintSystem::<Fq>::new_ref();
+//! // This rng is just for test purposes; do not use it
+//! // in real applications.
+//! let mut rng = ark_std::test_rng();
+//!
+//! // Generate some random `Fq` elements.
+//! let a_native = Fq::rand(&mut rng);
+//! let b_native = Fq::rand(&mut rng);
+//!
+//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
+//! let a = FqVar::new_witness(ark_relations::ns!(cs, "generate_a"), || Ok(a_native))?;
+//! let b = FqVar::new_witness(ark_relations::ns!(cs, "generate_b"), || Ok(b_native))?;
+//!
+//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
+//! // constraints or variables.
+//! let a_const = FqVar::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
+//! let b_const = FqVar::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
+//!
+//! let one = FqVar::one();
+//! let zero = FqVar::zero();
+//!
+//! // Sanity check one + one = two
+//! let two = &one + &one + &zero;
+//! two.enforce_equal(&one.double()?)?;
+//!
+//! assert!(cs.is_satisfied()?);
+//!
+//! // Check that the value of &a + &b is correct.
+//! assert_eq!((&a + &b).value()?, a_native + &b_native);
+//!
+//! // Check that the value of &a * &b is correct.
+//! assert_eq!((&a * &b).value()?, a_native * &b_native);
+//!
+//! // Check that operations on variables and constants are equivalent.
+//! (&a + &b).enforce_equal(&(&a_const + &b_const))?;
+//! assert!(cs.is_satisfied()?);
+//! # Ok(())
+//! # }
+//! ```
+//!
+//! One can also perform standard algebraic operations on `G1Var` and `G2Var`:
+//!
+//! ```
+//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+//! # use ark_std::UniformRand;
+//! # use ark_relations::r1cs::*;
+//! # use ark_r1cs_std::prelude::*;
+//! # use ark_bls12_377::{*, constraints::*};
+//!
+//! # let cs = ConstraintSystem::<Fq>::new_ref();
+//! # let mut rng = ark_std::test_rng();
+//!
+//! // Generate some random `G1` elements.
+//! let a_native = G1Projective::rand(&mut rng);
+//! let b_native = G1Projective::rand(&mut rng);
+//!
+//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
+//! let a = G1Var::new_witness(ark_relations::ns!(cs, "a"), || Ok(a_native))?;
+//! let b = G1Var::new_witness(ark_relations::ns!(cs, "b"), || Ok(b_native))?;
+//!
+//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
+//! // constraints or variables.
+//! let a_const = G1Var::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
+//! let b_const = G1Var::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
+//!
+//! // This returns the identity of `G1`.
+//! let zero = G1Var::zero();
+//!
+//! // Sanity check one + one = two
+//! let two_a = &a + &a + &zero;
+//! two_a.enforce_equal(&a.double()?)?;
+//!
+//! assert!(cs.is_satisfied()?);
+//!
+//! // Check that the value of &a + &b is correct.
+//! assert_eq!((&a + &b).value()?, a_native + &b_native);
+//!
+//! // Check that operations on variables and constants are equivalent.
+//! (&a + &b).enforce_equal(&(&a_const + &b_const))?;
+//! assert!(cs.is_satisfied()?);
+//! # Ok(())
+//! # }
+//! ```
+//!
+//! Finally, one can check pairing computations as well:
+//!
+//! ```
+//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+//! # use ark_std::UniformRand;
+//! # use ark_ec::pairing::Pairing;
+//! # use ark_relations::r1cs::*;
+//! # use ark_r1cs_std::prelude::*;
+//! # use ark_bls12_377::{*, constraints::*};
+//!
+//! # let cs = ConstraintSystem::<Fq>::new_ref();
+//! # let mut rng = ark_std::test_rng();
+//!
+//! // Generate random `G1` and `G2` elements.
+//! let a_native = G1Projective::rand(&mut rng);
+//! let b_native = G2Projective::rand(&mut rng);
+//!
+//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
+//! let a = G1Var::new_witness(ark_relations::ns!(cs, "a"), || Ok(a_native))?;
+//! let b = G2Var::new_witness(ark_relations::ns!(cs, "b"), || Ok(b_native))?;
+//!
+//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
+//! // constraints or variables.
+//! let a_const = G1Var::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
+//! let b_const = G2Var::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
+//!
+//! let pairing_result_native = Bls12_377::pairing(a_native, b_native);
+//!
+//! // Prepare `a` and `b` for pairing.
+//! let a_prep = constraints::PairingVar::prepare_g1(&a)?;
+//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! let pairing_result = constraints::PairingVar::pairing(a_prep, b_prep)?;
+//!
+//! // Check that the value of &a + &b is correct.
+//! assert_eq!(pairing_result.value()?, pairing_result_native.0);
+//!
+//! // Check that operations on variables and constants are equivalent.
+//! let a_prep_const = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
+//! println!("Done here 3");
+//!
+//! pairing_result.enforce_equal(&pairing_result_const)?;
+//! assert!(cs.is_satisfied()?);
+//! # Ok(())
+//! # }
+//! ```
+
+mod fields;
+pub use fields::*;
+
+#[cfg(feature = "curve")]
+mod curves;
+#[cfg(feature = "curve")]
+mod pairing;
+
+#[cfg(feature = "curve")]
+pub use curves::*;
+#[cfg(feature = "curve")]
+pub use pairing::*;

bls12_377/src/constraints/pairing.rs

@@ -0,0 +1,13 @@
+use crate::Config;
+
+/// Specifies the constraints for computing a pairing in the BLS12-377 bilinear
+/// group.
+pub type PairingVar = ark_r1cs_std::pairing::bls12::PairingVar<Config>;
+
+#[test]
+fn test() {
+    use crate::Bls12_377;
+    ark_curve_constraint_tests::pairing::bilinearity_test::<Bls12_377, PairingVar>().unwrap();
+    ark_curve_constraint_tests::pairing::g2_prepare_consistency_test::<Bls12_377, PairingVar>()
+        .unwrap();
+}

bls12_377/src/curves/g1.rs

@@ -1,77 +1,211 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{
-    biginteger::{BigInteger256, BigInteger384},
-    field_new, Zero,
+use ark_ec::models::{
+    short_weierstrass::{Affine as SWAffine, SWCurveConfig},
+    twisted_edwards::{
+        Affine as TEAffine, MontCurveConfig, Projective as TEProjective, TECurveConfig,
+    },
+    CurveConfig,
 };
+use ark_ff::{Field, MontFp, Zero};
+use core::ops::Neg;
 
 use crate::{Fq, Fr};
 
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Config {
     type BaseField = Fq;
     type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    const COEFF_A: Fq = field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0]));
-
-    /// COEFF_B = 1
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, BigInteger384([
-        0x2cdffffffffff68,
-        0x51409f837fffffb1,
-        0x9f7db3a98a7d3ff2,
-        0x7b4e97b76e7c6305,
-        0x4cf495bf803c84e8,
-        0x8d6661e2fdf49a,
-    ]));
 
     /// COFACTOR = (x - 1)^2 / 3  = 30631250834960419227450344600217059328
     const COFACTOR: &'static [u64] = &[0x0, 0x170b5d4430000000];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
     /// = 5285428838741532253824584287042945485047145357130994810877
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
-        2013239619100046060,
-        4201184776506987597,
-        2526766393982337036,
-        1114629510922847535,
-    ]));
+    const COFACTOR_INV: Fr = MontFp!("5285428838741532253824584287042945485047145357130994810877");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 1
+    const COEFF_B: Fq = Fq::ONE;
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1SWAffine = G1SWAffine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 
     #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
 }
 
+pub type G1SWAffine = SWAffine<Config>;
+pub type G1TEAffine = TEAffine<Config>;
+pub type G1TEProjective = TEProjective<Config>;
+
+/// Bls12_377::G1 also has a twisted Edwards form.
+/// It can be obtained via the following script, implementing
+/// 1. SW -> Montgomery -> TE1 transformation: <https://en.wikipedia.org/wiki/Montgomery_curve>
+/// 2. TE1 -> TE2 normalization (enforcing `a = -1`)
+/// ``` sage
+/// # modulus
+/// p = 0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001
+/// Fp = Zmod(p)
+///
+/// #####################################################
+/// # Weierstrass curve: y² = x³ + A * x + B
+/// #####################################################
+/// # curve y^2 = x^3 + 1
+/// WA = Fp(0)
+/// WB = Fp(1)
+///
+/// #####################################################
+/// # Montgomery curve: By² = x³ + A * x² + x
+/// #####################################################
+/// # root for x^3 + 1 = 0
+/// alpha = -1
+/// # s = 1 / (sqrt(3alpha^2 + a))
+/// s = 1/(Fp(3).sqrt())
+///
+/// # MA = 3 * alpha * s
+/// MA = Fp(228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384)
+/// # MB = s
+/// MB = Fp(10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931)
+///
+/// # #####################################################
+/// # # Twisted Edwards curve 1: a * x² + y² = 1 + d * x² * y²
+/// # #####################################################
+/// # We first convert to TE form obtaining a curve with a != -1, and then
+/// # apply a transformation to obtain a TE curve with a = -1.
+/// # a = (MA+2)/MB
+/// TE1a = Fp(61134141799337779744243169579317764548490943457438569789767076791016838392692895365021181670618017873462480451583)
+/// # b = (MA-2)/MB
+/// TE1d = Fp(197530284213631314266409564115575768987902569297476090750117185875703629955647927409947706468955342250977841006588)
+///
+/// # #####################################################
+/// # # Twisted Edwards curve 2: a * x² + y² = 1 + d * x² * y²
+/// # #####################################################
+/// # a = -1
+/// TE2a = Fp(-1)
+/// # b = -TE1d/TE1a
+/// TE2d = Fp(122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179)
+/// ```
+impl TECurveConfig for Config {
+    /// COEFF_A = -1
+    const COEFF_A: Fq = MontFp!("-1");
+
+    /// COEFF_D = 122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179 mod q
+    const COEFF_D: Fq = MontFp!("122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179");
+
+    /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
+    const GENERATOR: G1TEAffine = G1TEAffine::new_unchecked(TE_GENERATOR_X, TE_GENERATOR_Y);
+
+    type MontCurveConfig = Config;
+
+    /// Multiplication by `a` is multiply by `-1`.
+    #[inline(always)]
+    fn mul_by_a(elem: Self::BaseField) -> Self::BaseField {
+        elem.neg()
+    }
+}
+
+// BLS12-377::G1 also has a Montgomery form.
+// BLS12-377::G1 also has a twisted Edwards form.
+// It can be obtained via the following script, implementing
+// SW -> Montgomery transformation: <https://en.wikipedia.org/wiki/Montgomery_curve>
+// ``` sage
+// # modulus
+// p=0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001
+// Fp=Zmod(p)
+//
+// #####################################################
+// # Weierstrass curve: y² = x³ + A * x + B
+// #####################################################
+// # curve y^2 = x^3 + 1
+// WA=Fp(0)
+// WB=Fp(1)
+//
+// #####################################################
+// # Montgomery curve: By² = x³ + A * x² + x
+// #####################################################
+// # root for x^3 + 1 = 0
+// alpha = -1
+// # s = 1 / (sqrt(3alpha^2 + a))
+// s = 1/(Fp(3).sqrt())
+//
+// # MA = 3 * alpha * s
+// MA=Fp(228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384)
+// # MB = s
+// MB=Fp(10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931)
+// ```
+impl MontCurveConfig for Config {
+    /// COEFF_A = 228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384
+    const COEFF_A: Fq = MontFp!("228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384");
+
+    /// COEFF_B = 10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931
+    const COEFF_B: Fq = MontFp!("10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931");
+
+    type TECurveConfig = Config;
+}
+
 /// G1_GENERATOR_X =
 /// 81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger384([
-    0x260f33b9772451f4,
-    0xc54dd773169d5658,
-    0x5c1551c469a510dd,
-    0x761662e4425e1698,
-    0xc97d78cc6f065272,
-    0xa41206b361fd4d,
-]));
+pub const G1_GENERATOR_X: Fq = MontFp!("81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695");
 
 /// G1_GENERATOR_Y =
 /// 241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger384([
-    0x8193961fb8cb81f3,
-    0x638d4c5f44adb8,
-    0xfafaf3dad4daf54a,
-    0xc27849e2d655cd18,
-    0x2ec3ddb401d52814,
-    0x7da93326303c71,
-]));
+pub const G1_GENERATOR_Y: Fq = MontFp!("241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030");
+
+// The generator for twisted Edward form is the same SW generator converted into
+// the normalized TE form (TE2).
+//``` sage
+// # following scripts in previous section
+// #####################################################
+// # Weierstrass curve generator
+// #####################################################
+// Wx = Fp(81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695)
+// Wy = Fp(241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030)
+//
+// assert(Wy^2 - Wx^3 - WA * Wx - WB == 0)
+//
+// #####################################################
+// # Montgomery curve generator
+// #####################################################
+// # x = s * (x - alpha)
+// Mx = Fp(251803586774461569862800610331871502335378228972505599912537082323947581271784390797244487924068052270360793200630)
+// # y = s * y
+// My = Fp(77739247071951651095607889637653357561348174979132042929587539214321586851215673796661346812932566642719051699820)
+//
+// assert(MB * My^2 == Mx^3+ MA * Mx^2 + Mx)
+//
+// # #####################################################
+// # # Twisted Edwards curve 1 generator
+// # #####################################################
+// # x = Mx/My
+// TE1x = Fp(82241236807150726090333472814441006963902378430536027612759193445733851062772474760677400112551677454953925168208)
+// # y = (Mx - 1)/(Mx+1)
+// TE1y = Fp(6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235)
+//
+// assert( TE1a * TE1x^2 + TE1y^2 == 1 + TE1d * TE1x^2 * TE1y^2 )
+//
+//
+// # #####################################################
+// # # Twisted Edwards curve 2 generator
+// # #####################################################
+// beta = (-TE1a).sqrt()
+// # x = TE1x * sqrt(-TE1a)
+// TE2x = Fp(71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393)
+// # y = TE1y
+// TE2y = Fp(6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235)
+//
+// assert( TE2a * TE2x^2 + TE2y^2 == 1 + TE2d * TE2x^2 * TE2y^2 )
+// ```
+/// TE_GENERATOR_X =
+/// 71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393
+pub const TE_GENERATOR_X: Fq = MontFp!("71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393");
+
+/// TE_GENERATOR_Y =
+/// 6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235
+pub const TE_GENERATOR_Y: Fq = MontFp!("6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235");

bls12_377/src/curves/g2.rs

@@ -1,45 +1,18 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{
-    biginteger::{BigInteger256, BigInteger384},
-    field_new, Zero,
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
 };
+use ark_ff::{Field, MontFp, Zero};
 
 use crate::{g1, Fq, Fq2, Fr};
 
+pub type G2Affine = Affine<Config>;
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Config {
     type BaseField = Fq2;
     type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = [0, 0]
-    #[rustfmt::skip]
-    const COEFF_A: Fq2 = field_new!(Fq2,
-        g1::Parameters::COEFF_A,
-        g1::Parameters::COEFF_A,
-    );
-
-    // As per https://eprint.iacr.org/2012/072.pdf,
-    // this curve has b' = b/i, where b is the COEFF_B of G1, and x^6 -i is
-    // the irreducible poly used to extend from Fp2 to Fp12.
-    // In our case, i = u (App A.3, T_6).
-    /// COEFF_B = [0,
-    /// 155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906]
-    #[rustfmt::skip]
-    const COEFF_B: Fq2 = field_new!(Fq2,
-        field_new!(Fq, BigInteger384([0, 0, 0, 0, 0, 0])),
-        field_new!(Fq, BigInteger384([
-            9255502405446297221,
-            10229180150694123945,
-            9215585410771530959,
-            13357015519562362907,
-            5437107869987383107,
-            16259554076827459,
-        ])),
-    );
 
     /// COFACTOR =
     /// 7923214915284317143930293550643874566881017850177945424769256759165301436616933228209277966774092486467289478618404761412630691835764674559376407658497
@@ -57,73 +30,49 @@ impl SWModelParameters for Parameters {
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
     /// = 6764900296503390671038341982857278410319949526107311149686707033187604810669
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
-        15499857013495546999,
-        4613531467548868169,
-        14546778081091178013,
-        549402535258503313,
-    ]));
+    const COFACTOR_INV: Fr =
+        MontFp!("6764900296503390671038341982857278410319949526107311149686707033187604810669");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = [0, 0]
+    const COEFF_A: Fq2 = Fq2::new(g1::Config::COEFF_A, g1::Config::COEFF_A);
+
+    // As per https://eprint.iacr.org/2012/072.pdf,
+    // this curve has b' = b/i, where b is the COEFF_B of G1, and x^6 -i is
+    // the irreducible poly used to extend from Fp2 to Fp12.
+    // In our case, i = u (App A.3, T_6).
+    /// COEFF_B = [0,
+    /// 155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906]
+    const COEFF_B: Fq2 = Fq2::new(
+        Fq::ZERO,
+        MontFp!("155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906"),
+    );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
 }
 
-#[rustfmt::skip]
-pub const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
 
 /// G2_GENERATOR_X_C0 =
 /// 233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger384([
-    0x68904082f268725b,
-    0x668f2ea74f45328b,
-    0xebca7a65802be84f,
-    0x1e1850f4c1ada3e6,
-    0x830dc22d588ef1e9,
-    0x1862a81767c0982,
-]));
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294");
 
 /// G2_GENERATOR_X_C1 =
 /// 140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger384([
-    0x5f02a915c91c7f39,
-    0xf8c553ba388da2a7,
-    0xd51a416dbd198850,
-    0xe943c6f38ae3073a,
-    0xffe24aa8259a4981,
-    0x11853391e73dfdd,
-]));
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118");
 
 /// G2_GENERATOR_Y_C0 =
 /// 63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger384([
-    0xd5b19b897881430f,
-    0x5be9118a5b371ed,
-    0x6063f91f86c131ee,
-    0x3244a61be8f4ec19,
-    0xa02e425b9f9a3a12,
-    0x18af8c04f3360d2,
-]));
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423");
 
 /// G2_GENERATOR_Y_C1 =
 /// 149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger384([
-    0x57601ac71a5b96f5,
-    0xe99acc1714f2440e,
-    0x2339612f10118ea9,
-    0x8321e68a3b1cd722,
-    0x2b543b050cc74917,
-    0x590182b396c112,
-]));
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491");

bls12_377/src/curves/mod.rs

@@ -1,33 +1,36 @@
-use crate::*;
 use ark_ec::{
     bls12,
-    bls12::{Bls12, Bls12Parameters, TwistType},
+    bls12::{Bls12, Bls12Config, TwistType},
 };
 
+use crate::*;
+
 pub mod g1;
 pub mod g2;
 
 #[cfg(test)]
 mod tests;
 
-pub struct Parameters;
+pub struct Config;
 
-impl Bls12Parameters for Parameters {
+impl Bls12Config for Config {
     const X: &'static [u64] = &[0x8508c00000000001];
     /// `x` is positive.
     const X_IS_NEGATIVE: bool = false;
     const TWIST_TYPE: TwistType = TwistType::D;
     type Fp = Fq;
-    type Fp2Params = Fq2Parameters;
-    type Fp6Params = Fq6Parameters;
-    type Fp12Params = Fq12Parameters;
-    type G1Parameters = g1::Parameters;
-    type G2Parameters = g2::Parameters;
+    type Fp2Config = Fq2Config;
+    type Fp6Config = Fq6Config;
+    type Fp12Config = Fq12Config;
+    type G1Config = g1::Config;
+    type G2Config = g2::Config;
 }
 
-pub type Bls12_377 = Bls12<Parameters>;
+pub type Bls12_377 = Bls12<Config>;
 
-pub type G1Affine = bls12::G1Affine<Parameters>;
-pub type G1Projective = bls12::G1Projective<Parameters>;
-pub type G2Affine = bls12::G2Affine<Parameters>;
-pub type G2Projective = bls12::G2Projective<Parameters>;
+pub type G1Affine = bls12::G1Affine<Config>;
+pub type G1Projective = bls12::G1Projective<Config>;
+pub type G2Affine = bls12::G2Affine<Config>;
+pub type G2Projective = bls12::G2Projective<Config>;
+
+pub use g1::{G1TEAffine, G1TEProjective};

bls12_377/src/curves/tests.rs

@@ -1,121 +1,7 @@
-#![allow(unused_imports)]
-use ark_ff::{
-    fields::{Field, FpParameters, PrimeField, SquareRootField},
-    test_rng, One, Zero,
-};
-use ark_serialize::CanonicalSerialize;
+use crate::{Bls12_377, G1Projective, G2Projective};
+use ark_algebra_test_templates::*;
 
-use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
-use core::ops::{AddAssign, MulAssign};
-use rand::Rng;
-
-use crate::{g1, g2, Bls12_377, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
-
-use ark_curve_tests::{
-    curves::{curve_tests, sw_tests},
-    groups::group_test,
-};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let mut sa = a;
-    sa.mul_assign(s);
-    let mut sb = b;
-    sb.mul_assign(s);
-
-    let ans1 = Bls12_377::pairing(sa, b);
-    let ans2 = Bls12_377::pairing(a, sb);
-    let ans3 = Bls12_377::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq12::one());
-    assert_ne!(ans2, Fq12::one());
-    assert_ne!(ans3, Fq12::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq12::one());
-}
-
-#[test]
-fn test_g1_generator_raw() {
-    let mut x = Fq::zero();
-    let mut i = 0;
-    loop {
-        // y^2 = x^3 + b
-        let mut rhs = x;
-        rhs.square_in_place();
-        rhs.mul_assign(&x);
-        rhs.add_assign(&g1::Parameters::COEFF_B);
-
-        if let Some(y) = rhs.sqrt() {
-            let p = G1Affine::new(x, if y < -y { y } else { -y }, false);
-            assert!(!p.is_in_correct_subgroup_assuming_on_curve());
-
-            let g1 = p.scale_by_cofactor();
-            if !g1.is_zero() {
-                assert_eq!(i, 1);
-                let g1 = G1Affine::from(g1);
-
-                assert!(g1.is_in_correct_subgroup_assuming_on_curve());
-
-                assert_eq!(g1, G1Affine::prime_subgroup_generator());
-                break;
-            }
-        }
-
-        i += 1;
-        x.add_assign(&Fq::one());
-    }
-}
+test_group!(g1; G1Projective; sw);
+test_group!(g2; G2Projective; sw);
+test_group!(pairing_output; ark_ec::pairing::PairingOutput<Bls12_377>; msm);
+test_pairing!(pairing; crate::Bls12_377);

bls12_377/src/fields/fq.rs

@@ -1,114 +1,7 @@
-use ark_ff::{biginteger::BigInteger384 as BigInteger, field_new, fields::*};
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};
 
-pub type Fq = Fp384<FqParameters>;
-
-pub struct FqParameters;
-
-impl Fp384Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 46u32;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        2022196864061697551u64,
-        17419102863309525423u64,
-        8564289679875062096u64,
-        17152078065055548215u64,
-        17966377291017729567u64,
-        68610905582439508u64,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0x8508c00000000001,
-        0x170b5d4430000000,
-        0x1ef3622fba094800,
-        0x1a22d9f300f5138f,
-        0xc63b05c06ca1493b,
-        0x1ae3a4617c510ea,
-    ]);
-
-    const MODULUS_BITS: u32 = 377;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 7;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        202099033278250856u64,
-        5854854902718660529u64,
-        11492539364873682930u64,
-        8885205928937022213u64,
-        5545221690922665192u64,
-        39800542322357402u64,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xb786686c9400cd22,
-        0x329fcaab00431b1,
-        0x22a5f11162d6b46d,
-        0xbfdf7d03827dc3ac,
-        0x837e92f041790bf9,
-        0x6dfccb1e914b88,
-    ]);
-
-    const INV: u64 = 9586122913090633727u64;
-
-    // GENERATOR = -5
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0xfc0b8000000002fa,
-        0x97d39cf6e000018b,
-        0x2072420fbfa05044,
-        0xcbbcbd50d97c3802,
-        0xbaf1ec35813f9eb,
-        0x9974a2c0945ad2,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x4284600000000000,
-        0xb85aea218000000,
-        0x8f79b117dd04a400,
-        0x8d116cf9807a89c7,
-        0x631d82e03650a49d,
-        0xd71d230be28875,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-
-    // T = (MODULUS - 1) // 2^S =
-    // 3675842578061421676390135839012792950148785745837396071634149488243117337281387659330802195819009059
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x7510c00000021423,
-        0x88bee82520005c2d,
-        0x67cc03d44e3c7bcd,
-        0x1701b28524ec688b,
-        0xe9185f1443ab18ec,
-        0x6b8,
-    ]);
-
-    // (T - 1) // 2 =
-    // 1837921289030710838195067919506396475074392872918698035817074744121558668640693829665401097909504529
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xba88600000010a11,
-        0xc45f741290002e16,
-        0xb3e601ea271e3de6,
-        0xb80d94292763445,
-        0x748c2f8a21d58c76,
-        0x35c,
-    ]);
-}
-
-#[allow(dead_code)]
-pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
-#[allow(dead_code)]
-pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0]));
+#[derive(MontConfig)]
+#[modulus = "258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177"]
+#[generator = "15"]
+pub struct FqConfig;
+pub type Fq = Fp384<MontBackend<FqConfig, 6>>;

bls12_377/src/fields/fq12.rs

@@ -1,161 +1,74 @@
-use super::*;
-use ark_ff::{biginteger::BigInteger384, field_new, fields::*};
+use ark_ff::{fields::*, MontFp};
 
-pub type Fq12 = Fp12<Fq12Parameters>;
+use crate::*;
+
+pub type Fq12 = Fp12<Fq12Config>;
 
 #[derive(Clone, Copy)]
-pub struct Fq12Parameters;
+pub struct Fq12Config;
 
-impl Fp12Parameters for Fq12Parameters {
-    type Fp6Params = Fq6Parameters;
+impl Fp12Config for Fq12Config {
+    type Fp6Config = Fq6Config;
 
-    const NONRESIDUE: Fq6 = field_new!(Fq6, FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x2cdffffffffff68,
-                0x51409f837fffffb1,
-                0x9f7db3a98a7d3ff2,
-                0x7b4e97b76e7c6305,
-                0x4cf495bf803c84e8,
-                0x8d6661e2fdf49a,
-            ])),
-            FQ_ZERO,
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x6ec47a04a3f7ca9e,
-                0xa42e0cb968c1fa44,
-                0x578d5187fbd2bd23,
-                0x930eeb0ac79dd4bd,
-                0xa24883de1e09a9ee,
-                0xdaa7058067d46f,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("92949345220277864758624960506473182677953048909283248980960104381795901929519566951595905490535835115111760994353"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x5892506da58478da,
-                0x133366940ac2a74b,
-                0x9b64a150cdf726cf,
-                0x5cc426090a9c587e,
-                0x5cf848adfdcd640c,
-                0x4702bf3ac02380,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x982c13d9d084771f,
-                0xfd49de0c6da34a32,
-                0x61a530d183ab0e53,
-                0xdf8fe44106dd9879,
-                0x40f29b58d88472bc,
-                0x158723199046d5d,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("216465761340224619389371505802605247630151569547285782856803747159100223055385581585702401816380679166954762214499"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xdacd106da5847973,
-                0xd8fe2454bac2a79a,
-                0x1ada4fd6fd832edc,
-                0xfb9868449d150908,
-                0xd63eb8aeea32285e,
-                0x167d6a36f873fd0,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x296799d52c8cac81,
-                0x591bd15304e14fee,
-                0xa17df4987d85130,
-                0x4c80f9363f3fc3bc,
-                0x9eaa177aba7ac8ce,
-                0x7dcb2c189c98ed,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("123516416119946754630746545296132064952198520638002533875843642777304321125866014634106496325844844051843001220146"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x823ac00000000099,
-                0xc5cabdc0b000004f,
-                0x7f75ae862f8c080d,
-                0x9ed4423b9278b089,
-                0x79467000ec64c452,
-                0x120d3e434c71c50,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x164445fb5c083563,
-                0x72dd508ac73e05bc,
-                0xc76610a7be368adc,
-                0x8713eee839573ed1,
-                0x23f281e24e979f4c,
-                0xd39340975d3c7b,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("165715080792691229252027773188420350858440463845631411558924158284924566418821255823372982649037525009328560463824"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x2c766f925a7b8727,
-                0x3d7f6b0253d58b5,
-                0x838ec0deec122131,
-                0xbd5eb3e9f658bb10,
-                0x6942bd126ed3e52e,
-                0x1673786dd04ed6a,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xecdcac262f7b88e2,
-                0x19c17f37c25cb5cd,
-                0xbd4e315e365e39ac,
-                0x3a92f5b1fa177b15,
-                0x85486a67941cd67e,
-                0x55c8147ec0a38d,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("42198664672744474621281227892288285906241943207628877683080515507620245292955241189266486323192680957485559243678"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xaa3baf925a7b868e,
-                0x3e0d38ef753d5865,
-                0x4191258bc861923,
-                0x1e8a71ae63e00a87,
-                0xeffc4d11826f20dc,
-                0x4663a2a83dd119,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x5ba1262ad3735380,
-                0xbdef8bf12b1eb012,
-                0x14db82e63230f6cf,
-                0xcda1e0bcc1b54fd3,
-                0x2790ee45b226806c,
-                0x1306f19ff2877fd,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("135148009893022339379906188398761468584194992116912126664040619889416147222474808140862391813728516072597320238031"),
+            Fq::ZERO,
         ),
     ];
 }

bls12_377/src/fields/fq2.rs

@@ -1,69 +1,51 @@
-use super::*;
-use ark_ff::{biginteger::BigInteger384 as BigInteger, field_new, fields::*};
+use ark_ff::{fields::*, MontFp};
 
-pub type Fq2 = Fp2<Fq2Parameters>;
+use crate::*;
 
-pub struct Fq2Parameters;
+pub type Fq2 = Fp2<Fq2Config>;
 
-impl Fp2Parameters for Fq2Parameters {
+pub struct Fq2Config;
+
+impl Fp2Config for Fq2Config {
     type Fp = Fq;
 
     /// NONRESIDUE = -5
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
-        0xfc0b8000000002fa,
-        0x97d39cf6e000018b,
-        0x2072420fbfa05044,
-        0xcbbcbd50d97c3802,
-        0xbaf1ec35813f9eb,
-        0x9974a2c0945ad2,
-    ]));
-
-    /// QUADRATIC_NONRESIDUE = U
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE: (Fq, Fq) = (
-        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0])),
-        field_new!(Fq, BigInteger([
-            202099033278250856u64,
-            5854854902718660529u64,
-            11492539364873682930u64,
-            8885205928937022213u64,
-            5545221690922665192u64,
-            39800542322357402u64,
-        ])),
-    );
+    const NONRESIDUE: Fq = MontFp!("-5");
 
     /// Coefficients for the Frobenius automorphism.
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // NONRESIDUE**(((q^0) - 1) / 2)
-        field_new!(Fq, BigInteger([
-            0x2cdffffffffff68,
-            0x51409f837fffffb1,
-            0x9f7db3a98a7d3ff2,
-            0x7b4e97b76e7c6305,
-            0x4cf495bf803c84e8,
-            0x8d6661e2fdf49a,
-        ])),
+        Fq::ONE,
         // NONRESIDUE**(((q^1) - 1) / 2)
-        field_new!(Fq, BigInteger([
-            0x823ac00000000099,
-            0xc5cabdc0b000004f,
-            0x7f75ae862f8c080d,
-            0x9ed4423b9278b089,
-            0x79467000ec64c452,
-            0x120d3e434c71c50,
-        ])),
+        MontFp!("-1"),
     ];
 
     #[inline(always)]
-    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
-        let original = fe;
-        let mut fe = -fe.double();
-        fe.double_in_place();
-        fe - original
+    fn mul_fp_by_nonresidue_in_place(fe: &mut Self::Fp) -> &mut Self::Fp {
+        fe.neg_in_place();
+        *fe = *fe + fe.double_in_place().double_in_place();
+        fe
+    }
+
+    #[inline(always)]
+    fn sub_and_mul_fp_by_nonresidue(y: &mut Self::Fp, x: &Self::Fp) {
+        let mut original = *y;
+        original += x;
+        y.double_in_place().double_in_place();
+        *y += original;
+    }
+
+    #[inline(always)]
+    fn mul_fp_by_nonresidue_plus_one_and_add(y: &mut Self::Fp, x: &Self::Fp) {
+        y.double_in_place().double_in_place().neg_in_place();
+        *y += x;
+    }
+
+    fn mul_fp_by_nonresidue_and_add(y: &mut Self::Fp, x: &Self::Fp) {
+        let mut original = *y;
+        original.double_in_place().double_in_place();
+        original += &*y;
+        *y = *x;
+        *y -= original;
     }
 }
-
-pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = field_new!(Fq2, FQ_ONE, FQ_ZERO);

bls12_377/src/fields/fq6.rs

@@ -1,184 +1,79 @@
-use super::*;
-use ark_ff::{biginteger::BigInteger384, field_new, fields::*};
+use ark_ff::{fields::*, MontFp};
 
-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::*;
+
+pub type Fq6 = Fp6<Fq6Config>;
 
 #[derive(Clone, Copy)]
-pub struct Fq6Parameters;
+pub struct Fq6Config;
 
-impl Fp6Parameters for Fq6Parameters {
-    type Fp2Params = Fq2Parameters;
+impl Fp6Config for Fq6Config {
+    type Fp2Config = Fq2Config;
 
     /// NONRESIDUE = U
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq2 = field_new!(Fq2,
-        field_new!(Fq, BigInteger384([0, 0, 0, 0, 0, 0])),
-        field_new!(Fq, BigInteger384([
-            202099033278250856u64,
-            5854854902718660529u64,
-            11492539364873682930u64,
-            8885205928937022213u64,
-            5545221690922665192u64,
-            39800542322357402u64,
-        ])),
-    );
+    const NONRESIDUE: Fq2 = Fq2::new(Fq::ZERO, Fq::ONE);
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x2cdffffffffff68,
-                0x51409f837fffffb1,
-                0x9f7db3a98a7d3ff2,
-                0x7b4e97b76e7c6305,
-                0x4cf495bf803c84e8,
-                0x8d6661e2fdf49a,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x5892506da58478da,
-                0x133366940ac2a74b,
-                0x9b64a150cdf726cf,
-                0x5cc426090a9c587e,
-                0x5cf848adfdcd640c,
-                0x4702bf3ac02380,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xdacd106da5847973,
-                0xd8fe2454bac2a79a,
-                0x1ada4fd6fd832edc,
-                0xfb9868449d150908,
-                0xd63eb8aeea32285e,
-                0x167d6a36f873fd0,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x823ac00000000099,
-                0xc5cabdc0b000004f,
-                0x7f75ae862f8c080d,
-                0x9ed4423b9278b089,
-                0x79467000ec64c452,
-                0x120d3e434c71c50,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
-        ),
+        Fq2::new(MontFp!("-1"), Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x2c766f925a7b8727,
-                0x3d7f6b0253d58b5,
-                0x838ec0deec122131,
-                0xbd5eb3e9f658bb10,
-                0x6942bd126ed3e52e,
-                0x1673786dd04ed6a,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xaa3baf925a7b868e,
-                0x3e0d38ef753d5865,
-                0x4191258bc861923,
-                0x1e8a71ae63e00a87,
-                0xeffc4d11826f20dc,
-                0x4663a2a83dd119,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
+            Fq::ZERO,
         ),
     ];
-    #[rustfmt::skip]
+
     const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x2cdffffffffff68,
-                0x51409f837fffffb1,
-                0x9f7db3a98a7d3ff2,
-                0x7b4e97b76e7c6305,
-                0x4cf495bf803c84e8,
-                0x8d6661e2fdf49a,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xdacd106da5847973,
-                0xd8fe2454bac2a79a,
-                0x1ada4fd6fd832edc,
-                0xfb9868449d150908,
-                0xd63eb8aeea32285e,
-                0x167d6a36f873fd0,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO
         ),
         // Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x2c766f925a7b8727,
-                0x3d7f6b0253d58b5,
-                0x838ec0deec122131,
-                0xbd5eb3e9f658bb10,
-                0x6942bd126ed3e52e,
-                0x1673786dd04ed6a,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x2cdffffffffff68,
-                0x51409f837fffffb1,
-                0x9f7db3a98a7d3ff2,
-                0x7b4e97b76e7c6305,
-                0x4cf495bf803c84e8,
-                0x8d6661e2fdf49a,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xdacd106da5847973,
-                0xd8fe2454bac2a79a,
-                0x1ada4fd6fd832edc,
-                0xfb9868449d150908,
-                0xd63eb8aeea32285e,
-                0x167d6a36f873fd0,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x2c766f925a7b8727,
-                0x3d7f6b0253d58b5,
-                0x838ec0deec122131,
-                0xbd5eb3e9f658bb10,
-                0x6942bd126ed3e52e,
-                0x1673786dd04ed6a,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
         ),
     ];
 
     #[inline(always)]
-    fn mul_fp2_by_nonresidue(fe: &Fq2) -> Fq2 {
+    fn mul_fp2_by_nonresidue_in_place(fe: &mut Fq2) -> &mut Fq2 {
         // Karatsuba multiplication with constant other = u.
-        let c0 = Fq2Parameters::mul_fp_by_nonresidue(&fe.c1);
-        let c1 = fe.c0;
-        field_new!(Fq2, c0, c1)
+        let old_c0 = fe.c0;
+        fe.c0 = fe.c1;
+        Fq2Config::mul_fp_by_nonresidue_in_place(&mut fe.c0);
+        fe.c1 = old_c0;
+        fe
     }
 }

bls12_377/src/fields/fr.rs

@@ -1,95 +1,27 @@
-use ark_ff::{biginteger::BigInteger256 as BigInteger, fields::*};
+//! Bls12-377 scalar field.
+/// Roots of unity computed from modulus and R using this sage code:
+///
+/// ```ignore
+/// q = 8444461749428370424248824938781546531375899335154063827935233455917409239041
+/// R = 6014086494747379908336260804527802945383293308637734276299549080986809532403 # Montgomery R
+/// s = 47
+/// o = q - 1
+/// F = GF(q)
+/// g = F.multiplicative_generator()
+/// g = F.multiplicative_generator()
+/// assert g.multiplicative_order() == o
+/// g2 = g ** (o/2**s)
+/// assert g2.multiplicative_order() == 2**s
+/// def into_chunks(val, width, n):
+///     return [int(int(val) // (2 ** (width * i)) % 2 ** width) for i in range(n)]
+/// print("Gen: ", g * R % q)
+/// print("Gen: ", into_chunks(g * R % q, 64, 4))
+/// print("2-adic gen: ", into_chunks(g2 * R % q, 64, 4))
+/// ```
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
 
-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 47;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        0x3c3d3ca739381fb2,
-        0x9a14cda3ec99772b,
-        0xd7aacc7c59724826,
-        0xd1ba211c5cc349c,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// MODULUS = 8444461749428370424248824938781546531375899335154063827935233455917409239041
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        725501752471715841u64,
-        6461107452199829505u64,
-        6968279316240510977u64,
-        1345280370688173398u64,
-    ]);
-
-    const MODULUS_BITS: u32 = 253;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 3;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        9015221291577245683u64,
-        8239323489949974514u64,
-        1646089257421115374u64,
-        958099254763297437u64,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        2726216793283724667u64,
-        14712177743343147295u64,
-        12091039717619697043u64,
-        81024008013859129u64,
-    ]);
-
-    const INV: u64 = 725501752471715839u64;
-
-    // GENERATOR = 11
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        1855201571499933546u64,
-        8511318076631809892u64,
-        6222514765367795509u64,
-        1122129207579058019u64,
-    ]);
-
-    /// (r - 1)/2 =
-    /// 4222230874714185212124412469390773265687949667577031913967616727958704619520
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x8508c00000000000,
-        0xacd53b7f68000000,
-        0x305a268f2e1bd800,
-        0x955b2af4d1652ab,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where r - 1 = 2^s * t
-
-    /// t = (r - 1) / 2^s =
-    /// 60001509534603559531609739528203892656505753216962260608619555
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0xedfda00000021423,
-        0x9a3cb86f6002b354,
-        0xcabd34594aacc168,
-        0x2556,
-    ]);
-
-    /// (t - 1) / 2 =
-    /// 30000754767301779765804869764101946328252876608481130304309777
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x76fed00000010a11,
-        0x4d1e5c37b00159aa,
-        0x655e9a2ca55660b4,
-        0x12ab,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "8444461749428370424248824938781546531375899335154063827935233455917409239041"]
+#[generator = "22"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;

bls12_377/src/fields/tests.rs

@@ -1,127 +1,52 @@
+use ark_algebra_test_templates::*;
 use ark_ff::{
-    biginteger::{BigInteger, BigInteger384},
-    fields::{
-        fp6_3over2::Fp6Parameters, FftField, FftParameters, Field, Fp2Parameters, FpParameters,
-        PrimeField, SquareRootField,
-    },
-    test_rng, One, UniformRand, Zero,
+    biginteger::{BigInt, BigInteger, BigInteger384},
+    fields::{FftField, Field, Fp6Config, PrimeField},
+    Fp384, One, UniformRand, Zero,
 };
-use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
-use core::{
+use ark_std::{
     cmp::Ordering,
-    ops::{AddAssign, MulAssign, SubAssign},
+    ops::{AddAssign, MulAssign},
+    test_rng,
 };
-use rand::{Rng, SeedableRng};
-use rand_xorshift::XorShiftRng;
 
-use crate::{Fq, Fq12, Fq2, Fq2Parameters, Fq6, Fq6Parameters, FqParameters, Fr};
+use crate::{Fq, Fq12, Fq2, Fq6, Fq6Config, Fr};
 
-use ark_curve_tests::fields::*;
-
-pub(crate) const ITERATIONS: usize = 5;
-
-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fr = rng.gen();
-        let b: Fr = rng.gen();
-        field_test(a, b);
-        primefield_test::<Fr>();
-        sqrt_field_test(b);
-        let byte_size = a.serialized_size();
-        field_serialization_test::<Fr>(byte_size);
-    }
-}
-
-#[test]
-fn test_fq() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fq = rng.gen();
-        let b: Fq = rng.gen();
-        field_test(a, b);
-        primefield_test::<Fq>();
-        sqrt_field_test(a);
-        let byte_size = a.serialized_size();
-        let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
-        assert_eq!(byte_size, buffer_size);
-        field_serialization_test::<Fq>(byte_size);
-    }
-}
-
-#[test]
-fn test_fq2() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fq2 = rng.gen();
-        let b: Fq2 = rng.gen();
-        field_test(a, b);
-        sqrt_field_test(a);
-    }
-    frobenius_test::<Fq2, _>(Fq::characteristic(), 13);
-    let byte_size = Fq2::zero().serialized_size();
-    field_serialization_test::<Fq2>(byte_size);
-}
-
-#[test]
-fn test_fq6() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let g: Fq6 = rng.gen();
-        let h: Fq6 = rng.gen();
-        field_test(g, h);
-    }
-    frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
-    let byte_size = Fq6::zero().serialized_size();
-    field_serialization_test::<Fq6>(byte_size);
-}
-
-#[test]
-fn test_fq12() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let g: Fq12 = rng.gen();
-        let h: Fq12 = rng.gen();
-        field_test(g, h);
-    }
-    frobenius_test::<Fq12, _>(Fq::characteristic(), 13);
-    let byte_size = Fq12::zero().serialized_size();
-    field_serialization_test::<Fq12>(byte_size);
-}
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
+test_field!(fq2; Fq2);
+test_field!(fq6; Fq6);
+test_field!(fq12; Fq12);
 
 #[test]
 fn test_fq_repr_from() {
-    assert_eq!(
-        BigInteger384::from(100),
-        BigInteger384([100, 0, 0, 0, 0, 0])
-    );
+    assert_eq!(BigInt::from(100u64), BigInt::new([100, 0, 0, 0, 0, 0]));
 }
 
 #[test]
 fn test_fq_repr_is_odd() {
-    assert!(!BigInteger384::from(0).is_odd());
-    assert!(BigInteger384::from(0).is_even());
-    assert!(BigInteger384::from(1).is_odd());
-    assert!(!BigInteger384::from(1).is_even());
-    assert!(!BigInteger384::from(324834872).is_odd());
-    assert!(BigInteger384::from(324834872).is_even());
-    assert!(BigInteger384::from(324834873).is_odd());
-    assert!(!BigInteger384::from(324834873).is_even());
+    assert!(!BigInteger384::from(0u64).is_odd());
+    assert!(BigInteger384::from(0u64).is_even());
+    assert!(BigInteger384::from(1u64).is_odd());
+    assert!(!BigInteger384::from(1u64).is_even());
+    assert!(!BigInteger384::from(324834872u64).is_odd());
+    assert!(BigInteger384::from(324834872u64).is_even());
+    assert!(BigInteger384::from(324834873u64).is_odd());
+    assert!(!BigInteger384::from(324834873u64).is_even());
 }
 
 #[test]
 fn test_fq_repr_is_zero() {
-    assert!(BigInteger384::from(0).is_zero());
-    assert!(!BigInteger384::from(1).is_zero());
-    assert!(!BigInteger384([0, 0, 0, 0, 1, 0]).is_zero());
+    assert!(BigInteger384::from(0u64).is_zero());
+    assert!(!BigInteger384::from(1u64).is_zero());
+    assert!(!BigInt::new([0, 0, 0, 0, 1, 0]).is_zero());
 }
 
 #[test]
 fn test_fq_repr_num_bits() {
-    let mut a = BigInteger384::from(0);
+    let mut a = BigInteger384::from(0u64);
     assert_eq!(0, a.num_bits());
-    a = BigInteger384::from(1);
+    a = BigInteger384::from(1u64);
     for i in 1..385 {
         assert_eq!(i, a.num_bits());
         a.mul2();
@@ -129,229 +54,16 @@ fn test_fq_repr_num_bits() {
     assert_eq!(0, a.num_bits());
 }
 
-#[test]
-fn test_fq_add_assign() {
-    // Test associativity
-
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000 {
-        // Generate a, b, c and ensure (a + b) + c == a + (b + c).
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-        let c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.add_assign(&b);
-        tmp1.add_assign(&c);
-
-        let mut tmp2 = b;
-        tmp2.add_assign(&c);
-        tmp2.add_assign(&a);
-
-        assert_eq!(tmp1, tmp2);
-    }
-}
-
-#[test]
-fn test_fq_sub_assign() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000 {
-        // Ensure that (a - b) + (b - a) = 0.
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.sub_assign(&b);
-
-        let mut tmp2 = b;
-        tmp2.sub_assign(&a);
-
-        tmp1.add_assign(&tmp2);
-        assert!(tmp1.is_zero());
-    }
-}
-
-#[test]
-fn test_fq_mul_assign() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000000 {
-        // Ensure that (a * b) * c = a * (b * c)
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-        let c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.mul_assign(&b);
-        tmp1.mul_assign(&c);
-
-        let mut tmp2 = b;
-        tmp2.mul_assign(&c);
-        tmp2.mul_assign(&a);
-
-        assert_eq!(tmp1, tmp2);
-    }
-
-    for _ in 0..1000000 {
-        // Ensure that r * (a + b + c) = r*a + r*b + r*c
-
-        let r = Fq::rand(&mut rng);
-        let mut a = Fq::rand(&mut rng);
-        let mut b = Fq::rand(&mut rng);
-        let mut c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.add_assign(&b);
-        tmp1.add_assign(&c);
-        tmp1.mul_assign(&r);
-
-        a.mul_assign(&r);
-        b.mul_assign(&r);
-        c.mul_assign(&r);
-
-        a.add_assign(&b);
-        a.add_assign(&c);
-
-        assert_eq!(tmp1, a);
-    }
-}
-
-#[test]
-fn test_fq_squaring() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000000 {
-        // Ensure that (a * a) = a^2
-        let a = Fq::rand(&mut rng);
-
-        let mut tmp = a;
-        tmp.square_in_place();
-
-        let mut tmp2 = a;
-        tmp2.mul_assign(&a);
-
-        assert_eq!(tmp, tmp2);
-    }
-}
-
-#[test]
-fn test_fq_inverse() {
-    assert!(Fq::zero().inverse().is_none());
-
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    let one = Fq::one();
-
-    for _ in 0..1000 {
-        // Ensure that a * a^-1 = 1
-        let mut a = Fq::rand(&mut rng);
-        let ainv = a.inverse().unwrap();
-        a.mul_assign(&ainv);
-        assert_eq!(a, one);
-    }
-}
-
-#[test]
-fn test_fq_double_in_place() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000 {
-        // Ensure doubling a is equivalent to adding a to itself.
-        let mut a = Fq::rand(&mut rng);
-        let mut b = a;
-        b.add_assign(&a);
-        a.double_in_place();
-        assert_eq!(a, b);
-    }
-}
-
-#[test]
-fn test_fq_negate() {
-    {
-        let a = -Fq::zero();
-
-        assert!(a.is_zero());
-    }
-
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000 {
-        // Ensure (a - (-a)) = 0.
-        let mut a = Fq::rand(&mut rng);
-        let b = -a;
-        a.add_assign(&b);
-
-        assert!(a.is_zero());
-    }
-}
-
-#[test]
-fn test_fq_pow() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for i in 0..1000 {
-        // Exponentiate by various small numbers and ensure it consists with repeated
-        // multiplication.
-        let a = Fq::rand(&mut rng);
-        let target = a.pow(&[i]);
-        let mut c = Fq::one();
-        for _ in 0..i {
-            c.mul_assign(&a);
-        }
-        assert_eq!(c, target);
-    }
-
-    for _ in 0..1000 {
-        // Exponentiating by the modulus should have no effect in a prime field.
-        let a = Fq::rand(&mut rng);
-
-        assert_eq!(a, a.pow(Fq::characteristic()));
-    }
-}
-
-#[test]
-fn test_fq_sqrt() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    assert_eq!(Fq::zero().sqrt().unwrap(), Fq::zero());
-
-    for _ in 0..1000 {
-        // Ensure sqrt(a^2) = a or -a
-        let a = Fq::rand(&mut rng);
-        let nega = -a;
-        let mut b = a;
-        b.square_in_place();
-
-        let b = b.sqrt().unwrap();
-
-        assert!(a == b || nega == b);
-    }
-
-    for _ in 0..1000 {
-        // Ensure sqrt(a)^2 = a for random a
-        let a = Fq::rand(&mut rng);
-
-        if let Some(mut tmp) = a.sqrt() {
-            tmp.square_in_place();
-
-            assert_eq!(a, tmp);
-        }
-    }
-}
-
 #[test]
 fn test_fq_num_bits() {
-    assert_eq!(FqParameters::MODULUS_BITS, 377);
-    assert_eq!(FqParameters::CAPACITY, 376);
+    assert_eq!(Fq::MODULUS_BIT_SIZE, 377);
 }
 
 #[test]
 fn test_fq_root_of_unity() {
-    assert_eq!(FqParameters::TWO_ADICITY, 46);
+    assert_eq!(Fq::TWO_ADICITY, 46);
     assert_eq!(
-        Fq::multiplicative_generator().pow([
+        Fq::GENERATOR.pow([
             0x7510c00000021423,
             0x88bee82520005c2d,
             0x67cc03d44e3c7bcd,
@@ -359,21 +71,21 @@ fn test_fq_root_of_unity() {
             0xe9185f1443ab18ec,
             0x6b8
         ]),
-        Fq::two_adic_root_of_unity()
+        Fq::TWO_ADIC_ROOT_OF_UNITY
     );
     assert_eq!(
-        Fq::two_adic_root_of_unity().pow([1 << FqParameters::TWO_ADICITY]),
+        Fq::TWO_ADIC_ROOT_OF_UNITY.pow([1 << Fq::TWO_ADICITY]),
         Fq::one()
     );
-    assert!(Fq::multiplicative_generator().sqrt().is_none());
+    assert!(Fq::GENERATOR.sqrt().is_none());
 }
 
 #[test]
 fn test_fq_ordering() {
     // BigInteger384's ordering is well-tested, but we still need to make sure the
     // Fq elements aren't being compared in Montgomery form.
-    for i in 0..100 {
-        assert!(Fq::from(BigInteger384::from(i + 1)) > Fq::from(BigInteger384::from(i)));
+    for i in 0..100u64 {
+        assert!(Fq::from(Fp384::from(i + 1)) > Fq::from(Fp384::from(i)));
     }
 }
 
@@ -383,14 +95,8 @@ fn test_fq_legendre() {
 
     assert_eq!(QuadraticResidue, Fq::one().legendre());
     assert_eq!(Zero, Fq::zero().legendre());
-    assert_eq!(
-        QuadraticResidue,
-        Fq::from(BigInteger384::from(4)).legendre()
-    );
-    assert_eq!(
-        QuadraticNonResidue,
-        Fq::from(BigInteger384::from(5)).legendre()
-    );
+    assert_eq!(QuadraticResidue, Fq::from(Fp384::from(4u64)).legendre());
+    assert_eq!(QuadraticNonResidue, Fq::from(Fp384::from(5u64)).legendre());
 }
 
 #[test]
@@ -430,33 +136,13 @@ fn test_fq2_legendre() {
     // i^2 = -1
     let mut m1 = -Fq2::one();
     assert_eq!(QuadraticResidue, m1.legendre());
-    m1 = Fq6Parameters::mul_fp2_by_nonresidue(&m1);
+    Fq6Config::mul_fp2_by_nonresidue_in_place(&mut m1);
     assert_eq!(QuadraticNonResidue, m1.legendre());
 }
 
-#[test]
-fn test_fq2_mul_nonresidue() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    let nqr = Fq2::new(Fq::zero(), Fq::one());
-
-    let quadratic_non_residue = Fq2::new(
-        Fq2Parameters::QUADRATIC_NONRESIDUE.0,
-        Fq2Parameters::QUADRATIC_NONRESIDUE.1,
-    );
-    for _ in 0..1000 {
-        let mut a = Fq2::rand(&mut rng);
-        let mut b = a;
-        a = quadratic_non_residue * &a;
-        b.mul_assign(&nqr);
-
-        assert_eq!(a, b);
-    }
-}
-
 #[test]
 fn test_fq6_mul_by_1() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+    let mut rng = test_rng();
 
     for _ in 0..1000 {
         let c1 = Fq2::rand(&mut rng);
@@ -472,7 +158,7 @@ fn test_fq6_mul_by_1() {
 
 #[test]
 fn test_fq6_mul_by_01() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+    let mut rng = test_rng();
 
     for _ in 0..1000 {
         let c0 = Fq2::rand(&mut rng);
@@ -489,7 +175,7 @@ fn test_fq6_mul_by_01() {
 
 #[test]
 fn test_fq12_mul_by_014() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+    let mut rng = test_rng();
 
     for _ in 0..1000 {
         let c0 = Fq2::rand(&mut rng);
@@ -510,7 +196,7 @@ fn test_fq12_mul_by_014() {
 
 #[test]
 fn test_fq12_mul_by_034() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+    let mut rng = test_rng();
 
     for _ in 0..1000 {
         let c0 = Fq2::rand(&mut rng);

bls12_377/src/lib.rs

@@ -8,16 +8,18 @@
 )]
 #![forbid(unsafe_code)]
 
-//! This library implements the BLS12_377 curve generated in [[BCGMMW20, “Zexe”]](https://eprint.iacr.org/2018/962).
-//! The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree 12,
-//! defined over a 377-bit (prime) field. The main feature of this curve is that
-//! both the scalar field and the base field are highly 2-adic.
-//! (This is in contrast to the BLS12_381 curve for which only the scalar field is highly 2-adic.)
+//! This library implements the BLS12_377 curve generated in [\[BCGMMW20, “Zexe”\]](https://eprint.iacr.org/2018/962).
+//! The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree
+//! 12, defined over a 377-bit (prime) field. The main feature of this curve is
+//! that both the scalar field and the base field are highly 2-adic.
+//! (This is in contrast to the BLS12_381 curve for which only the scalar field
+//! is highly 2-adic.)
 //!
 //!
 //! Curve information:
 //! * Base field: q = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
-//! * Scalar field: r = 8444461749428370424248824938781546531375899335154063827935233455917409239041
+//! * Scalar field: r =
+//!   8444461749428370424248824938781546531375899335154063827935233455917409239041
 //! * valuation(q - 1, 2) = 46
 //! * valuation(r - 1, 2) = 47
 //! * G1 curve equation: y^2 = x^3 + 1
@@ -29,6 +31,9 @@ mod curves;
 
 mod fields;
 
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+
 #[cfg(feature = "curve")]
 pub use curves::*;
 

bls12_381/Cargo.toml

@@ -1,27 +1,27 @@
 [package]
 name = "ark-bls12-381"
-version = "0.1.0"
+version = "0.4.0-alpha.2"
 authors = [ "arkworks contributors" ]
 description = "The BLS12-381 pairing-friendly elliptic curve"
-homepage = "https://arworks.rs"
-repository = "https://github.com/arkworks/algebra"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
 documentation = "https://docs.rs/ark-bls12-381/"
-keywords = ["cryptography", "finite fields", "elliptic curves" ]
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"
 
 [dependencies]
-ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-ff = { version="0.4.0-alpha", default-features = false }
+ark-ec = { version="0.4.0-alpha", default-features = false }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
 
 [dev-dependencies]
-ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-curve-tests = { path = "../curve-tests", default-features = false }
-rand = { version = "0.7", default-features = false }
-rand_xorshift = "0.2"
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }
+hex = "^0.4.0"
 
 [features]
 default = [ "curve" ]
@@ -29,3 +29,8 @@ std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
 
 curve = [ "scalar_field" ]
 scalar_field = []
+
+[[bench]]
+name = "bls12_381"
+path = "benches/bls12_381.rs"
+harness = false

bls12_381/benches/bls12_381.rs

@@ -0,0 +1,16 @@
+use ark_algebra_bench_templates::*;
+
+use ark_bls12_381::{
+    fq::Fq, fq2::Fq2, fr::Fr, Bls12_381, Fq12, G1Projective as G1, G2Projective as G2,
+};
+
+bench!(
+    Name = "Bls12_381",
+    Pairing = Bls12_381,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq2,
+    TargetField = Fq12,
+);

bls12_381/scripts/base_field.sage

@@ -0,0 +1,28 @@
+modulus = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

bls12_381/scripts/scalar_field.sage

@@ -0,0 +1,28 @@
+modulus = 52435875175126190479447740508185965837690552500527637822603658699938581184513
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

bls12_381/src/curves/g1.rs

@@ -1,82 +1,194 @@
 use crate::*;
 use ark_ec::{
     bls12,
-    models::{ModelParameters, SWModelParameters},
+    bls12::Bls12Config,
+    models::CurveConfig,
+    short_weierstrass::{Affine, SWCurveConfig},
+    AffineRepr, Group,
 };
-use ark_ff::{
-    biginteger::{BigInteger256, BigInteger384},
-    field_new, Zero,
+use ark_ff::{Field, MontFp, PrimeField, Zero};
+use ark_serialize::{Compress, SerializationError};
+use ark_std::{ops::Neg, One};
+
+use crate::util::{
+    read_g1_compressed, read_g1_uncompressed, serialize_fq, EncodingFlags, G1_SERIALIZED_SIZE,
 };
 
-pub type G1Affine = bls12::G1Affine<crate::Parameters>;
-pub type G1Projective = bls12::G1Projective<crate::Parameters>;
+pub type G1Affine = bls12::G1Affine<crate::Config>;
+pub type G1Projective = bls12::G1Projective<crate::Config>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Config {
     type BaseField = Fq;
     type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    const COEFF_A: Fq = field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0]));
-
-    /// COEFF_B = 4
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, BigInteger384([
-        0xaa270000000cfff3,
-        0x53cc0032fc34000a,
-        0x478fe97a6b0a807f,
-        0xb1d37ebee6ba24d7,
-        0x8ec9733bbf78ab2f,
-        0x9d645513d83de7e,
-    ]));
 
     /// COFACTOR = (x - 1)^2 / 3  = 76329603384216526031706109802092473003
     const COFACTOR: &'static [u64] = &[0x8c00aaab0000aaab, 0x396c8c005555e156];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
     /// = 52435875175126190458656871551744051925719901746859129887267498875565241663483
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
-        288839107172787499,
-        1152722415086798946,
-        2612889808468387987,
-        5124657601728438008,
-    ]));
+    const COFACTOR_INV: Fr =
+        MontFp!("52435875175126190458656871551744051925719901746859129887267498875565241663483");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 4
+    const COEFF_B: Fq = MontFp!("4");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 
     #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
+
+    #[inline]
+    fn is_in_correct_subgroup_assuming_on_curve(p: &G1Affine) -> bool {
+        // Algorithm from Section 6 of https://eprint.iacr.org/2021/1130.
+        //
+        // Check that endomorphism_p(P) == -[X^2]P
+
+        // An early-out optimization described in Section 6.
+        // If uP == P but P != point of infinity, then the point is not in the right
+        // subgroup.
+        let x_times_p = p.mul_bigint(crate::Config::X);
+        if x_times_p.eq(p) && !p.infinity {
+            return false;
+        }
+
+        let minus_x_squared_times_p = x_times_p.mul_bigint(crate::Config::X).neg();
+        let endomorphism_p = endomorphism(p);
+        minus_x_squared_times_p.eq(&endomorphism_p)
+    }
+
+    #[inline]
+    fn clear_cofactor(p: &G1Affine) -> G1Affine {
+        // Using the effective cofactor, as explained in
+        // Section 5 of https://eprint.iacr.org/2019/403.pdf.
+        //
+        // It is enough to multiply by (1 - x), instead of (x - 1)^2 / 3
+        let h_eff = one_minus_x().into_bigint();
+        Config::mul_affine(&p, h_eff.as_ref()).into()
+    }
+
+    fn deserialize_with_mode<R: ark_serialize::Read>(
+        mut reader: R,
+        compress: ark_serialize::Compress,
+        validate: ark_serialize::Validate,
+    ) -> Result<Affine<Self>, ark_serialize::SerializationError> {
+        let p = if compress == ark_serialize::Compress::Yes {
+            read_g1_compressed(&mut reader)?
+        } else {
+            read_g1_uncompressed(&mut reader)?
+        };
+
+        if validate == ark_serialize::Validate::Yes && !p.is_in_correct_subgroup_assuming_on_curve()
+        {
+            return Err(SerializationError::InvalidData);
+        }
+        Ok(p)
+    }
+
+    fn serialize_with_mode<W: ark_serialize::Write>(
+        item: &Affine<Self>,
+        mut writer: W,
+        compress: ark_serialize::Compress,
+    ) -> Result<(), SerializationError> {
+        let encoding = EncodingFlags {
+            is_compressed: compress == ark_serialize::Compress::Yes,
+            is_infinity: item.is_zero(),
+            is_lexographically_largest: item.y > -item.y,
+        };
+        let mut p = *item;
+        if encoding.is_infinity {
+            p = G1Affine::zero();
+        }
+        // need to access the field struct `x` directly, otherwise we get None from xy()
+        // method
+        let x_bytes = serialize_fq(p.x);
+        if encoding.is_compressed {
+            let mut bytes: [u8; G1_SERIALIZED_SIZE] = x_bytes;
+
+            encoding.encode_flags(&mut bytes);
+            writer.write_all(&bytes)?;
+        } else {
+            let mut bytes = [0u8; 2 * G1_SERIALIZED_SIZE];
+            bytes[0..G1_SERIALIZED_SIZE].copy_from_slice(&x_bytes[..]);
+            bytes[G1_SERIALIZED_SIZE..].copy_from_slice(&serialize_fq(p.y)[..]);
+
+            encoding.encode_flags(&mut bytes);
+            writer.write_all(&bytes)?;
+        };
+
+        Ok(())
+    }
+
+    fn serialized_size(compress: Compress) -> usize {
+        if compress == Compress::Yes {
+            G1_SERIALIZED_SIZE
+        } else {
+            G1_SERIALIZED_SIZE * 2
+        }
+    }
+}
+
+fn one_minus_x() -> Fr {
+    const X: Fr = Fr::from_sign_and_limbs(!crate::Config::X_IS_NEGATIVE, crate::Config::X);
+    Fr::one() - X
 }
 
 /// G1_GENERATOR_X =
 /// 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger384([
-    0x5cb38790fd530c16,
-    0x7817fc679976fff5,
-    0x154f95c7143ba1c1,
-    0xf0ae6acdf3d0e747,
-    0xedce6ecc21dbf440,
-    0x120177419e0bfb75,
-]));
+pub const G1_GENERATOR_X: Fq = MontFp!("3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");
 
 /// G1_GENERATOR_Y =
 /// 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger384([
-    0xbaac93d50ce72271,
-    0x8c22631a7918fd8e,
-    0xdd595f13570725ce,
-    0x51ac582950405194,
-    0xe1c8c3fad0059c0,
-    0xbbc3efc5008a26a,
-]));
+pub const G1_GENERATOR_Y: Fq = MontFp!("1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");
+
+/// BETA is a non-trivial cubic root of unity in Fq.
+pub const BETA: Fq = MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");
+
+pub fn endomorphism(p: &Affine<Config>) -> Affine<Config> {
+    // Endomorphism of the points on the curve.
+    // endomorphism_p(x,y) = (BETA * x, y)
+    // where BETA is a non-trivial cubic root of unity in Fq.
+    let mut res = (*p).clone();
+    res.x *= BETA;
+    res
+}
+
+#[cfg(test)]
+mod test {
+
+    use super::*;
+    use ark_std::{rand::Rng, UniformRand};
+
+    fn sample_unchecked() -> Affine<g1::Config> {
+        let mut rng = ark_std::test_rng();
+        loop {
+            let x = Fq::rand(&mut rng);
+            let greatest = rng.gen();
+
+            if let Some(p) = Affine::get_point_from_x_unchecked(x, greatest) {
+                return p;
+            }
+        }
+    }
+
+    #[test]
+    fn test_cofactor_clearing() {
+        const SAMPLES: usize = 100;
+        for _ in 0..SAMPLES {
+            let p: Affine<g1::Config> = sample_unchecked();
+            let p = p.clear_cofactor();
+            assert!(p.is_on_curve());
+            assert!(p.is_in_correct_subgroup_assuming_on_curve());
+        }
+    }
+}

bls12_381/src/curves/g2.rs

@@ -1,30 +1,30 @@
-use crate::*;
+use ark_std::ops::Neg;
+
 use ark_ec::{
     bls12,
-    models::{ModelParameters, SWModelParameters},
+    bls12::Bls12Config,
+    models::CurveConfig,
+    short_weierstrass::{Affine, Projective, SWCurveConfig},
+    AffineRepr, CurveGroup, Group,
 };
-use ark_ff::{
-    biginteger::{BigInteger256, BigInteger384},
-    field_new, Zero,
+use ark_ff::{Field, MontFp, Zero};
+use ark_serialize::{Compress, SerializationError};
+
+use super::util::{serialize_fq, EncodingFlags, G2_SERIALIZED_SIZE};
+use crate::{
+    util::{read_g2_compressed, read_g2_uncompressed},
+    *,
 };
 
-pub type G2Affine = bls12::G2Affine<crate::Parameters>;
-pub type G2Projective = bls12::G2Projective<crate::Parameters>;
+pub type G2Affine = bls12::G2Affine<crate::Config>;
+pub type G2Projective = bls12::G2Projective<crate::Config>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Config {
     type BaseField = Fq2;
     type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = [0, 0]
-    const COEFF_A: Fq2 = field_new!(Fq2, g1::Parameters::COEFF_A, g1::Parameters::COEFF_A,);
-
-    /// COEFF_B = [4, 4]
-    const COEFF_B: Fq2 = field_new!(Fq2, g1::Parameters::COEFF_B, g1::Parameters::COEFF_B,);
 
     /// COFACTOR = (x^8 - 4 x^7 + 5 x^6) - (4 x^4 + 6 x^3 - 4 x^2 - 4 x + 13) //
     /// 9
@@ -43,71 +43,254 @@ impl SWModelParameters for Parameters {
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
     /// 26652489039290660355457965112010883481355318854675681319708643586776743290055
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
-        6746407649509787816,
-        1304054119431494378,
-        2461312685643913071,
-        5956596749362435284,
-    ]));
+    const COFACTOR_INV: Fr =
+        MontFp!("26652489039290660355457965112010883481355318854675681319708643586776743290055");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = [0, 0]
+    const COEFF_A: Fq2 = Fq2::new(g1::Config::COEFF_A, g1::Config::COEFF_A);
+
+    /// COEFF_B = [4, 4]
+    const COEFF_B: Fq2 = Fq2::new(g1::Config::COEFF_B, g1::Config::COEFF_B);
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
+
+    fn is_in_correct_subgroup_assuming_on_curve(point: &G2Affine) -> bool {
+        // Algorithm from Section 4 of https://eprint.iacr.org/2021/1130.
+        //
+        // Checks that [p]P = [X]P
+
+        let mut x_times_point = point.mul_bigint(crate::Config::X);
+        if crate::Config::X_IS_NEGATIVE {
+            x_times_point = -x_times_point;
+        }
+
+        let p_times_point = p_power_endomorphism(point);
+
+        x_times_point.eq(&p_times_point)
+    }
+
+    #[inline]
+    fn clear_cofactor(p: &G2Affine) -> G2Affine {
+        // Based on Section 4.1 of https://eprint.iacr.org/2017/419.pdf
+        // [h(ψ)]P = [x^2 − x − 1]P + [x − 1]ψ(P) + (ψ^2)(2P)
+
+        // x = -15132376222941642752
+        // When multiplying, use -c1 instead, and then negate the result. That's much
+        // more efficient, since the scalar -c1 has less limbs and a much lower Hamming
+        // weight.
+        let x: &'static [u64] = crate::Config::X;
+        let p_projective = p.into_group();
+
+        // [x]P
+        let x_p = Config::mul_affine(p, &x).neg();
+        // ψ(P)
+        let psi_p = p_power_endomorphism(&p);
+        // (ψ^2)(2P)
+        let mut psi2_p2 = double_p_power_endomorphism(&p_projective.double());
+
+        // tmp = [x]P + ψ(P)
+        let mut tmp = x_p.clone();
+        tmp += &psi_p;
+
+        // tmp2 = [x^2]P + [x]ψ(P)
+        let mut tmp2: Projective<Config> = tmp;
+        tmp2 = tmp2.mul_bigint(x).neg();
+
+        // add up all the terms
+        psi2_p2 += tmp2;
+        psi2_p2 -= x_p;
+        psi2_p2 += &-psi_p;
+        (psi2_p2 - p_projective).into_affine()
+    }
+
+    fn deserialize_with_mode<R: ark_serialize::Read>(
+        mut reader: R,
+        compress: ark_serialize::Compress,
+        validate: ark_serialize::Validate,
+    ) -> Result<Affine<Self>, ark_serialize::SerializationError> {
+        let p = if compress == ark_serialize::Compress::Yes {
+            read_g2_compressed(&mut reader)?
+        } else {
+            read_g2_uncompressed(&mut reader)?
+        };
+
+        if validate == ark_serialize::Validate::Yes && !p.is_in_correct_subgroup_assuming_on_curve()
+        {
+            return Err(SerializationError::InvalidData);
+        }
+        Ok(p)
+    }
+
+    fn serialize_with_mode<W: ark_serialize::Write>(
+        item: &Affine<Self>,
+        mut writer: W,
+        compress: ark_serialize::Compress,
+    ) -> Result<(), SerializationError> {
+        let encoding = EncodingFlags {
+            is_compressed: compress == ark_serialize::Compress::Yes,
+            is_infinity: item.is_zero(),
+            is_lexographically_largest: item.y > -item.y,
+        };
+        let mut p = *item;
+        if encoding.is_infinity {
+            p = G2Affine::zero();
+        }
+
+        let mut x_bytes = [0u8; G2_SERIALIZED_SIZE];
+        let c1_bytes = serialize_fq(p.x.c1);
+        let c0_bytes = serialize_fq(p.x.c0);
+        x_bytes[0..48].copy_from_slice(&c1_bytes[..]);
+        x_bytes[48..96].copy_from_slice(&c0_bytes[..]);
+        if encoding.is_compressed {
+            let mut bytes: [u8; G2_SERIALIZED_SIZE] = x_bytes;
+
+            encoding.encode_flags(&mut bytes);
+            writer.write_all(&bytes)?;
+        } else {
+            let mut bytes = [0u8; 2 * G2_SERIALIZED_SIZE];
+
+            let mut y_bytes = [0u8; G2_SERIALIZED_SIZE];
+            let c1_bytes = serialize_fq(p.y.c1);
+            let c0_bytes = serialize_fq(p.y.c0);
+            y_bytes[0..48].copy_from_slice(&c1_bytes[..]);
+            y_bytes[48..96].copy_from_slice(&c0_bytes[..]);
+            bytes[0..G2_SERIALIZED_SIZE].copy_from_slice(&x_bytes);
+            bytes[G2_SERIALIZED_SIZE..].copy_from_slice(&y_bytes);
+
+            encoding.encode_flags(&mut bytes);
+            writer.write_all(&bytes)?;
+        };
+
+        Ok(())
+    }
+
+    fn serialized_size(compress: ark_serialize::Compress) -> usize {
+        if compress == Compress::Yes {
+            G2_SERIALIZED_SIZE
+        } else {
+            2 * G2_SERIALIZED_SIZE
+        }
+    }
 }
 
-pub const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
 
 /// G2_GENERATOR_X_C0 =
 /// 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger384([
-    0xf5f28fa202940a10,
-    0xb3f5fb2687b4961a,
-    0xa1a893b53e2ae580,
-    0x9894999d1a3caee9,
-    0x6f67b7631863366b,
-    0x58191924350bcd7,
-]));
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160");
 
 /// G2_GENERATOR_X_C1 =
 /// 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger384([
-    0xa5a9c0759e23f606,
-    0xaaa0c59dbccd60c3,
-    0x3bb17e18e2867806,
-    0x1b1ab6cc8541b367,
-    0xc2b6ed0ef2158547,
-    0x11922a097360edf3,
-]));
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758");
 
 /// G2_GENERATOR_Y_C0 =
 /// 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger384([
-    0x4c730af860494c4a,
-    0x597cfa1f5e369c5a,
-    0xe7e6856caa0a635a,
-    0xbbefb5e96e0d495f,
-    0x7d3a975f0ef25a2,
-    0x83fd8e7e80dae5,
-]));
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905");
 
 /// G2_GENERATOR_Y_C1 =
 /// 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger384([
-    0xadc0fc92df64b05d,
-    0x18aa270a2b1461dc,
-    0x86adac6a3be4eba0,
-    0x79495c4ec93da33a,
-    0xe7175850a43ccaed,
-    0xb2bc2a163de1bf2,
-]));
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582");
+
+// psi(x,y) = (x**p * PSI_X, y**p * PSI_Y) is the Frobenius composed
+// with the quadratic twist and its inverse
+
+// PSI_X = 1/(u+1)^((p-1)/3)
+pub const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = Fq2::new(
+    Fq::ZERO,
+    MontFp!(
+                "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"
+    )
+);
+
+// PSI_Y = 1/(u+1)^((p-1)/2)
+pub const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = Fq2::new(
+    MontFp!(
+                "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
+    MontFp!(
+                "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257")
+);
+
+pub const DOUBLE_P_POWER_ENDOMORPHISM: Fq2 = Fq2::new(
+    MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+    Fq::ZERO
+);
+
+pub fn p_power_endomorphism(p: &Affine<Config>) -> Affine<Config> {
+    // The p-power endomorphism for G2 is defined as follows:
+    // 1. Note that G2 is defined on curve E': y^2 = x^3 + 4(u+1).
+    //    To map a point (x, y) in E' to (s, t) in E,
+    //    one set s = x / ((u+1) ^ (1/3)), t = y / ((u+1) ^ (1/2)),
+    //    because E: y^2 = x^3 + 4.
+    // 2. Apply the Frobenius endomorphism (s, t) => (s', t'),
+    //    another point on curve E, where s' = s^p, t' = t^p.
+    // 3. Map the point from E back to E'; that is,
+    //    one set x' = s' * ((u+1) ^ (1/3)), y' = t' * ((u+1) ^ (1/2)).
+    //
+    // To sum up, it maps
+    // (x,y) -> (x^p / ((u+1)^((p-1)/3)), y^p / ((u+1)^((p-1)/2)))
+    // as implemented in the code as follows.
+
+    let mut res = *p;
+    res.x.frobenius_map_in_place(1);
+    res.y.frobenius_map_in_place(1);
+
+    let tmp_x = res.x.clone();
+    res.x.c0 = -P_POWER_ENDOMORPHISM_COEFF_0.c1 * &tmp_x.c1;
+    res.x.c1 = P_POWER_ENDOMORPHISM_COEFF_0.c1 * &tmp_x.c0;
+    res.y *= P_POWER_ENDOMORPHISM_COEFF_1;
+
+    res
+}
+
+/// For a p-power endomorphism psi(P), compute psi(psi(P))
+pub fn double_p_power_endomorphism(p: &Projective<Config>) -> Projective<Config> {
+    let mut res = *p;
+
+    res.x *= DOUBLE_P_POWER_ENDOMORPHISM;
+    res.y = res.y.neg();
+
+    res
+}
+
+#[cfg(test)]
+mod test {
+
+    use super::*;
+    use ark_std::UniformRand;
+
+    #[test]
+    fn test_cofactor_clearing() {
+        // multiplying by h_eff and clearing the cofactor by the efficient
+        // endomorphism-based method should yield the same result.
+        let h_eff: &'static [u64] = &[
+            0xe8020005aaa95551,
+            0x59894c0adebbf6b4,
+            0xe954cbc06689f6a3,
+            0x2ec0ec69d7477c1a,
+            0x6d82bf015d1212b0,
+            0x329c2f178731db95,
+            0x9986ff031508ffe1,
+            0x88e2a8e9145ad768,
+            0x584c6a0ea91b3528,
+            0xbc69f08f2ee75b3,
+        ];
+
+        let mut rng = ark_std::test_rng();
+        const SAMPLES: usize = 10;
+        for _ in 0..SAMPLES {
+            let p = Affine::<g2::Config>::rand(&mut rng);
+            let optimised = p.clear_cofactor().into_group();
+            let naive = g2::Config::mul_affine(&p, h_eff);
+            assert_eq!(optimised, naive);
+        }
+    }
+}

bls12_381/src/curves/mod.rs

@@ -1,9 +1,10 @@
-use ark_ec::bls12::{Bls12, Bls12Parameters, TwistType};
+use ark_ec::bls12::{Bls12, Bls12Config, TwistType};
 
-use crate::{Fq, Fq12Parameters, Fq2Parameters, Fq6Parameters};
+use crate::{Fq, Fq12Config, Fq2Config, Fq6Config};
 
 pub mod g1;
 pub mod g2;
+pub(crate) mod util;
 
 #[cfg(test)]
 mod tests;
@@ -13,18 +14,18 @@ pub use self::{
     g2::{G2Affine, G2Projective},
 };
 
-pub type Bls12_381 = Bls12<Parameters>;
+pub type Bls12_381 = Bls12<Config>;
 
-pub struct Parameters;
+pub struct Config;
 
-impl Bls12Parameters for Parameters {
+impl Bls12Config for Config {
     const X: &'static [u64] = &[0xd201000000010000];
     const X_IS_NEGATIVE: bool = true;
     const TWIST_TYPE: TwistType = TwistType::M;
     type Fp = Fq;
-    type Fp2Params = Fq2Parameters;
-    type Fp6Params = Fq6Parameters;
-    type Fp12Params = Fq12Parameters;
-    type G1Parameters = self::g1::Parameters;
-    type G2Parameters = self::g2::Parameters;
+    type Fp2Config = Fq2Config;
+    type Fp6Config = Fq6Config;
+    type Fp12Config = Fq12Config;
+    type G1Config = self::g1::Config;
+    type G2Config = self::g2::Config;
 }

bls12_381/src/curves/tests.rs

@@ -1,116 +0,0 @@
-#![allow(unused_imports)]
-use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    fields::{Field, FpParameters, PrimeField, SquareRootField},
-    test_rng, One, Zero,
-};
-use ark_serialize::CanonicalSerialize;
-use core::ops::{AddAssign, MulAssign};
-use rand::Rng;
-
-use crate::{g1, g2, Bls12_381, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
-use ark_curve_tests::{curves::*, groups::*};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let mut sa = a;
-    sa.mul_assign(s);
-    let mut sb = b;
-    sb.mul_assign(s);
-
-    let ans1 = Bls12_381::pairing(sa, b);
-    let ans2 = Bls12_381::pairing(a, sb);
-    let ans3 = Bls12_381::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq12::one());
-    assert_ne!(ans2, Fq12::one());
-    assert_ne!(ans3, Fq12::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq12::one());
-}
-
-#[test]
-fn test_g1_generator_raw() {
-    let mut x = Fq::zero();
-    let mut i = 0;
-    loop {
-        // y^2 = x^3 + b
-        let mut rhs = x;
-        rhs.square_in_place();
-        rhs.mul_assign(&x);
-        rhs.add_assign(&g1::Parameters::COEFF_B);
-
-        if let Some(y) = rhs.sqrt() {
-            let p = G1Affine::new(x, if y < -y { y } else { -y }, false);
-            assert!(!p.is_in_correct_subgroup_assuming_on_curve());
-
-            let g1 = p.scale_by_cofactor();
-            if !g1.is_zero() {
-                assert_eq!(i, 4);
-                let g1 = G1Affine::from(g1);
-
-                assert!(g1.is_in_correct_subgroup_assuming_on_curve());
-
-                assert_eq!(g1, G1Affine::prime_subgroup_generator());
-                break;
-            }
-        }
-
-        i += 1;
-        x.add_assign(&Fq::one());
-    }
-}

bls12_381/src/curves/tests/mod.rs

@@ -0,0 +1,119 @@
+use ark_algebra_test_templates::*;
+use ark_ec::{AffineRepr, CurveGroup, Group};
+use ark_ff::{fields::Field, One, UniformRand, Zero};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Compress, Validate};
+use ark_std::{rand::Rng, test_rng, vec};
+
+use crate::{Bls12_381, Fq, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
+
+test_group!(g1; G1Projective; sw);
+test_group!(g2; G2Projective; sw);
+test_group!(pairing_output; ark_ec::pairing::PairingOutput<Bls12_381>; msm);
+test_pairing!(pairing; crate::Bls12_381);
+
+#[test]
+fn test_g1_endomorphism_beta() {
+    assert!(crate::g1::BETA.pow(&[3u64]).is_one());
+}
+
+#[test]
+fn test_g1_subgroup_membership_via_endomorphism() {
+    let mut rng = test_rng();
+    let generator = G1Projective::rand(&mut rng).into_affine();
+    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+}
+
+#[test]
+fn test_g1_subgroup_non_membership_via_endomorphism() {
+    let mut rng = test_rng();
+    loop {
+        let x = Fq::rand(&mut rng);
+        let greatest = rng.gen();
+
+        if let Some(p) = G1Affine::get_point_from_x_unchecked(x, greatest) {
+            if !p.mul_bigint(Fr::characteristic()).is_zero() {
+                assert!(!p.is_in_correct_subgroup_assuming_on_curve());
+                return;
+            }
+        }
+    }
+}
+
+#[test]
+fn test_g2_subgroup_membership_via_endomorphism() {
+    let mut rng = test_rng();
+    let generator = G2Projective::rand(&mut rng).into_affine();
+    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+}
+
+#[test]
+fn test_g2_subgroup_non_membership_via_endomorphism() {
+    let mut rng = test_rng();
+    loop {
+        let x = Fq2::rand(&mut rng);
+        let greatest = rng.gen();
+
+        if let Some(p) = G2Affine::get_point_from_x_unchecked(x, greatest) {
+            if !p.mul_bigint(Fr::characteristic()).is_zero() {
+                assert!(!p.is_in_correct_subgroup_assuming_on_curve());
+                return;
+            }
+        }
+    }
+}
+
+// Test vectors and macro adapted from https://github.com/zkcrypto/bls12_381/blob/e224ad4ea1babfc582ccd751c2bf128611d10936/src/tests/mod.rs
+macro_rules! test_vectors {
+    ($projective:ident, $affine:ident, $compress:expr, $expected:ident) => {
+        let mut e = $projective::zero();
+
+        let mut v = vec![];
+        {
+            let mut expected = $expected;
+            for _ in 0..1000 {
+                let e_affine = $affine::from(e);
+                let mut serialized = vec![0u8; e.serialized_size($compress)];
+                e_affine
+                    .serialize_with_mode(serialized.as_mut_slice(), $compress)
+                    .unwrap();
+                v.extend_from_slice(&serialized[..]);
+
+                let mut decoded = serialized;
+                let len_of_encoding = decoded.len();
+                (&mut decoded[..]).copy_from_slice(&expected[0..len_of_encoding]);
+                expected = &expected[len_of_encoding..];
+                let decoded =
+                    $affine::deserialize_with_mode(&decoded[..], $compress, Validate::Yes).unwrap();
+                assert_eq!(e_affine, decoded);
+
+                e += &$projective::generator();
+            }
+        }
+
+        assert_eq!(&v[..], $expected);
+    };
+}
+
+#[test]
+fn g1_compressed_valid_test_vectors() {
+    let bytes: &'static [u8] = include_bytes!("g1_compressed_valid_test_vectors.dat");
+    test_vectors!(G1Projective, G1Affine, Compress::Yes, bytes);
+}
+
+#[test]
+fn g1_uncompressed_valid_test_vectors() {
+    let bytes: &'static [u8] = include_bytes!("g1_uncompressed_valid_test_vectors.dat");
+    test_vectors!(G1Projective, G1Affine, Compress::No, bytes);
+}
+
+#[test]
+fn g2_compressed_valid_test_vectors() {
+    let bytes: &'static [u8] = include_bytes!("g2_compressed_valid_test_vectors.dat");
+    test_vectors!(G2Projective, G2Affine, Compress::Yes, bytes);
+}
+
+#[test]
+fn g2_uncompressed_valid_test_vectors() {
+    let bytes: &'static [u8] = include_bytes!("g2_uncompressed_valid_test_vectors.dat");
+    test_vectors!(G2Projective, G2Affine, Compress::No, bytes);
+}

bls12_381/src/curves/util.rs

@@ -0,0 +1,215 @@
+use ark_ec::{short_weierstrass::Affine, AffineRepr};
+use ark_ff::{BigInteger384, PrimeField};
+use ark_serialize::SerializationError;
+
+use crate::{g1::Config as G1Config, g2::Config as G2Config, Fq, Fq2, G1Affine, G2Affine};
+
+pub const G1_SERIALIZED_SIZE: usize = 48;
+pub const G2_SERIALIZED_SIZE: usize = 96;
+
+pub struct EncodingFlags {
+    pub is_compressed: bool,
+    pub is_infinity: bool,
+    pub is_lexographically_largest: bool,
+}
+
+impl EncodingFlags {
+    pub fn get_flags(bytes: &[u8]) -> Self {
+        let compression_flag_set = (bytes[0] >> 7) & 1;
+        let infinity_flag_set = (bytes[0] >> 6) & 1;
+        let sort_flag_set = (bytes[0] >> 5) & 1;
+
+        Self {
+            is_compressed: compression_flag_set == 1,
+            is_infinity: infinity_flag_set == 1,
+            is_lexographically_largest: sort_flag_set == 1,
+        }
+    }
+    pub fn encode_flags(&self, bytes: &mut [u8]) {
+        if self.is_compressed {
+            bytes[0] |= 1 << 7;
+        }
+
+        if self.is_infinity {
+            bytes[0] |= 1 << 6;
+        }
+
+        if self.is_compressed && !self.is_infinity && self.is_lexographically_largest {
+            bytes[0] |= 1 << 5;
+        }
+    }
+}
+
+pub(crate) fn deserialize_fq(bytes: [u8; 48]) -> Option<Fq> {
+    let mut tmp = BigInteger384::new([0, 0, 0, 0, 0, 0]);
+
+    // Note: The following unwraps are if the compiler cannot convert
+    // the byte slice into [u8;8], we know this is infallible since we
+    // are providing the indices at compile time and bytes has a fixed size
+    tmp.0[5] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[0..8]).unwrap());
+    tmp.0[4] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[8..16]).unwrap());
+    tmp.0[3] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[16..24]).unwrap());
+    tmp.0[2] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[24..32]).unwrap());
+    tmp.0[1] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[32..40]).unwrap());
+    tmp.0[0] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[40..48]).unwrap());
+
+    Fq::from_bigint(tmp)
+}
+
+pub(crate) fn serialize_fq(field: Fq) -> [u8; 48] {
+    let mut result = [0u8; 48];
+
+    let rep = field.into_bigint();
+
+    result[0..8].copy_from_slice(&rep.0[5].to_be_bytes());
+    result[8..16].copy_from_slice(&rep.0[4].to_be_bytes());
+    result[16..24].copy_from_slice(&rep.0[3].to_be_bytes());
+    result[24..32].copy_from_slice(&rep.0[2].to_be_bytes());
+    result[32..40].copy_from_slice(&rep.0[1].to_be_bytes());
+    result[40..48].copy_from_slice(&rep.0[0].to_be_bytes());
+
+    result
+}
+
+pub(crate) fn read_fq_with_offset(
+    bytes: &[u8],
+    offset: usize,
+    mask: bool,
+) -> Result<Fq, ark_serialize::SerializationError> {
+    let mut tmp = [0; G1_SERIALIZED_SIZE];
+    // read `G1_SERIALIZED_SIZE` bytes
+    tmp.copy_from_slice(&bytes[offset * G1_SERIALIZED_SIZE..G1_SERIALIZED_SIZE * (offset + 1)]);
+
+    if mask {
+        // Mask away the flag bits
+        tmp[0] &= 0b0001_1111;
+    }
+    deserialize_fq(tmp).ok_or(SerializationError::InvalidData)
+}
+
+pub(crate) fn read_g1_compressed<R: ark_serialize::Read>(
+    mut reader: R,
+) -> Result<Affine<G1Config>, ark_serialize::SerializationError> {
+    let mut bytes = [0u8; G1_SERIALIZED_SIZE];
+    reader
+        .read_exact(&mut bytes)
+        .ok()
+        .ok_or(SerializationError::InvalidData)?;
+
+    // Obtain the three flags from the start of the byte sequence
+    let flags = EncodingFlags::get_flags(&bytes[..]);
+
+    // we expect to be deserializing a compressed point
+    if !flags.is_compressed {
+        return Err(SerializationError::UnexpectedFlags);
+    }
+
+    if flags.is_infinity {
+        return Ok(G1Affine::zero());
+    }
+
+    // Attempt to obtain the x-coordinate
+    let x = read_fq_with_offset(&bytes, 0, true)?;
+
+    let p = G1Affine::get_point_from_x_unchecked(x, flags.is_lexographically_largest)
+        .ok_or(SerializationError::InvalidData)?;
+
+    Ok(p)
+}
+
+pub(crate) fn read_g1_uncompressed<R: ark_serialize::Read>(
+    mut reader: R,
+) -> Result<Affine<G1Config>, ark_serialize::SerializationError> {
+    let mut bytes = [0u8; 2 * G1_SERIALIZED_SIZE];
+    reader
+        .read_exact(&mut bytes)
+        .map_err(|_| SerializationError::InvalidData)?;
+
+    // Obtain the three flags from the start of the byte sequence
+    let flags = EncodingFlags::get_flags(&bytes[..]);
+
+    // we expect to be deserializing an uncompressed point
+    if flags.is_compressed {
+        return Err(SerializationError::UnexpectedFlags);
+    }
+
+    if flags.is_infinity {
+        return Ok(G1Affine::zero());
+    }
+
+    // Attempt to obtain the x-coordinate
+    let x = read_fq_with_offset(&bytes, 0, true)?;
+    // Attempt to obtain the y-coordinate
+    let y = read_fq_with_offset(&bytes, 1, false)?;
+
+    let p = G1Affine::new_unchecked(x, y);
+
+    Ok(p)
+}
+
+pub(crate) fn read_g2_compressed<R: ark_serialize::Read>(
+    mut reader: R,
+) -> Result<Affine<G2Config>, ark_serialize::SerializationError> {
+    let mut bytes = [0u8; G2_SERIALIZED_SIZE];
+    reader
+        .read_exact(&mut bytes)
+        .map_err(|_| SerializationError::InvalidData)?;
+
+    // Obtain the three flags from the start of the byte sequence
+    let flags = EncodingFlags::get_flags(&bytes);
+
+    // we expect to be deserializing a compressed point
+    if !flags.is_compressed {
+        return Err(SerializationError::UnexpectedFlags);
+    }
+
+    if flags.is_infinity {
+        return Ok(G2Affine::zero());
+    }
+
+    // Attempt to obtain the x-coordinate
+    let xc1 = read_fq_with_offset(&bytes, 0, true)?;
+    let xc0 = read_fq_with_offset(&bytes, 1, false)?;
+
+    let x = Fq2::new(xc0, xc1);
+
+    let p = G2Affine::get_point_from_x_unchecked(x, flags.is_lexographically_largest)
+        .ok_or(SerializationError::InvalidData)?;
+
+    Ok(p)
+}
+
+pub(crate) fn read_g2_uncompressed<R: ark_serialize::Read>(
+    mut reader: R,
+) -> Result<Affine<G2Config>, ark_serialize::SerializationError> {
+    let mut bytes = [0u8; 2 * G2_SERIALIZED_SIZE];
+    reader
+        .read_exact(&mut bytes)
+        .map_err(|_| SerializationError::InvalidData)?;
+
+    // Obtain the three flags from the start of the byte sequence
+    let flags = EncodingFlags::get_flags(&bytes);
+
+    // we expect to be deserializing an uncompressed point
+    if flags.is_compressed {
+        return Err(SerializationError::UnexpectedFlags);
+    }
+
+    if flags.is_infinity {
+        return Ok(G2Affine::zero());
+    }
+
+    // Attempt to obtain the x-coordinate
+    let xc1 = read_fq_with_offset(&bytes, 0, true)?;
+    let xc0 = read_fq_with_offset(&bytes, 1, false)?;
+    let x = Fq2::new(xc0, xc1);
+
+    // Attempt to obtain the y-coordinate
+    let yc1 = read_fq_with_offset(&bytes, 2, false)?;
+    let yc0 = read_fq_with_offset(&bytes, 3, false)?;
+    let y = Fq2::new(yc0, yc1);
+
+    let p = G2Affine::new_unchecked(x, y);
+
+    Ok(p)
+}

bls12_381/src/fields/fq.rs

@@ -1,112 +1,9 @@
-use ark_ff::{
-    biginteger::BigInteger384 as BigInteger,
-    field_new,
-    fields::{FftParameters, Fp384, Fp384Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};
 
-pub type Fq = Fp384<FqParameters>;
-
-pub struct FqParameters;
-
-impl Fp384Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 1;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        0x43f5fffffffcaaae,
-        0x32b7fff2ed47fffd,
-        0x7e83a49a2e99d69,
-        0xeca8f3318332bb7a,
-        0xef148d1ea0f4c069,
-        0x40ab3263eff0206,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0xb9feffffffffaaab,
-        0x1eabfffeb153ffff,
-        0x6730d2a0f6b0f624,
-        0x64774b84f38512bf,
-        0x4b1ba7b6434bacd7,
-        0x1a0111ea397fe69a,
-    ]);
-
-    const MODULUS_BITS: u32 = 381;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 3;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        0x760900000002fffd,
-        0xebf4000bc40c0002,
-        0x5f48985753c758ba,
-        0x77ce585370525745,
-        0x5c071a97a256ec6d,
-        0x15f65ec3fa80e493,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xf4df1f341c341746,
-        0xa76e6a609d104f1,
-        0x8de5476c4c95b6d5,
-        0x67eb88a9939d83c0,
-        0x9a793e85b519952d,
-        0x11988fe592cae3aa,
-    ]);
-
-    const INV: u64 = 0x89f3fffcfffcfffd;
-
-    // GENERATOR = 2
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0x321300000006554f,
-        0xb93c0018d6c40005,
-        0x57605e0db0ddbb51,
-        0x8b256521ed1f9bcb,
-        0x6cf28d7901622c03,
-        0x11ebab9dbb81e28c,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xdcff7fffffffd555,
-        0xf55ffff58a9ffff,
-        0xb39869507b587b12,
-        0xb23ba5c279c2895f,
-        0x258dd3db21a5d66b,
-        0xd0088f51cbff34d,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0xdcff7fffffffd555,
-        0xf55ffff58a9ffff,
-        0xb39869507b587b12,
-        0xb23ba5c279c2895f,
-        0x258dd3db21a5d66b,
-        0xd0088f51cbff34d,
-    ]);
-
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xee7fbfffffffeaaa,
-        0x7aaffffac54ffff,
-        0xd9cc34a83dac3d89,
-        0xd91dd2e13ce144af,
-        0x92c6e9ed90d2eb35,
-        0x680447a8e5ff9a6,
-    ]);
-}
-
-pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
-pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0]));
+#[derive(MontConfig)]
+#[modulus = "4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787"]
+#[generator = "2"]
+#[small_subgroup_base = "3"]
+#[small_subgroup_power = "2"]
+pub struct FqConfig;
+pub type Fq = Fp384<MontBackend<FqConfig, 6>>;

bls12_381/src/fields/fq12.rs

@@ -1,193 +1,77 @@
-use crate::*;
-use ark_ff::{biginteger::BigInteger384, field_new, fields::*};
+use ark_ff::{fields::*, MontFp};
 
-pub type Fq12 = Fp12<Fq12Parameters>;
+use crate::*;
+
+pub type Fq12 = Fp12<Fq12Config>;
 
 #[derive(Clone, Copy)]
-pub struct Fq12Parameters;
+pub struct Fq12Config;
 
-impl Fp12Parameters for Fq12Parameters {
-    type Fp6Params = Fq6Parameters;
+impl Fp12Config for Fq12Config {
+    type Fp6Config = Fq6Config;
 
-    const NONRESIDUE: Fq6 = field_new!(Fq6, FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
-        // Fq2(u + 1)**(((q^0) - 1) / 6)
-        FQ2_ONE,
-        // Fq2(u + 1)**(((q^1) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x7089552b319d465,
-                0xc6695f92b50a8313,
-                0x97e83cccd117228f,
-                0xa35baecab2dc29ee,
-                0x1ce393ea5daace4d,
-                0x8f2220fb0fb66eb,
-            ])),
-            field_new!(Fq, BigInteger384([
-                0xb2f66aad4ce5d646,
-                0x5842a06bfc497cec,
-                0xcf4895d42599d394,
-                0xc11b9cba40a8e8d0,
-                0x2e3813cbe5a0de89,
-                0x110eefda88847faf,
-            ])),
+        // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
         ),
-        // Fq2(u + 1)**(((q^2) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xecfb361b798dba3a,
-                0xc100ddb891865a2c,
-                0xec08ff1232bda8e,
-                0xd5c13cc6f1ca4721,
-                0x47222a47bf7b5c04,
-                0x110f184e51c5f59,
-            ])),
-            FQ_ZERO,
+        // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
+        Fq2::new(
+            MontFp!("3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
+            MontFp!("151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
         ),
-        // Fq2(u + 1)**(((q^3) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x3e2f585da55c9ad1,
-                0x4294213d86c18183,
-                0x382844c88b623732,
-                0x92ad2afd19103e18,
-                0x1d794e4fac7cf0b9,
-                0xbd592fc7d825ec8,
-            ])),
-            field_new!(Fq, BigInteger384([
-                0x7bcfa7a25aa30fda,
-                0xdc17dec12a927e7c,
-                0x2f088dd86b4ebef1,
-                0xd1ca2087da74d4a7,
-                0x2da2596696cebc1d,
-                0xe2b7eedbbfd87d2,
-            ])),
+        // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
+            Fq::ZERO,
         ),
-        // Fq2(u + 1)**(((q^4) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x30f1361b798a64e8,
-                0xf3b8ddab7ece5a2a,
-                0x16a8ca3ac61577f7,
-                0xc26a2ff874fd029b,
-                0x3636b76660701c6e,
-                0x51ba4ab241b6160,
-            ])),
-            FQ_ZERO,
+        // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
+        Fq2::new(
+            MontFp!("2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
+            MontFp!("1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
         ),
-        // Fq2(u + 1)**(((q^5) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x3726c30af242c66c,
-                0x7c2ac1aad1b6fe70,
-                0xa04007fbba4b14a2,
-                0xef517c3266341429,
-                0x95ba654ed2226b,
-                0x2e370eccc86f7dd,
-            ])),
-            field_new!(Fq, BigInteger384([
-                0x82d83cf50dbce43f,
-                0xa2813e53df9d018f,
-                0xc6f0caa53c65e181,
-                0x7525cf528d50fe95,
-                0x4a85ed50f4798a6b,
-                0x171da0fd6cf8eebd,
-            ])),
+        // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
         ),
-        // Fq2(u + 1)**(((q^6) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x43f5fffffffcaaae,
-                0x32b7fff2ed47fffd,
-                0x7e83a49a2e99d69,
-                0xeca8f3318332bb7a,
-                0xef148d1ea0f4c069,
-                0x40ab3263eff0206,
-            ])),
-            FQ_ZERO,
+        // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
+        Fq2::new(
+            MontFp!("3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
+            MontFp!("877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
         ),
-        // Fq2(u + 1)**(((q^7) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xb2f66aad4ce5d646,
-                0x5842a06bfc497cec,
-                0xcf4895d42599d394,
-                0xc11b9cba40a8e8d0,
-                0x2e3813cbe5a0de89,
-                0x110eefda88847faf,
-            ])),
-            field_new!(Fq, BigInteger384([
-                0x7089552b319d465,
-                0xc6695f92b50a8313,
-                0x97e83cccd117228f,
-                0xa35baecab2dc29ee,
-                0x1ce393ea5daace4d,
-                0x8f2220fb0fb66eb,
-            ])),
+        // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
         ),
-        // Fq2(u + 1)**(((q^8) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xcd03c9e48671f071,
-                0x5dab22461fcda5d2,
-                0x587042afd3851b95,
-                0x8eb60ebe01bacb9e,
-                0x3f97d6e83d050d2,
-                0x18f0206554638741,
-            ])),
-            FQ_ZERO,
+        // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
+        Fq2::new(
+            MontFp!("151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
+            MontFp!("3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
         ),
-        // Fq2(u + 1)**(((q^9) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x7bcfa7a25aa30fda,
-                0xdc17dec12a927e7c,
-                0x2f088dd86b4ebef1,
-                0xd1ca2087da74d4a7,
-                0x2da2596696cebc1d,
-                0xe2b7eedbbfd87d2,
-            ])),
-            field_new!(Fq, BigInteger384([
-                0x3e2f585da55c9ad1,
-                0x4294213d86c18183,
-                0x382844c88b623732,
-                0x92ad2afd19103e18,
-                0x1d794e4fac7cf0b9,
-                0xbd592fc7d825ec8,
-            ])),
+        // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
         ),
-        // Fq2(u + 1)**(((q^10) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x890dc9e4867545c3,
-                0x2af322533285a5d5,
-                0x50880866309b7e2c,
-                0xa20d1b8c7e881024,
-                0x14e4f04fe2db9068,
-                0x14e56d3f1564853a,
-            ])),
-            FQ_ZERO,
+        // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
+        Fq2::new(
+            MontFp!("1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
+            MontFp!("2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
         ),
-        // Fq2(u + 1)**(((q^11) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x82d83cf50dbce43f,
-                0xa2813e53df9d018f,
-                0xc6f0caa53c65e181,
-                0x7525cf528d50fe95,
-                0x4a85ed50f4798a6b,
-                0x171da0fd6cf8eebd,
-            ])),
-            field_new!(Fq, BigInteger384([
-                0x3726c30af242c66c,
-                0x7c2ac1aad1b6fe70,
-                0xa04007fbba4b14a2,
-                0xef517c3266341429,
-                0x95ba654ed2226b,
-                0x2e370eccc86f7dd,
-            ])),
+        // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
+            Fq::ZERO,
+        ),
+        // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
+        Fq2::new(
+            MontFp!("877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
+            MontFp!("3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
         ),
     ];
 }

bls12_381/src/fields/fq2.rs

@@ -1,73 +1,42 @@
+use ark_ff::{fields::*, MontFp};
+
 use crate::*;
-use ark_ff::{biginteger::BigInteger384 as BigInteger, field_new, fields::*};
 
-pub type Fq2 = Fp2<Fq2Parameters>;
+pub type Fq2 = Fp2<Fq2Config>;
 
-pub struct Fq2Parameters;
+pub struct Fq2Config;
 
-impl Fp2Parameters for Fq2Parameters {
+impl Fp2Config for Fq2Config {
     type Fp = Fq;
 
     /// NONRESIDUE = -1
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
-        0x43f5fffffffcaaae,
-        0x32b7fff2ed47fffd,
-        0x7e83a49a2e99d69,
-        0xeca8f3318332bb7a,
-        0xef148d1ea0f4c069,
-        0x40ab3263eff0206,
-    ]));
-
-    /// QUADRATIC_NONRESIDUE = (U + 1)
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE: (Fq, Fq) = (
-        field_new!(Fq, BigInteger([
-            0x760900000002fffd,
-            0xebf4000bc40c0002,
-            0x5f48985753c758ba,
-            0x77ce585370525745,
-            0x5c071a97a256ec6d,
-            0x15f65ec3fa80e493,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x760900000002fffd,
-            0xebf4000bc40c0002,
-            0x5f48985753c758ba,
-            0x77ce585370525745,
-            0x5c071a97a256ec6d,
-            0x15f65ec3fa80e493,
-        ])),
-    );
+    const NONRESIDUE: Fq = MontFp!("-1");
 
     /// Coefficients for the Frobenius automorphism.
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // Fq(-1)**(((q^0) - 1) / 2)
-        field_new!(Fq, BigInteger([
-            0x760900000002fffd,
-            0xebf4000bc40c0002,
-            0x5f48985753c758ba,
-            0x77ce585370525745,
-            0x5c071a97a256ec6d,
-            0x15f65ec3fa80e493,
-        ])),
+        Fq::ONE,
         // Fq(-1)**(((q^1) - 1) / 2)
-        field_new!(Fq, BigInteger([
-            0x43f5fffffffcaaae,
-            0x32b7fff2ed47fffd,
-            0x7e83a49a2e99d69,
-            0xeca8f3318332bb7a,
-            0xef148d1ea0f4c069,
-            0x40ab3263eff0206,
-        ])),
+        MontFp!("-1"),
     ];
 
     #[inline(always)]
-    fn mul_fp_by_nonresidue(fp: &Self::Fp) -> Self::Fp {
-        -(*fp)
+    fn mul_fp_by_nonresidue_in_place(fp: &mut Self::Fp) -> &mut Self::Fp {
+        fp.neg_in_place()
+    }
+
+    #[inline(always)]
+    fn sub_and_mul_fp_by_nonresidue(y: &mut Self::Fp, x: &Self::Fp) {
+        *y += x;
+    }
+
+    #[inline(always)]
+    fn mul_fp_by_nonresidue_plus_one_and_add(y: &mut Self::Fp, x: &Self::Fp) {
+        *y = *x;
+    }
+
+    fn mul_fp_by_nonresidue_and_add(y: &mut Self::Fp, x: &Self::Fp) {
+        y.neg_in_place();
+        *y += x;
     }
 }
-
-pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = field_new!(Fq2, FQ_ONE, FQ_ZERO);

bls12_381/src/fields/fq6.rs

@@ -1,194 +1,91 @@
-use crate::*;
-use ark_ff::{biginteger::BigInteger384, field_new, fields::*};
+use ark_ff::{fields::*, MontFp};
 
-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::*;
+
+pub type Fq6 = Fp6<Fq6Config>;
 
 #[derive(Clone, Copy)]
-pub struct Fq6Parameters;
+pub struct Fq6Config;
 
-impl Fp6Parameters for Fq6Parameters {
-    type Fp2Params = Fq2Parameters;
+impl Fp6Config for Fq6Config {
+    type Fp2Config = Fq2Config;
 
     /// NONRESIDUE = (U + 1)
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq2 = field_new!(Fq2,
-        field_new!(Fq, BigInteger384([
-            0x760900000002fffd,
-            0xebf4000bc40c0002,
-            0x5f48985753c758ba,
-            0x77ce585370525745,
-            0x5c071a97a256ec6d,
-            0x15f65ec3fa80e493,
-        ])),
-        field_new!(Fq, BigInteger384([
-            0x760900000002fffd,
-            0xebf4000bc40c0002,
-            0x5f48985753c758ba,
-            0x77ce585370525745,
-            0x5c071a97a256ec6d,
-            0x15f65ec3fa80e493,
-        ])),
-    );
+    const NONRESIDUE: Fq2 = Fq2::new(Fq::ONE, Fq::ONE);
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
-        // Fq2(u + 1)**(((q^0) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x760900000002fffd,
-                0xebf4000bc40c0002,
-                0x5f48985753c758ba,
-                0x77ce585370525745,
-                0x5c071a97a256ec6d,
-                0x15f65ec3fa80e493,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
         ),
-        // Fq2(u + 1)**(((q^1) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
-            field_new!(Fq, BigInteger384([
-                0xcd03c9e48671f071,
-                0x5dab22461fcda5d2,
-                0x587042afd3851b95,
-                0x8eb60ebe01bacb9e,
-                0x3f97d6e83d050d2,
-                0x18f0206554638741,
-            ])),
+        // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
+        Fq2::new(
+            Fq::ZERO,
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
         ),
-        // Fq2(u + 1)**(((q^2) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x30f1361b798a64e8,
-                0xf3b8ddab7ece5a2a,
-                0x16a8ca3ac61577f7,
-                0xc26a2ff874fd029b,
-                0x3636b76660701c6e,
-                0x51ba4ab241b6160,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
         ),
-        // Fq2(u + 1)**(((q^3) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
-            field_new!(Fq, BigInteger384([
-                0x760900000002fffd,
-                0xebf4000bc40c0002,
-                0x5f48985753c758ba,
-                0x77ce585370525745,
-                0x5c071a97a256ec6d,
-                0x15f65ec3fa80e493,
-            ])),
+        // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
+        Fq2::new(
+            Fq::ZERO,
+            Fq::ONE,
         ),
-        // Fq2(u + 1)**(((q^4) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xcd03c9e48671f071,
-                0x5dab22461fcda5d2,
-                0x587042afd3851b95,
-                0x8eb60ebe01bacb9e,
-                0x3f97d6e83d050d2,
-                0x18f0206554638741,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
         ),
-        // Fq2(u + 1)**(((q^5) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
-            field_new!(Fq, BigInteger384([
-                0x30f1361b798a64e8,
-                0xf3b8ddab7ece5a2a,
-                0x16a8ca3ac61577f7,
-                0xc26a2ff874fd029b,
-                0x3636b76660701c6e,
-                0x51ba4ab241b6160,
-            ])),
+        // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
+        Fq2::new(
+            Fq::ZERO,
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
         ),
-    ];
+];
 
     #[rustfmt::skip]
     const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
         // Fq2(u + 1)**(((2q^0) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x760900000002fffd,
-                0xebf4000bc40c0002,
-                0x5f48985753c758ba,
-                0x77ce585370525745,
-                0x5c071a97a256ec6d,
-                0x15f65ec3fa80e493,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^1) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x890dc9e4867545c3,
-                0x2af322533285a5d5,
-                0x50880866309b7e2c,
-                0xa20d1b8c7e881024,
-                0x14e4f04fe2db9068,
-                0x14e56d3f1564853a,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^2) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xcd03c9e48671f071,
-                0x5dab22461fcda5d2,
-                0x587042afd3851b95,
-                0x8eb60ebe01bacb9e,
-                0x3f97d6e83d050d2,
-                0x18f0206554638741,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^3) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x43f5fffffffcaaae,
-                0x32b7fff2ed47fffd,
-                0x7e83a49a2e99d69,
-                0xeca8f3318332bb7a,
-                0xef148d1ea0f4c069,
-                0x40ab3263eff0206,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^4) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0x30f1361b798a64e8,
-                0xf3b8ddab7ece5a2a,
-                0x16a8ca3ac61577f7,
-                0xc26a2ff874fd029b,
-                0x3636b76660701c6e,
-                0x51ba4ab241b6160,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
         ),
         // Fq2(u + 1)**(((2q^5) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger384([
-                0xecfb361b798dba3a,
-                0xc100ddb891865a2c,
-                0xec08ff1232bda8e,
-                0xd5c13cc6f1ca4721,
-                0x47222a47bf7b5c04,
-                0x110f184e51c5f59,
-            ])),
-            field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
+            Fq::ZERO,
         ),
     ];
 
     /// Multiply this element by the quadratic nonresidue 1 + u.
     /// Make this generic.
-    fn mul_fp2_by_nonresidue(fe: &Fq2) -> Fq2 {
-        let mut copy = *fe;
-        let t0 = copy.c0;
-        copy.c0 -= &fe.c1;
-        copy.c1 += &t0;
-        copy
+    fn mul_fp2_by_nonresidue_in_place(fe: &mut Fq2) -> &mut Fq2 {
+        let t0 = fe.c0;
+        fe.c0 -= &fe.c1;
+        fe.c1 += &t0;
+        fe
     }
 }

bls12_381/src/fields/fr.rs

@@ -1,96 +1,9 @@
-use ark_ff::{
-    biginteger::BigInteger256 as BigInteger,
-    fields::{FftParameters, Fp256, Fp256Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
 
-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 32;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        0xb9b58d8c5f0e466a,
-        0x5b1b4c801819d7ec,
-        0xaf53ae352a31e64,
-        0x5bf3adda19e9b27b,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// MODULUS = 52435875175126190479447740508185965837690552500527637822603658699938581184513
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0xffffffff00000001,
-        0x53bda402fffe5bfe,
-        0x3339d80809a1d805,
-        0x73eda753299d7d48,
-    ]);
-
-    const MODULUS_BITS: u32 = 255;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 1;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        0x1fffffffe,
-        0x5884b7fa00034802,
-        0x998c4fefecbc4ff5,
-        0x1824b159acc5056f,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xc999e990f3f29c6d,
-        0x2b6cedcb87925c23,
-        0x5d314967254398f,
-        0x748d9d99f59ff11,
-    ]);
-
-    const INV: u64 = 0xfffffffeffffffff;
-
-    //
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0xefffffff1,
-        0x17e363d300189c0f,
-        0xff9c57876f8457b0,
-        0x351332208fc5a8c4,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x7fffffff80000000,
-        0xa9ded2017fff2dff,
-        0x199cec0404d0ec02,
-        0x39f6d3a994cebea4,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-
-    // T = (MODULUS - 1) / 2^S =
-    // 12208678567578594777604504606729831043093128246378069236549469339647
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0xfffe5bfeffffffff,
-        0x9a1d80553bda402,
-        0x299d7d483339d808,
-        0x73eda753,
-    ]);
-
-    // (T - 1) / 2 =
-    // 6104339283789297388802252303364915521546564123189034618274734669823
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x7fff2dff7fffffff,
-        0x4d0ec02a9ded201,
-        0x94cebea4199cec04,
-        0x39f6d3a9,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "52435875175126190479447740508185965837690552500527637822603658699938581184513"]
+#[generator = "7"]
+#[small_subgroup_base = "3"]
+#[small_subgroup_power = "1"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;

bls12_381/src/fields/mod.rs

@@ -23,5 +23,5 @@ pub mod fq12;
 #[cfg(feature = "curve")]
 pub use self::fq12::*;
 
-#[cfg(all(feature = "curve", feature = "std", test))]
+#[cfg(all(feature = "curve", test))]
 mod tests;

bls12_381/src/lib.rs

@@ -9,15 +9,16 @@
 #![forbid(unsafe_code)]
 
 //! This library implements the BLS12_381 curve generated by [Sean Bowe](https://electriccoin.co/blog/new-snark-curve/).
-//! The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree 12,
-//! defined over a 381-bit (prime) field.
-//! This curve was intended to replace the BN254 curve to provide a higher security
-//! level without incurring a large performance overhead.
+//! The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree
+//! 12, defined over a 381-bit (prime) field.
+//! This curve was intended to replace the BN254 curve to provide a higher
+//! security level without incurring a large performance overhead.
 //!
 //!
 //! Curve information:
 //! * Base field: q = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
-//! * Scalar field: r = 52435875175126190479447740508185965837690552500527637822603658699938581184513
+//! * Scalar field: r =
+//!   52435875175126190479447740508185965837690552500527637822603658699938581184513
 //! * valuation(q - 1, 2) = 1
 //! * valuation(r - 1, 2) = 32
 //! * G1 curve equation: y^2 = x^3 + 4

bn254/Cargo.toml

@@ -1,31 +1,37 @@
 [package]
 name = "ark-bn254"
-version = "0.1.0"
+version = "0.4.0"
 authors = [ "arkworks contributors" ]
 description = "The BN254 pairing-friendly elliptic curve"
-homepage = "https://arworks.rs"
-repository = "https://github.com/arkworks/algebra"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
 documentation = "https://docs.rs/ark-bn254/"
-keywords = ["cryptography", "finite fields", "elliptic curves" ]
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"
 
 [dependencies]
-ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-ff = { version="0.4.0-alpha", default-features = false }
+ark-ec = { version="0.4.0-alpha", default-features = false }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+ark-r1cs-std = { version = "0.4.0-alpha", default-features = false, optional = true }
 
 [dev-dependencies]
-ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-curve-tests = { path = "../curve-tests", default-features = false }
-rand = { version = "0.7", default-features = false }
-rand_xorshift = "0.2"
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }
 
 [features]
 default = [ "curve" ]
 std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
+r1cs = [ "ark-r1cs-std" ]
 
 curve = [ "scalar_field" ]
 scalar_field = []
+
+[[bench]]
+name = "bn254"
+path = "benches/bn254.rs"
+harness = false

bn254/benches/bn254.rs

@@ -0,0 +1,13 @@
+use ark_algebra_bench_templates::*;
+use ark_bn254::{fq::Fq, fq2::Fq2, fr::Fr, Bn254, Fq12, G1Projective as G1, G2Projective as G2};
+
+bench!(
+    Name = "BN254",
+    Pairing = Bn254,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq2,
+    TargetField = Fq12,
+);

bn254/scripts/base_field.sage

@@ -0,0 +1,28 @@
+modulus = 21888242871839275222246405745257275088696311157297823662689037894645226208583
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

bn254/scripts/scalar_field.sage

@@ -0,0 +1,28 @@
+modulus = 21888242871839275222246405745257275088548364400416034343698204186575808495617
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

bn254/src/constraints/curves.rs

@@ -0,0 +1,11 @@
+use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;
+
+use crate::{constraints::FBaseVar, g1::Config};
+
+/// A group element in the Bn254 prime-order group.
+pub type GVar = ProjectiveVar<Config, FBaseVar>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::curves::sw_test::<Config, GVar>().unwrap();
+}

bn254/src/constraints/fields.rs

@@ -0,0 +1,11 @@
+use ark_r1cs_std::fields::fp::FpVar;
+
+use crate::fq::Fq;
+
+/// A variable that is the R1CS equivalent of `crate::Fq`.
+pub type FBaseVar = FpVar<Fq>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::fields::field_test::<_, _, FBaseVar>().unwrap();
+}

bn254/src/constraints/mod.rs

@@ -0,0 +1,107 @@
+//! This module implements the R1CS equivalent of `ark_bn254`.
+//!
+//! It implements field variables for `crate::Fq`,
+//! and group variables for `crate::G1Projective`.
+//!
+//! The field underlying these constraints is `crate::Fq`.
+//!
+//! # Examples
+//!
+//! One can perform standard algebraic operations on `FBaseVar`:
+//!
+//! ```
+//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+//! use ark_std::UniformRand;
+//! use ark_relations::r1cs::*;
+//! use ark_r1cs_std::prelude::*;
+//! use ark_bn254::{*, constraints::*};
+//!
+//! let cs = ConstraintSystem::<Fq>::new_ref();
+//! // This rng is just for test purposes; do not use it
+//! // in real applications.
+//! let mut rng = ark_std::test_rng();
+//!
+//! // Generate some random `Fq` elements.
+//! let a_native = Fq::rand(&mut rng);
+//! let b_native = Fq::rand(&mut rng);
+//!
+//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
+//! let a = FBaseVar::new_witness(ark_relations::ns!(cs, "generate_a"), || Ok(a_native))?;
+//! let b = FBaseVar::new_witness(ark_relations::ns!(cs, "generate_b"), || Ok(b_native))?;
+//!
+//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
+//! // constraints or variables.
+//! let a_const = FBaseVar::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
+//! let b_const = FBaseVar::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
+//!
+//! let one = FBaseVar::one();
+//! let zero = FBaseVar::zero();
+//!
+//! // Sanity check one + one = two
+//! let two = &one + &one + &zero;
+//! two.enforce_equal(&one.double()?)?;
+//!
+//! assert!(cs.is_satisfied()?);
+//!
+//! // Check that the value of &a + &b is correct.
+//! assert_eq!((&a + &b).value()?, a_native + &b_native);
+//!
+//! // Check that the value of &a * &b is correct.
+//! assert_eq!((&a * &b).value()?, a_native * &b_native);
+//!
+//! // Check that operations on variables and constants are equivalent.
+//! (&a + &b).enforce_equal(&(&a_const + &b_const))?;
+//! assert!(cs.is_satisfied()?);
+//! # Ok(())
+//! # }
+//! ```
+//!
+//! One can also perform standard algebraic operations on `GVar`:
+//!
+//! ```
+//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+//! # use ark_std::UniformRand;
+//! # use ark_relations::r1cs::*;
+//! # use ark_r1cs_std::prelude::*;
+//! # use ark_bn254::{*, constraints::*};
+//!
+//! # let cs = ConstraintSystem::<Fq>::new_ref();
+//! # let mut rng = ark_std::test_rng();
+//!
+//! // Generate some random `G1Projective` elements.
+//! let a_native = G1Projective::rand(&mut rng);
+//! let b_native = G1Projective::rand(&mut rng);
+//!
+//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
+//! let a = GVar::new_witness(ark_relations::ns!(cs, "a"), || Ok(a_native))?;
+//! let b = GVar::new_witness(ark_relations::ns!(cs, "b"), || Ok(b_native))?;
+//!
+//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
+//! // constraints or variables.
+//! let a_const = GVar::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
+//! let b_const = GVar::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
+//!
+//! // This returns the identity.
+//! let zero = GVar::zero();
+//!
+//! // Sanity check one + one = two
+//! let two_a = &a + &a + &zero;
+//! two_a.enforce_equal(&a.double()?)?;
+//!
+//! assert!(cs.is_satisfied()?);
+//!
+//! // Check that the value of &a + &b is correct.
+//! assert_eq!((&a + &b).value()?, a_native + &b_native);
+//!
+//! // Check that operations on variables and constants are equivalent.
+//! (&a + &b).enforce_equal(&(&a_const + &b_const))?;
+//! assert!(cs.is_satisfied()?);
+//! # Ok(())
+//! # }
+//! ```
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

bn254/src/curves/g1.rs

@@ -1,67 +1,45 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{biginteger::BigInteger256, field_new, Zero};
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
+};
+use ark_ff::{Field, MontFp, Zero};
 
 use crate::{Fq, Fr};
 
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl ModelParameters for Parameters {
+pub type G1Affine = Affine<Config>;
+
+impl CurveConfig for Config {
     type BaseField = Fq;
     type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    const COEFF_A: Fq = field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0]));
-
-    /// COEFF_B = 3
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, BigInteger256([
-        0x7a17caa950ad28d7,
-        0x1f6ac17ae15521b9,
-        0x334bea4e696bd284,
-        0x2a1f6744ce179d8e,
-    ]));
 
     /// COFACTOR = 1
     const COFACTOR: &'static [u64] = &[0x1];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
-        0xac96341c4ffffffb,
-        0x36fc76959f60cd29,
-        0x666ea36f7879462e,
-        0xe0a77c19a07df2f,
-    ]));
+    const COFACTOR_INV: Fr = Fr::ONE;
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 3
+    const COEFF_B: Fq = MontFp!("3");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 
     #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
 }
 
-/// G1_GENERATOR_X =
-/// 1
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger256([
-    0xd35d438dc58f0d9d,
-    0x0a78eb28f5c70b3d,
-    0x666ea36f7879462c,
-    0x0e0a77c19a07df2f,
-]));
+/// G1_GENERATOR_X = 1
+pub const G1_GENERATOR_X: Fq = Fq::ONE;
 
-/// G1_GENERATOR_Y =
-/// 2
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger256([
-    0xa6ba871b8b1e1b3a,
-    0x14f1d651eb8e167b,
-    0xccdd46def0f28c58,
-    0x1c14ef83340fbe5e,
-]));
+/// G1_GENERATOR_Y = 2
+pub const G1_GENERATOR_Y: Fq = MontFp!("2");

bn254/src/curves/g2.rs

@@ -1,44 +1,22 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{biginteger::BigInteger256, field_new, Zero};
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
+};
+use ark_ff::{Field, MontFp, Zero};
 
-use crate::{g1, Fq, Fq2, Fr};
+use crate::{Fq, Fq2, Fr};
+
+pub type G2Affine = Affine<Config>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Config {
     type BaseField = Fq2;
     type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = [0, 0]
-    #[rustfmt::skip]
-    const COEFF_A: Fq2 = field_new!(Fq2,
-        g1::Parameters::COEFF_A,
-        g1::Parameters::COEFF_A,
-    );
-
-    /// COEFF_B = 3/(u+9)
-    ///         = (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
-    #[rustfmt::skip]
-    const COEFF_B: Fq2 = field_new!(Fq2,
-        field_new!(Fq, BigInteger256([
-            0x3bf938e377b802a8,
-            0x020b1b273633535d,
-            0x26b7edf049755260,
-            0x2514c6324384a86d,
-        ])),
-        field_new!(Fq, BigInteger256([
-            0x38e7ecccd1dcff67,
-            0x65f0b37d93ce0d3e,
-            0xd749d0dd22ac00aa,
-            0x0141b9ce4a688d4d,
-        ])),
-    );
 
     /// COFACTOR = (36 * X^4) + (36 * X^3) + (30 * X^2) + 6*X + 1
-    ///          = 21888242871839275222246405745257275088844257914179612981679871602714643921549
+    /// 21888242871839275222246405745257275088844257914179612981679871602714643921549
     #[rustfmt::skip]
     const COFACTOR: &'static [u64] = &[
         0x345f2299c0f9fa8d,
@@ -48,65 +26,49 @@ impl SWModelParameters for Parameters {
     ];
 
     /// COFACTOR_INV = COFACTOR^{-1} mod r
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
-        0x7fff17d53ff2895e,
-        0xd0617390cf7919e5,
-        0xb9af426b22d0eb61,
-        0x270485e31bd72a4d,
-    ]));
+    const COFACTOR_INV: Fr =
+        MontFp!("10944121435919637613327163357776759465618812564592884533313067514031822496649");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = [0, 0]
+    const COEFF_A: Fq2 = Fq2::ZERO;
+
+    /// COEFF_B = 3/(u+9)
+    /// (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
+    const COEFF_B: Fq2 = Fq2::new(
+        MontFp!("19485874751759354771024239261021720505790618469301721065564631296452457478373"),
+        MontFp!("266929791119991161246907387137283842545076965332900288569378510910307636690"),
+    );
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
 
     #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
 }
 
-#[rustfmt::skip]
-pub const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
 
 /// G2_GENERATOR_X_C0 =
 /// 10857046999023057135944570762232829481370756359578518086990519993285655852781
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger256([
-    0x8e83b5d102bc2026,
-    0xdceb1935497b0172,
-    0xfbb8264797811adf,
-    0x19573841af96503b,
-]));
+pub const G2_GENERATOR_X_C0: Fq =
+    MontFp!("10857046999023057135944570762232829481370756359578518086990519993285655852781");
 
 /// G2_GENERATOR_X_C1 =
 /// 11559732032986387107991004021392285783925812861821192530917403151452391805634
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger256([
-    0xafb4737da84c6140,
-    0x6043dd5a5802d8c4,
-    0x09e950fc52a02f86,
-    0x14fef0833aea7b6b,
-]));
+pub const G2_GENERATOR_X_C1: Fq =
+    MontFp!("11559732032986387107991004021392285783925812861821192530917403151452391805634");
 
 /// G2_GENERATOR_Y_C0 =
 /// 8495653923123431417604973247489272438418190587263600148770280649306958101930
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger256([
-    0x619dfa9d886be9f6,
-    0xfe7fd297f59e9b78,
-    0xff9e1a62231b7dfe,
-    0x28fd7eebae9e4206,
-]));
+pub const G2_GENERATOR_Y_C0: Fq =
+    MontFp!("8495653923123431417604973247489272438418190587263600148770280649306958101930");
 
 /// G2_GENERATOR_Y_C1 =
 /// 4082367875863433681332203403145435568316851327593401208105741076214120093531
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger256([
-    0x64095b56c71856ee,
-    0xdc57f922327d3cbb,
-    0x55f935be33351076,
-    0x0da4a0e693fd6482,
-]));
+pub const G2_GENERATOR_Y_C1: Fq =
+    MontFp!("4082367875863433681332203403145435568316851327593401208105741076214120093531");

bn254/src/curves/mod.rs

@@ -1,18 +1,20 @@
-use crate::*;
 use ark_ec::{
     bn,
-    bn::{Bn, BnParameters, TwistType},
+    bn::{Bn, BnConfig, TwistType},
 };
-use ark_ff::{biginteger::BigInteger256, field_new};
+use ark_ff::MontFp;
+
+use crate::*;
+
 pub mod g1;
 pub mod g2;
 
 #[cfg(test)]
 mod tests;
 
-pub struct Parameters;
+pub struct Config;
 
-impl BnParameters for Parameters {
+impl BnConfig for Config {
     const X: &'static [u64] = &[4965661367192848881];
     /// `x` is positive.
     const X_IS_NEGATIVE: bool = false;
@@ -21,62 +23,27 @@ impl BnParameters for Parameters {
         0, 1, 1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 1, 1, 0,
         -1, 0, 0, 1, 0, 1, 1,
     ];
-    /// `ate_loop_count` is positive.
-    const ATE_LOOP_COUNT_IS_NEGATIVE: bool = false;
-    const TWIST_MUL_BY_Q_X: Fq2 = field_new!(
-        Fq2,
-        field_new!(
-            Fq,
-            BigInteger256([
-                0xb5773b104563ab30,
-                0x347f91c8a9aa6454,
-                0x7a007127242e0991,
-                0x1956bcd8118214ec,
-            ])
-        ),
-        field_new!(
-            Fq,
-            BigInteger256([
-                0x6e849f1ea0aa4757,
-                0xaa1c7b6d89f89141,
-                0xb6e713cdfae0ca3a,
-                0x26694fbb4e82ebc3,
-            ])
-        ),
+
+    const TWIST_MUL_BY_Q_X: Fq2 = Fq2::new(
+        MontFp!("21575463638280843010398324269430826099269044274347216827212613867836435027261"),
+        MontFp!("10307601595873709700152284273816112264069230130616436755625194854815875713954"),
     );
-    const TWIST_MUL_BY_Q_Y: Fq2 = field_new!(
-        Fq2,
-        field_new!(
-            Fq,
-            BigInteger256([
-                0xe4bbdd0c2936b629,
-                0xbb30f162e133bacb,
-                0x31a9d1b6f9645366,
-                0x253570bea500f8dd,
-            ])
-        ),
-        field_new!(
-            Fq,
-            BigInteger256([
-                0xa1d77ce45ffe77c7,
-                0x07affd117826d1db,
-                0x6d16bd27bb7edc6b,
-                0x2c87200285defecc,
-            ])
-        ),
+    const TWIST_MUL_BY_Q_Y: Fq2 = Fq2::new(
+        MontFp!("2821565182194536844548159561693502659359617185244120367078079554186484126554"),
+        MontFp!("3505843767911556378687030309984248845540243509899259641013678093033130930403"),
     );
     const TWIST_TYPE: TwistType = TwistType::D;
     type Fp = Fq;
-    type Fp2Params = Fq2Parameters;
-    type Fp6Params = Fq6Parameters;
-    type Fp12Params = Fq12Parameters;
-    type G1Parameters = g1::Parameters;
-    type G2Parameters = g2::Parameters;
+    type Fp2Config = Fq2Config;
+    type Fp6Config = Fq6Config;
+    type Fp12Config = Fq12Config;
+    type G1Config = g1::Config;
+    type G2Config = g2::Config;
 }
 
-pub type Bn254 = Bn<Parameters>;
+pub type Bn254 = Bn<Config>;
 
-pub type G1Affine = bn::G1Affine<Parameters>;
-pub type G1Projective = bn::G1Projective<Parameters>;
-pub type G2Affine = bn::G2Affine<Parameters>;
-pub type G2Projective = bn::G2Projective<Parameters>;
+pub type G1Affine = bn::G1Affine<Config>;
+pub type G1Projective = bn::G1Projective<Config>;
+pub type G2Affine = bn::G2Affine<Config>;
+pub type G2Projective = bn::G2Projective<Config>;

bn254/src/curves/tests.rs

@@ -1,85 +1,9 @@
-#![allow(unused_imports)]
-use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    fields::{Field, FpParameters, PrimeField, SquareRootField},
-    test_rng, One, Zero,
-};
-use ark_serialize::CanonicalSerialize;
-use core::ops::{AddAssign, MulAssign};
-use rand::Rng;
+use ark_algebra_test_templates::*;
+use ark_ff::fields::Field;
 
-use crate::{g1, g2, Bn254, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
+use crate::{Bn254, G1Projective, G2Projective};
 
-use ark_curve_tests::{curves::*, groups::*};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let mut sa = a;
-    sa.mul_assign(s);
-    let mut sb = b;
-    sb.mul_assign(s);
-
-    let ans1 = Bn254::pairing(sa, b);
-    let ans2 = Bn254::pairing(a, sb);
-    let ans3 = Bn254::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq12::one());
-    assert_ne!(ans2, Fq12::one());
-    assert_ne!(ans3, Fq12::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq12::one());
-}
+test_group!(g1; G1Projective; sw);
+test_group!(g2; G2Projective; sw);
+test_group!(pairing_output; ark_ec::pairing::PairingOutput<Bn254>; msm);
+test_pairing!(pairing; crate::Bn254);

bn254/src/fields/fq.rs

@@ -1,96 +1,7 @@
-use ark_ff::{biginteger::BigInteger256 as BigInteger, field_new, fields::*};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
 
-pub type Fq = Fp256<FqParameters>;
-
-pub struct FqParameters;
-
-impl Fp256Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 1;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        0x68c3488912edefaa,
-        0x8d087f6872aabf4f,
-        0x51e1a24709081231,
-        0x2259d6b14729c0fa,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0x3c208c16d87cfd47,
-        0x97816a916871ca8d,
-        0xb85045b68181585d,
-        0x30644e72e131a029,
-    ]);
-
-    const MODULUS_BITS: u32 = 254;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 2;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        0xd35d438dc58f0d9d,
-        0x0a78eb28f5c70b3d,
-        0x666ea36f7879462c,
-        0xe0a77c19a07df2f,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xf32cfc5b538afa89,
-        0xb5e71911d44501fb,
-        0x47ab1eff0a417ff6,
-        0x6d89f71cab8351f,
-    ]);
-
-    const INV: u64 = 9786893198990664585u64;
-
-    // GENERATOR = 3
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0x7a17caa950ad28d7,
-        0x1f6ac17ae15521b9,
-        0x334bea4e696bd284,
-        0x2a1f6744ce179d8e,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x9e10460b6c3e7ea3,
-        0xcbc0b548b438e546,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-
-    // T = (MODULUS - 1) // 2^S =
-    // 10944121435919637611123202872628637544348155578648911831344518947322613104291
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x9e10460b6c3e7ea3,
-        0xcbc0b548b438e546,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // (T - 1) // 2 =
-    // 1837921289030710838195067919506396475074392872918698035817074744121558668640693829665401097909504529
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x4f082305b61f3f51,
-        0x65e05aa45a1c72a3,
-        0x6e14116da0605617,
-        0xc19139cb84c680a,
-    ]);
-}
-
-pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
-pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger([0, 0, 0, 0]));
+#[derive(MontConfig)]
+#[modulus = "21888242871839275222246405745257275088696311157297823662689037894645226208583"]
+#[generator = "3"]
+pub struct FqConfig;
+pub type Fq = Fp256<MontBackend<FqConfig, 4>>;

bn254/src/fields/fq12.rs

@@ -1,159 +1,89 @@
-use super::*;
-use ark_ff::{biginteger::BigInteger256, field_new, fields::*};
+use ark_ff::{fields::*, MontFp};
 
-pub type Fq12 = Fp12<Fq12Parameters>;
+use crate::*;
+
+pub type Fq12 = Fp12<Fq12Config>;
 
 #[derive(Clone, Copy)]
-pub struct Fq12Parameters;
+pub struct Fq12Config;
 
-impl Fp12Parameters for Fq12Parameters {
-    type Fp6Params = Fq6Parameters;
+impl Fp12Config for Fq12Config {
+    type Fp6Config = Fq6Config;
 
-    const NONRESIDUE: Fq6 = field_new!(Fq6, FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        FQ2_ONE,
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0xaf9ba69633144907,
-                0xca6b1d7387afb78a,
-                0x11bded5ef08a2087,
-                0x02f34d751a1f3a7c,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0xa222ae234c492d72,
-                0xd00f02a4565de15b,
-                0xdc2ff3a253dfc926,
-                0x10a75716b3899551,
-            ])),
+        Fq2::new(
+            MontFp!("8376118865763821496583973867626364092589906065868298776909617916018768340080"),
+            MontFp!(
+                "16469823323077808223889137241176536799009286646108169935659301613961712198316"
+            ),
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0xca8d800500fa1bf2,
-                0xf0c5d61468b39769,
-                0x0e201271ad0d4418,
-                0x04290f65bad856e6,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!(
+                "21888242871839275220042445260109153167277707414472061641714758635765020556617"
+            ),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x365316184e46d97d,
-                0x0af7129ed4c96d9f,
-                0x659da72fca1009b5,
-                0x08116d8983a20d23,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0xb1df4af7c39c1939,
-                0x3d9f02878a73bf7f,
-                0x9b2220928caf0ae0,
-                0x26684515eff054a6,
-            ])),
+        Fq2::new(
+            MontFp!(
+                "11697423496358154304825782922584725312912383441159505038794027105778954184319"
+            ),
+            MontFp!("303847389135065887422783454877609941456349188919719272345083954437860409601"),
         ),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x3350c88e13e80b9c,
-                0x7dce557cdb5e56b9,
-                0x6001b4b8b615564a,
-                0x2682e617020217e0,
-        ])),
-        FQ_ZERO,
+        Fq2::new(
+            MontFp!(
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x86b76f821b329076,
-                0x408bf52b4d19b614,
-                0x53dfb9d0d985e92d,
-                0x051e20146982d2a7,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0x0fbc9cd47752ebc7,
-                0x6d8fffe33415de24,
-                0xbef22cf038cf41b9,
-                0x15c0edff3c66bf54,
-            ])),
+        Fq2::new(
+            MontFp!("3321304630594332808241809054958361220322477375291206261884409189760185844239"),
+            MontFp!("5722266937896532885780051958958348231143373700109372999374820235121374419868"),
         ),
         // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x68c3488912edefaa,
-                0x8d087f6872aabf4f,
-                0x51e1a24709081231,
-                0x2259d6b14729c0fa,
-            ])),
-            FQ_ZERO,
-        ),
+        Fq2::new(MontFp!("-1"), Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x8c84e580a568b440,
-                0xcd164d1de0c21302,
-                0xa692585790f737d5,
-                0x2d7100fdc71265ad,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0x99fdddf38c33cfd5,
-                0xc77267ed1213e931,
-                0xdc2052142da18f36,
-                0x1fbcf75c2da80ad7,
-            ])),
+        Fq2::new(
+            MontFp!(
+                "13512124006075453725662431877630910996106405091429524885779419978626457868503"
+            ),
+            MontFp!("5418419548761466998357268504080738289687024511189653727029736280683514010267"),
         ),
         // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x71930c11d782e155,
-                0xa6bb947cffbe3323,
-                0xaa303344d4741444,
-                0x2c3b3f0d26594943,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x05cd75fe8a3623ca,
-                0x8c8a57f293a85cee,
-                0x52b29e86b7714ea8,
-                0x2852e0e95d8f9306,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0x8a41411f14e0e40e,
-                0x59e26809ddfe0b0d,
-                0x1d2e2523f4d24d7d,
-                0x09fc095cf1414b83,
-            ])),
+        Fq2::new(
+            MontFp!(
+                "10190819375481120917420622822672549775783927716138318623895010788866272024264"
+            ),
+            MontFp!(
+                "21584395482704209334823622290379665147239961968378104390343953940207365798982"
+            ),
         ),
         // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x08cfc388c494f1ab,
-                0x19b315148d1373d4,
-                0x584e90fdcb6c0213,
-                0x09e1685bdf2f8849,
-            ])),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651967"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0xb5691c94bd4a6cd1,
-                0x56f575661b581478,
-                0x64708be5a7fb6f30,
-                0x2b462e5e77aecd82,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0x2c63ef42612a1180,
-                0x29f16aae345bec69,
-                0xf95e18c648b216a4,
-                0x1aa36073a4cae0d4,
-            ])),
+        Fq2::new(
+            MontFp!(
+                "18566938241244942414004596690298913868373833782006617400804628704885040364344"
+            ),
+            MontFp!(
+                "16165975933942742336466353786298926857552937457188450663314217659523851788715"
+            ),
         ),
     ];
 }

bn254/src/fields/fq2.rs

@@ -1,63 +1,27 @@
-use super::*;
-use ark_ff::{biginteger::BigInteger256 as BigInteger, field_new, fields::*};
+use ark_ff::{fields::*, MontFp};
 
-pub type Fq2 = Fp2<Fq2Parameters>;
+use crate::*;
 
-pub struct Fq2Parameters;
+pub type Fq2 = Fp2<Fq2Config>;
 
-impl Fp2Parameters for Fq2Parameters {
+pub struct Fq2Config;
+
+impl Fp2Config for Fq2Config {
     type Fp = Fq;
 
     /// NONRESIDUE = -1
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
-        0x68c3488912edefaa,
-        0x8d087f6872aabf4f,
-        0x51e1a24709081231,
-        0x2259d6b14729c0fa,
-    ]));
-
-    /// QUADRATIC_NONRESIDUE = U+2
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE: (Fq, Fq) = (
-        field_new!(Fq, BigInteger([
-            12014063508332092218u64,
-            1509222997478479483u64,
-            14762033076929465432u64,
-            2023505479389396574u64,
-        ])),
-        field_new!(Fq, BigInteger([
-            202099033278250856u64,
-            8885205928937022213u64,
-            5545221690922665192u64,
-            39800542322357402u64,
-        ])),
-    );
+    const NONRESIDUE: Fq = MontFp!("-1");
 
     /// Coefficients for the Frobenius automorphism.
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // NONRESIDUE**(((q^0) - 1) / 2)
-        field_new!(Fq, BigInteger([
-            0xd35d438dc58f0d9d,
-            0x0a78eb28f5c70b3d,
-            0x666ea36f7879462c,
-            0xe0a77c19a07df2f,
-        ])),
+        Fq::ONE,
         // NONRESIDUE**(((q^1) - 1) / 2)
-        field_new!(Fq, BigInteger([
-            0x68c3488912edefaa,
-            0x8d087f6872aabf4f,
-            0x51e1a24709081231,
-            0x2259d6b14729c0fa,
-        ])),
+        MontFp!("-1"),
     ];
 
     #[inline(always)]
-    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
-        -(*fe)
+    fn mul_fp_by_nonresidue_in_place(fe: &mut Self::Fp) -> &mut Self::Fp {
+        fe.neg_in_place()
     }
 }
-
-pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = field_new!(Fq2, FQ_ONE, FQ_ZERO);

bn254/src/fields/fq6.rs

@@ -1,195 +1,105 @@
-use super::*;
-use ark_ff::{biginteger::BigInteger256, field_new, fields::*};
+use ark_ff::{fields::*, MontFp};
 
-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::*;
+
+pub type Fq6 = Fp6<Fq6Config>;
 
 #[derive(Clone, Copy)]
-pub struct Fq6Parameters;
+pub struct Fq6Config;
 
-impl Fp6Parameters for Fq6Parameters {
-    type Fp2Params = Fq2Parameters;
+impl Fp6Config for Fq6Config {
+    type Fp2Config = Fq2Config;
 
     /// NONRESIDUE = U+9
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq2 = field_new!(Fq2,
-       field_new!(Fq, BigInteger256([
-            0xf60647ce410d7ff7,
-            0x2f3d6f4dd31bd011,
-            0x2943337e3940c6d1,
-            0x1d9598e8a7e39857,
-        ])),
-        field_new!(Fq, BigInteger256([
-            202099033278250856u64,
-            8885205928937022213u64,
-            5545221690922665192u64,
-            39800542322357402u64,
-        ])),
-    );
+    const NONRESIDUE: Fq2 = Fq2::new(MontFp!("9"), Fq::ONE);
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0xd35d438dc58f0d9d,
-                0x0a78eb28f5c70b3d,
-                0x666ea36f7879462c,
-                0xe0a77c19a07df2f,
-            ])),
-            field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0xb5773b104563ab30,
-                0x347f91c8a9aa6454,
-                0x7a007127242e0991,
-                0x1956bcd8118214ec,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0x6e849f1ea0aa4757,
-                0xaa1c7b6d89f89141,
-                0xb6e713cdfae0ca3a,
-                0x26694fbb4e82ebc3,
-            ])),
+        Fq2::new(
+            MontFp!(
+                "21575463638280843010398324269430826099269044274347216827212613867836435027261"
+            ),
+            MontFp!(
+                "10307601595873709700152284273816112264069230130616436755625194854815875713954"
+            ),
         ),
         // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x3350c88e13e80b9c,
-                0x7dce557cdb5e56b9,
-                0x6001b4b8b615564a,
-                0x2682e617020217e0,
-            ])),
-            field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!(
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0xc9af22f716ad6bad,
-                0xb311782a4aa662b2,
-                0x19eeaf64e248c7f4,
-                0x20273e77e3439f82,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0xacc02860f7ce93ac,
-                0x3933d5817ba76b4c,
-                0x69e6188b446c8467,
-                0xa46036d4417cc55,
-            ])),
+        Fq2::new(
+            MontFp!("3772000881919853776433695186713858239009073593817195771773381919316419345261"),
+            MontFp!("2236595495967245188281701248203181795121068902605861227855261137820944008926"),
         ),
         // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x71930c11d782e155,
-                0xa6bb947cffbe3323,
-                0xaa303344d4741444,
-                0x2c3b3f0d26594943,
-            ])),
-            field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0xf91aba2654e8e3b1,
-                0x4771cb2fdc92ce12,
-                0xdcb16ae0fc8bdf35,
-                0x274aa195cd9d8be4,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0x5cfc50ae18811f8b,
-                0x4bb28433cb43988c,
-                0x4fd35f13c3b56219,
-                0x301949bd2fc8883a,
-            ])),
+        Fq2::new(
+            MontFp!(
+                "18429021223477853657660792034369865839114504446431234726392080002137598044644"
+            ),
+            MontFp!("9344045779998320333812420223237981029506012124075525679208581902008406485703"),
         ),
     ];
-    #[rustfmt::skip]
+
     const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
         // Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0xd35d438dc58f0d9d,
-                0x0a78eb28f5c70b3d,
-                0x666ea36f7879462c,
-                0xe0a77c19a07df2f,
-            ])),
-            field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
         // Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x7361d77f843abe92,
-                0xa5bb2bd3273411fb,
-                0x9c941f314b3e2399,
-                0x15df9cddbb9fd3ec,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0x5dddfd154bd8c949,
-                0x62cb29a5a4445b60,
-                0x37bc870a0c7dd2b9,
-                0x24830a9d3171f0fd,
-            ])),
+        Fq2::new(
+            MontFp!("2581911344467009335267311115468803099551665605076196740867805258568234346338"),
+            MontFp!(
+                "19937756971775647987995932169929341994314640652964949448313374472400716661030"
+            ),
         ),
         // Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x71930c11d782e155,
-                0xa6bb947cffbe3323,
-                0xaa303344d4741444,
-                0x2c3b3f0d26594943,
-            ])),
-            field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x448a93a57b6762df,
-                0xbfd62df528fdeadf,
-                0xd858f5d00e9bd47a,
-                0x6b03d4d3476ec58,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0x2b19daf4bcc936d1,
-                0xa1a54e7a56f4299f,
-                0xb533eee05adeaef1,
-                0x170c812b84dda0b2,
-            ])),
+        Fq2::new(
+            MontFp!("5324479202449903542726783395506214481928257762400643279780343368557297135718"),
+            MontFp!(
+                "16208900380737693084919495127334387981393726419856888799917914180988844123039"
+            ),
         ),
         // Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x3350c88e13e80b9c,
-                0x7dce557cdb5e56b9,
-                0x6001b4b8b615564a,
-                0x2682e617020217e0,
-            ])),
-            field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
+        Fq2::new(
+            MontFp!(
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            Fq::ZERO,
         ),
         // Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, BigInteger256([
-                0x843420f1d8dadbd6,
-                0x31f010c9183fcdb2,
-                0x436330b527a76049,
-                0x13d47447f11adfe4,
-            ])),
-            field_new!(Fq, BigInteger256([
-                0xef494023a857fa74,
-                0x2a925d02d5ab101a,
-                0x83b015829ba62f10,
-                0x2539111d0c13aea3,
-            ])),
+        Fq2::new(
+            MontFp!(
+                "13981852324922362344252311234282257507216387789820983642040889267519694726527"
+            ),
+            MontFp!("7629828391165209371577384193250820201684255241773809077146787135900891633097"),
         ),
     ];
 
     #[inline(always)]
-    fn mul_fp2_by_nonresidue(fe: &Fq2) -> Fq2 {
+    fn mul_fp2_by_nonresidue_in_place(fe: &mut Fq2) -> &mut Fq2 {
         // (c0+u*c1)*(9+u) = (9*c0-c1)+u*(9*c1+c0)
         let mut f = *fe;
         f.double_in_place().double_in_place().double_in_place();
-        let c0 = f.c0 + fe.c0 + Fq2Parameters::mul_fp_by_nonresidue(&fe.c1);
+        let mut c0 = fe.c1;
+        Fq2Config::mul_fp_by_nonresidue_in_place(&mut c0);
+        c0 += &f.c0;
+        c0 += &fe.c0;
         let c1 = f.c1 + fe.c1 + fe.c0;
-        field_new!(Fq2, c0, c1)
+        *fe = Fq2::new(c0, c1);
+        fe
     }
 }

bn254/src/fields/fr.rs

@@ -1,95 +1,7 @@
-use ark_ff::{biginteger::BigInteger256 as BigInteger, fields::*};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
 
-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 28;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        7164790868263648668u64,
-        11685701338293206998u64,
-        6216421865291908056u64,
-        1756667274303109607u64,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// MODULUS = 21888242871839275222246405745257275088548364400416034343698204186575808495617
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        4891460686036598785u64,
-        2896914383306846353u64,
-        13281191951274694749u64,
-        3486998266802970665u64,
-    ]);
-
-    const MODULUS_BITS: u32 = 254;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 2;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        12436184717236109307u64,
-        3962172157175319849u64,
-        7381016538464732718u64,
-        1011752739694698287u64,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        1997599621687373223u64,
-        6052339484930628067u64,
-        10108755138030829701u64,
-        150537098327114917u64,
-    ]);
-
-    const INV: u64 = 14042775128853446655u64;
-
-    // GENERATOR = 5
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        1949230679015292902u64,
-        16913946402569752895u64,
-        5177146667339417225u64,
-        1571765431670520771u64,
-    ]);
-
-    /// (r - 1)/2 =
-    /// 10944121435919637611123202872628637544274182200208017171849102093287904247808
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xa1f0fac9f8000000,
-        0x9419f4243cdcb848,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where r - 1 = 2^s * t
-
-    /// t = (r - 1) / 2^s =
-    /// 81540058820840996586704275553141814055101440848469862132140264610111
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x9b9709143e1f593f,
-        0x181585d2833e8487,
-        0x131a029b85045b68,
-        0x30644e72e,
-    ]);
-
-    /// (t - 1) / 2 =
-    /// 40770029410420498293352137776570907027550720424234931066070132305055
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xcdcb848a1f0fac9f,
-        0x0c0ac2e9419f4243,
-        0x098d014dc2822db4,
-        0x183227397,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "21888242871839275222246405745257275088548364400416034343698204186575808495617"]
+#[generator = "5"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;

bn254/src/fields/tests.rs

@@ -1,123 +1,51 @@
+use ark_algebra_test_templates::*;
 use ark_ff::{
-    biginteger::{BigInteger, BigInteger256},
-    fields::{
-        fp6_3over2::Fp6Parameters, FftField, FftParameters, Field, FpParameters, PrimeField,
-        SquareRootField,
-    },
-    test_rng, One, UniformRand, Zero,
+    biginteger::{BigInt, BigInteger, BigInteger256},
+    fields::{FftField, Field, Fp6Config, PrimeField},
+    One, UniformRand, Zero,
 };
-use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
-use core::{
+use ark_std::{
     cmp::Ordering,
-    ops::{AddAssign, MulAssign, SubAssign},
+    ops::{AddAssign, MulAssign},
 };
-use rand::{Rng, SeedableRng};
-use rand_xorshift::XorShiftRng;
 
-use crate::{Fq, Fq12, Fq2, Fq6, Fq6Parameters, FqParameters, Fr};
-use ark_curve_tests::fields::*;
+use crate::{Fq, Fq12, Fq2, Fq6, Fq6Config, Fr};
 
-pub(crate) const ITERATIONS: usize = 5;
-
-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fr = rng.gen();
-        let b: Fr = rng.gen();
-        field_test(a, b);
-        primefield_test::<Fr>();
-        sqrt_field_test(b);
-        let byte_size = a.serialized_size();
-        field_serialization_test::<Fr>(byte_size);
-    }
-}
-
-#[test]
-fn test_fq() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fq = rng.gen();
-        let b: Fq = rng.gen();
-        field_test(a, b);
-        primefield_test::<Fq>();
-        sqrt_field_test(a);
-        let byte_size = a.serialized_size();
-        let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
-        assert_eq!(byte_size, buffer_size);
-        field_serialization_test::<Fq>(byte_size);
-    }
-}
-
-#[test]
-fn test_fq2() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fq2 = rng.gen();
-        let b: Fq2 = rng.gen();
-        field_test(a, b);
-        sqrt_field_test(a);
-    }
-    frobenius_test::<Fq2, _>(Fq::characteristic(), 13);
-    let byte_size = Fq2::zero().serialized_size();
-    field_serialization_test::<Fq2>(byte_size);
-}
-
-#[test]
-fn test_fq6() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let g: Fq6 = rng.gen();
-        let h: Fq6 = rng.gen();
-        field_test(g, h);
-    }
-    frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
-    let byte_size = Fq6::zero().serialized_size();
-    field_serialization_test::<Fq6>(byte_size);
-}
-
-#[test]
-fn test_fq12() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let g: Fq12 = rng.gen();
-        let h: Fq12 = rng.gen();
-        field_test(g, h);
-    }
-    frobenius_test::<Fq12, _>(Fq::characteristic(), 13);
-    let byte_size = Fq12::zero().serialized_size();
-    field_serialization_test::<Fq12>(byte_size);
-}
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
+test_field!(fq2; Fq2);
+test_field!(fq6; Fq6);
+test_field!(fq12; Fq12);
 
 #[test]
 fn test_fq_repr_from() {
-    assert_eq!(BigInteger256::from(100), BigInteger256([100, 0, 0, 0]));
+    assert_eq!(BigInteger256::from(100u64), BigInt::new([100, 0, 0, 0]));
 }
 
 #[test]
 fn test_fq_repr_is_odd() {
-    assert!(!BigInteger256::from(0).is_odd());
-    assert!(BigInteger256::from(0).is_even());
-    assert!(BigInteger256::from(1).is_odd());
-    assert!(!BigInteger256::from(1).is_even());
-    assert!(!BigInteger256::from(324834872).is_odd());
-    assert!(BigInteger256::from(324834872).is_even());
-    assert!(BigInteger256::from(324834873).is_odd());
-    assert!(!BigInteger256::from(324834873).is_even());
+    assert!(!BigInteger256::from(0u64).is_odd());
+    assert!(BigInteger256::from(0u64).is_even());
+    assert!(BigInteger256::from(1u64).is_odd());
+    assert!(!BigInteger256::from(1u64).is_even());
+    assert!(!BigInteger256::from(324834872u64).is_odd());
+    assert!(BigInteger256::from(324834872u64).is_even());
+    assert!(BigInteger256::from(324834873u64).is_odd());
+    assert!(!BigInteger256::from(324834873u64).is_even());
 }
 
 #[test]
 fn test_fq_repr_is_zero() {
-    assert!(BigInteger256::from(0).is_zero());
-    assert!(!BigInteger256::from(1).is_zero());
-    assert!(!BigInteger256([0, 0, 1, 0]).is_zero());
+    assert!(BigInteger256::from(0u64).is_zero());
+    assert!(!BigInteger256::from(1u64).is_zero());
+    assert!(!BigInt::new([0, 0, 1, 0]).is_zero());
 }
 
 #[test]
 fn test_fq_repr_num_bits() {
-    let mut a = BigInteger256::from(0);
+    let mut a = BigInteger256::from(0u64);
     assert_eq!(0, a.num_bits());
-    a = BigInteger256::from(1);
+    a = BigInteger256::from(1u64);
     for i in 1..257 {
         assert_eq!(i, a.num_bits());
         a.mul2();
@@ -125,248 +53,35 @@ fn test_fq_repr_num_bits() {
     assert_eq!(0, a.num_bits());
 }
 
-#[test]
-fn test_fq_add_assign() {
-    // Test associativity
-
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000 {
-        // Generate a, b, c and ensure (a + b) + c == a + (b + c).
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-        let c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.add_assign(&b);
-        tmp1.add_assign(&c);
-
-        let mut tmp2 = b;
-        tmp2.add_assign(&c);
-        tmp2.add_assign(&a);
-
-        assert_eq!(tmp1, tmp2);
-    }
-}
-
-#[test]
-fn test_fq_sub_assign() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000 {
-        // Ensure that (a - b) + (b - a) = 0.
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.sub_assign(&b);
-
-        let mut tmp2 = b;
-        tmp2.sub_assign(&a);
-
-        tmp1.add_assign(&tmp2);
-        assert!(tmp1.is_zero());
-    }
-}
-
-#[test]
-fn test_fq_mul_assign() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000000 {
-        // Ensure that (a * b) * c = a * (b * c)
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-        let c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.mul_assign(&b);
-        tmp1.mul_assign(&c);
-
-        let mut tmp2 = b;
-        tmp2.mul_assign(&c);
-        tmp2.mul_assign(&a);
-
-        assert_eq!(tmp1, tmp2);
-    }
-
-    for _ in 0..1000000 {
-        // Ensure that r * (a + b + c) = r*a + r*b + r*c
-
-        let r = Fq::rand(&mut rng);
-        let mut a = Fq::rand(&mut rng);
-        let mut b = Fq::rand(&mut rng);
-        let mut c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.add_assign(&b);
-        tmp1.add_assign(&c);
-        tmp1.mul_assign(&r);
-
-        a.mul_assign(&r);
-        b.mul_assign(&r);
-        c.mul_assign(&r);
-
-        a.add_assign(&b);
-        a.add_assign(&c);
-
-        assert_eq!(tmp1, a);
-    }
-}
-
-#[test]
-fn test_fq_squaring() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000000 {
-        // Ensure that (a * a) = a^2
-        let a = Fq::rand(&mut rng);
-
-        let mut tmp = a;
-        tmp.square_in_place();
-
-        let mut tmp2 = a;
-        tmp2.mul_assign(&a);
-
-        assert_eq!(tmp, tmp2);
-    }
-}
-
-#[test]
-fn test_fq_inverse() {
-    assert!(Fq::zero().inverse().is_none());
-
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    let one = Fq::one();
-
-    for _ in 0..1000 {
-        // Ensure that a * a^-1 = 1
-        let mut a = Fq::rand(&mut rng);
-        let ainv = a.inverse().unwrap();
-        a.mul_assign(&ainv);
-        assert_eq!(a, one);
-    }
-}
-
-#[test]
-fn test_fq_double_in_place() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000 {
-        // Ensure doubling a is equivalent to adding a to itself.
-        let mut a = Fq::rand(&mut rng);
-        let mut b = a;
-        b.add_assign(&a);
-        a.double_in_place();
-        assert_eq!(a, b);
-    }
-}
-
-#[test]
-fn test_fq_negate() {
-    {
-        let a = -Fq::zero();
-
-        assert!(a.is_zero());
-    }
-
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for _ in 0..1000 {
-        // Ensure (a - (-a)) = 0.
-        let mut a = Fq::rand(&mut rng);
-        let b = -a;
-        a.add_assign(&b);
-
-        assert!(a.is_zero());
-    }
-}
-
-#[test]
-fn test_fq_pow() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    for i in 0..1000 {
-        // Exponentiate by various small numbers and ensure it consists with repeated
-        // multiplication.
-        let a = Fq::rand(&mut rng);
-        let target = a.pow(&[i]);
-        let mut c = Fq::one();
-        for _ in 0..i {
-            c.mul_assign(&a);
-        }
-        assert_eq!(c, target);
-    }
-
-    for _ in 0..1000 {
-        // Exponentiating by the modulus should have no effect in a prime field.
-        let a = Fq::rand(&mut rng);
-
-        assert_eq!(a, a.pow(Fq::characteristic()));
-    }
-}
-
-#[test]
-fn test_fq_sqrt() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
-
-    assert_eq!(Fq::zero().sqrt().unwrap(), Fq::zero());
-
-    for _ in 0..1000 {
-        // Ensure sqrt(a^2) = a or -a
-        let a = Fq::rand(&mut rng);
-        let nega = -a;
-        let mut b = a;
-        b.square_in_place();
-
-        let b = b.sqrt().unwrap();
-
-        assert!(a == b || nega == b);
-    }
-
-    for _ in 0..1000 {
-        // Ensure sqrt(a)^2 = a for random a
-        let a = Fq::rand(&mut rng);
-
-        if let Some(mut tmp) = a.sqrt() {
-            tmp.square_in_place();
-
-            assert_eq!(a, tmp);
-        }
-    }
-}
-
 #[test]
 fn test_fq_num_bits() {
-    assert_eq!(FqParameters::MODULUS_BITS, 254);
-    assert_eq!(FqParameters::CAPACITY, 253);
+    assert_eq!(Fq::MODULUS_BIT_SIZE, 254);
 }
 
 #[test]
 fn test_fq_root_of_unity() {
-    assert_eq!(FqParameters::TWO_ADICITY, 1);
+    assert_eq!(Fq::TWO_ADICITY, 1);
     assert_eq!(
-        Fq::multiplicative_generator().pow([
+        Fq::GENERATOR.pow([
             0x9e10460b6c3e7ea3,
             0xcbc0b548b438e546,
             0xdc2822db40c0ac2e,
             0x183227397098d014,
         ]),
-        Fq::two_adic_root_of_unity()
+        Fq::TWO_ADIC_ROOT_OF_UNITY
     );
     assert_eq!(
-        Fq::two_adic_root_of_unity().pow([1 << FqParameters::TWO_ADICITY]),
+        Fq::TWO_ADIC_ROOT_OF_UNITY.pow([1 << Fq::TWO_ADICITY]),
         Fq::one()
     );
-    assert!(Fq::multiplicative_generator().sqrt().is_none());
+    assert!(Fq::GENERATOR.sqrt().is_none());
 }
 
 #[test]
 fn test_fq_ordering() {
     // BigInteger256's ordering is well-tested, but we still need to make sure the
     // Fq elements aren't being compared in Montgomery form.
-    for i in 0..100 {
+    for i in 0..100u64 {
         assert!(Fq::from(BigInteger256::from(i + 1)) > Fq::from(BigInteger256::from(i)));
     }
 }
@@ -379,11 +94,11 @@ fn test_fq_legendre() {
     assert_eq!(Zero, Fq::zero().legendre());
     assert_eq!(
         QuadraticResidue,
-        Fq::from(BigInteger256::from(4)).legendre()
+        Fq::from(BigInteger256::from(4u64)).legendre()
     );
     assert_eq!(
         QuadraticNonResidue,
-        Fq::from(BigInteger256::from(5)).legendre()
+        Fq::from(BigInteger256::from(5u64)).legendre()
     );
 }
 
@@ -424,13 +139,13 @@ fn test_fq2_legendre() {
     // i^2 = -1
     let mut m1 = -Fq2::one();
     assert_eq!(QuadraticResidue, m1.legendre());
-    m1 = Fq6Parameters::mul_fp2_by_nonresidue(&m1);
+    Fq6Config::mul_fp2_by_nonresidue_in_place(&mut m1);
     assert_eq!(QuadraticNonResidue, m1.legendre());
 }
 
 #[test]
 fn test_fq6_mul_by_1() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+    let mut rng = ark_std::test_rng();
 
     for _ in 0..1000 {
         let c1 = Fq2::rand(&mut rng);
@@ -446,7 +161,7 @@ fn test_fq6_mul_by_1() {
 
 #[test]
 fn test_fq6_mul_by_01() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+    let mut rng = ark_std::test_rng();
 
     for _ in 0..1000 {
         let c0 = Fq2::rand(&mut rng);
@@ -463,7 +178,7 @@ fn test_fq6_mul_by_01() {
 
 #[test]
 fn test_fq12_mul_by_014() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+    let mut rng = ark_std::test_rng();
 
     for _ in 0..1000 {
         let c0 = Fq2::rand(&mut rng);
@@ -484,7 +199,7 @@ fn test_fq12_mul_by_014() {
 
 #[test]
 fn test_fq12_mul_by_034() {
-    let mut rng = XorShiftRng::seed_from_u64(1231275789u64);
+    let mut rng = ark_std::test_rng();
 
     for _ in 0..1000 {
         let c0 = Fq2::rand(&mut rng);

bn254/src/lib.rs

@@ -8,7 +8,7 @@
 )]
 #![forbid(unsafe_code)]
 
-//! This library implements the BN254 curve that was sampled as part of the [[BCTV14]][https://eprint.iacr.org/2013/879.pdf] paper .
+//! This library implements the BN254 curve that was sampled as part of the [\[BCTV14\]](https://eprint.iacr.org/2013/879.pdf) paper .
 //! The name denotes that it is a Barreto--Naehrig curve of embedding degree 12,
 //! defined over a 254-bit (prime) field. The scalar field is highly 2-adic.
 //!
@@ -20,14 +20,17 @@
 //!
 //!
 //! Curve information:
-//! * Base field: q = 21888242871839275222246405745257275088696311157297823662689037894645226208583
-//! * Scalar field: r = 21888242871839275222246405745257275088548364400416034343698204186575808495617
+//! * Base field: q =
+//!   21888242871839275222246405745257275088696311157297823662689037894645226208583
+//! * Scalar field: r =
+//!   21888242871839275222246405745257275088548364400416034343698204186575808495617
 //! * valuation(q - 1, 2) = 1
 //! * valuation(r - 1, 2) = 28
 //! * G1 curve equation: y^2 = x^3 + 3
 //! * G2 curve equation: y^2 = x^3 + B, where
-//!    * B = 3/(u+9) where Fq2[u]=Fq/u+1
-//!        = Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
+//!    * B = 3/(u+9) where Fq2 is represented as Fq\[u\]/(u^2+1) =
+//!      Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373,
+//!      266929791119991161246907387137283842545076965332900288569378510910307636690)
 
 #[cfg(feature = "curve")]
 mod curves;
@@ -38,3 +41,6 @@ mod fields;
 pub use curves::*;
 
 pub use fields::*;
+
+#[cfg(feature = "r1cs")]
+pub mod constraints;

bw6_761/Cargo.toml

@@ -1,29 +1,33 @@
 [package]
 name = "ark-bw6-761"
-version = "0.1.0"
+version = "0.4.0-alpha.2"
 authors = [ "arkworks contributors" ]
 description = "The BW6-761 pairing-friendly elliptic curve"
-homepage = "https://arworks.rs"
-repository = "https://github.com/arkworks/algebra"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
 documentation = "https://docs.rs/ark-bw6-761/"
-keywords = ["cryptography", "finite fields", "elliptic curves" ]
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"
 
 [dependencies]
-ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
-ark-bls12-377 = { path = "../bls12_377", default-features = false, features = [ "base_field" ] }
+ark-ff = { version="0.4.0-alpha", default-features = false }
+ark-ec = { version="0.4.0-alpha", default-features = false }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+ark-bls12-377 = { version = "0.4.0-alpha", path = "../bls12_377", default-features = false, features = [ "base_field" ] }
 
 [dev-dependencies]
-ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-curve-tests = { path = "../curve-tests", default-features = false }
-rand = { version = "0.7", default-features = false }
-rand_xorshift = "0.2"
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }
 
 [features]
 default = []
 std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-bls12-377/std" ]
+
+[[bench]]
+name = "bw6_761"
+path = "benches/bw6_761.rs"
+harness = false

bw6_761/benches/bw6_761.rs

@@ -0,0 +1,16 @@
+use ark_algebra_bench_templates::*;
+
+use ark_bw6_761::{
+    fq::Fq, fq3::Fq3, fq6::Fq6, fr::Fr, g1::G1Projective as G1, g2::G2Projective as G2, BW6_761,
+};
+
+bench!(
+    Name = "BW6_761",
+    Pairing = BW6_761,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq3,
+    TargetField = Fq6,
+);

bw6_761/scripts/base_field.sage

@@ -0,0 +1,28 @@
+modulus = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

bw6_761/scripts/scalar_field.sage

@@ -0,0 +1,28 @@
+modulus = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

bw6_761/src/curves/g1.rs

@@ -1,46 +1,20 @@
-use crate::{Fq, Fr};
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
-};
-use ark_ff::{
-    biginteger::{BigInteger384, BigInteger768},
-    field_new,
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
 };
+use ark_ff::{Field, MontFp};
 
-pub type G1Affine = GroupAffine<Parameters>;
-pub type G1Projective = GroupProjective<Parameters>;
+use crate::{Fq, Fr};
+
+pub type G1Affine = Affine<Config>;
+pub type G1Projective = Projective<Config>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Config {
     type BaseField = Fq;
     type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    #[rustfmt::skip]
-
-    const COEFF_A: Fq = field_new!(Fq, BigInteger768([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
-
-    /// COEFF_B = -1
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, BigInteger768([
-        0xf29a000000007ab6,
-        0x8c391832e000739b,
-        0x77738a6b6870f959,
-        0xbe36179047832b03,
-        0x84f3089e56574722,
-        0xc5a3614ac0b1d984,
-        0x5c81153f4906e9fe,
-        0x4d28be3a9f55c815,
-        0xd72c1d6f77d5f5c5,
-        0x73a18e069ac04458,
-        0xf9dfaa846595555f,
-        0xd0f0a60a5be58c,
-    ]));
 
     /// COFACTOR =
     /// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194876
@@ -56,21 +30,20 @@ impl SWModelParameters for Parameters {
 
     /// COFACTOR^(-1) mod r =
     /// 91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger384([
-        489703175600125849,
-        3883341943836920852,
-        1678256062427438196,
-        5848789333018172718,
-        7127967896440782320,
-        71512347676739162,
-    ]));
+    const COFACTOR_INV: Fr = MontFp!("91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = -1
+    const COEFF_B: Fq = MontFp!("-1");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
     #[inline(always)]
-    fn mul_by_a(_elem: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_elem: Self::BaseField) -> Self::BaseField {
         use ark_ff::Zero;
         Self::BaseField::zero()
     }
@@ -78,36 +51,8 @@ impl SWModelParameters for Parameters {
 
 /// G1_GENERATOR_X =
 /// 6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
-    0xd6e42d7614c2d770,
-    0x4bb886eddbc3fc21,
-    0x64648b044098b4d2,
-    0x1a585c895a422985,
-    0xf1a9ac17cf8685c9,
-    0x352785830727aea5,
-    0xddf8cb12306266fe,
-    0x6913b4bfbc9e949a,
-    0x3a4b78d67ba5f6ab,
-    0x0f481c06a8d02a04,
-    0x91d4e7365c43edac,
-    0xf4d17cd48beca5,
-]));
+pub const G1_GENERATOR_X: Fq = MontFp!("6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237");
 
 /// G1_GENERATOR_Y =
 /// 2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
-    0x97e805c4bd16411f,
-    0x870d844e1ee6dd08,
-    0x1eba7a37cb9eab4d,
-    0xd544c4df10b9889a,
-    0x8fe37f21a33897be,
-    0xe9bf99a43a0885d2,
-    0xd7ee0c9e273de139,
-    0xaa6a9ec7a38dd791,
-    0x8f95d3fcf765da8e,
-    0x42326e7db7357c99,
-    0xe217e407e218695f,
-    0x9d1eb23b7cf684,
-]));
+pub const G1_GENERATOR_Y: Fq = MontFp!("2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099");

bw6_761/src/curves/g2.rs

@@ -1,46 +1,20 @@
-use crate::{Fq, Fr};
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
-};
-use ark_ff::{
-    biginteger::{BigInteger384, BigInteger768},
-    field_new,
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
 };
+use ark_ff::{Field, MontFp};
 
-pub type G2Affine = GroupAffine<Parameters>;
-pub type G2Projective = GroupProjective<Parameters>;
+use crate::{Fq, Fr};
+
+pub type G2Affine = Affine<Config>;
+pub type G2Projective = Projective<Config>;
 
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl ModelParameters for Parameters {
+impl CurveConfig for Config {
     type BaseField = Fq;
     type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    #[rustfmt::skip]
-
-    const COEFF_A: Fq = field_new!(Fq, BigInteger768([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
-
-    /// COEFF_B = 4
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, BigInteger768([
-        0x136efffffffe16c9,
-        0x82cf5a6dcffe3319,
-        0x6458c05f1f0e0741,
-        0xd10ae605e52a4eda,
-        0x41ca591c0266e100,
-        0x7d0fd59c3626929f,
-        0x9967dc004d00c112,
-        0x1ccff9c033379af5,
-        0x9ad6ec10a23f63af,
-        0x5cec11251a72c235,
-        0x8d18b1ae789ba83e,
-        10403402007434220,
-    ]));
 
     /// COFACTOR =
     /// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194869
@@ -56,21 +30,21 @@ impl SWModelParameters for Parameters {
 
     /// COFACTOR^(-1) mod r =
     /// 214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger384([
-        14378295991815829998,
-        14586153992421458638,
-        9788477762582722914,
-        12654821707953664524,
-        15185631607604703397,
-        26723985783783076,
-    ]));
+    const COFACTOR_INV: Fr = MontFp!("214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 4
+    const COEFF_B: Fq = MontFp!("4");
 
     /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
+
     #[inline(always)]
-    fn mul_by_a(_elem: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_elem: Self::BaseField) -> Self::BaseField {
         use ark_ff::Zero;
         Self::BaseField::zero()
     }
@@ -78,36 +52,8 @@ impl SWModelParameters for Parameters {
 
 /// G2_GENERATOR_X =
 ///  6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428
-#[rustfmt::skip]
-pub const G2_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
-    0x3d902a84cd9f4f78,
-    0x864e451b8a9c05dd,
-    0xc2b3c0d6646c5673,
-    0x17a7682def1ecb9d,
-    0xbe31a1e0fb768fe3,
-    0x4df125e09b92d1a6,
-    0x0943fce635b02ee9,
-    0xffc8e7ad0605e780,
-    0x8165c00a39341e95,
-    0x8ccc2ae90a0f094f,
-    0x73a8b8cc0ad09e0c,
-    0x11027e203edd9f4,
-]));
+pub const G2_GENERATOR_X: Fq = MontFp!("6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428");
 
 /// G2_GENERATOR_Y =
 /// 562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
-    0x9a159be4e773f67c,
-    0x6b957244aa8f4e6b,
-    0xa27b70c9c945a38c,
-    0xacb6a09fda11d0ab,
-    0x3abbdaa9bb6b1291,
-    0xdbdf642af5694c36,
-    0xb6360bb9560b369f,
-    0xac0bd1e822b8d6da,
-    0xfa355d17afe6945f,
-    0x8d6a0fc1fbcad35e,
-    0x72a63c7874409840,
-    0x114976e5b0db280,
-]));
+pub const G2_GENERATOR_Y: Fq = MontFp!("562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041");

bw6_761/src/curves/mod.rs

@@ -1,9 +1,10 @@
-use crate::*;
 use ark_ec::{
     bw6,
-    bw6::{BW6Parameters, TwistType, BW6},
+    bw6::{BW6Config, TwistType, BW6},
 };
-use ark_ff::biginteger::BigInteger768 as BigInteger;
+use ark_ff::{biginteger::BigInteger768 as BigInteger, BigInt};
+
+use crate::*;
 
 pub mod g1;
 pub mod g2;
@@ -12,10 +13,10 @@ pub mod g2;
 mod tests;
 
 #[derive(PartialEq, Eq)]
-pub struct Parameters;
+pub struct Config;
 
-impl BW6Parameters for Parameters {
-    const X: BigInteger = BigInteger([
+impl BW6Config for Config {
+    const X: BigInteger = BigInt::new([
         0x8508c00000000001,
         0x0,
         0x0,
@@ -47,15 +48,15 @@ impl BW6Parameters for Parameters {
     const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool = false;
     const TWIST_TYPE: TwistType = TwistType::M;
     type Fp = Fq;
-    type Fp3Params = Fq3Parameters;
-    type Fp6Params = Fq6Parameters;
-    type G1Parameters = g1::Parameters;
-    type G2Parameters = g2::Parameters;
+    type Fp3Config = Fq3Config;
+    type Fp6Config = Fq6Config;
+    type G1Config = g1::Config;
+    type G2Config = g2::Config;
 }
 
-pub type BW6_761 = BW6<Parameters>;
+pub type BW6_761 = BW6<Config>;
 
-pub type G1Affine = bw6::G1Affine<Parameters>;
-pub type G1Projective = bw6::G1Projective<Parameters>;
-pub type G2Affine = bw6::G2Affine<Parameters>;
-pub type G2Projective = bw6::G2Projective<Parameters>;
+pub type G1Affine = bw6::G1Affine<Config>;
+pub type G1Projective = bw6::G1Projective<Config>;
+pub type G2Affine = bw6::G2Affine<Config>;
+pub type G2Projective = bw6::G2Projective<Config>;

bw6_761/src/curves/tests.rs

@@ -1,77 +1,8 @@
-use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
-use ark_ff::{test_rng, Field, One, PrimeField};
-use rand::Rng;
-
 use crate::*;
+use ark_algebra_test_templates::*;
+use ark_ff::Field;
 
-use ark_curve_tests::{curves::*, groups::*};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let sa = a.mul(s);
-    let sb = b.mul(s);
-
-    let ans1 = BW6_761::pairing(sa, b);
-    let ans2 = BW6_761::pairing(a, sb);
-    let ans3 = BW6_761::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq6::one());
-    assert_ne!(ans2, Fq6::one());
-    assert_ne!(ans3, Fq6::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq6::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq6::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq6::one());
-}
+test_group!(g1; G1Projective; sw);
+test_group!(g2; G2Projective; sw);
+test_group!(pairing_output; ark_ec::pairing::PairingOutput<BW6_761>; msm);
+test_pairing!(pairing; crate::BW6_761);

bw6_761/src/fields/fq.rs

@@ -1,175 +1,7 @@
-use ark_ff::{
-    biginteger::BigInteger768 as BigInteger,
-    field_new,
-    fields::{FftParameters, Fp768, Fp768Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp768, MontBackend, MontConfig};
 
-pub type Fq = Fp768<FqParameters>;
-
-pub struct FqParameters;
-
-pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
-pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
-
-impl Fp768Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    // The internal representation of this type is six 64-bit unsigned
-    // integers in little-endian order. Values are always in
-    // Montgomery form; i.e., Scalar(a) = aR mod p, with R=2^768.
-
-    // (MODULUS - 1) % 2^TWO_ADICITY == 0
-    const TWO_ADICITY: u32 = 1;
-
-    // least_quadratic_nonresidue(MODULUS) in Sage.
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        17481284903592032950u64,
-        10104133845767975835u64,
-        8607375506753517913u64,
-        13706168424391191299u64,
-        9580010308493592354u64,
-        14241333420363995524u64,
-        6665632285037357566u64,
-        5559902898979457045u64,
-        15504799981718861253u64,
-        8332096944629367896u64,
-        18005297320867222879u64,
-        58811391084848524u64,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-       0xf49d00000000008b,
-       0xe6913e6870000082,
-       0x160cf8aeeaf0a437,
-       0x98a116c25667a8f8,
-       0x71dcd3dc73ebff2e,
-       0x8689c8ed12f9fd90,
-       0x03cebaff25b42304,
-       0x707ba638e584e919,
-       0x528275ef8087be41,
-       0xb926186a81d14688,
-       0xd187c94004faff3e,
-       0x122e824fb83ce0a
-    ]);
-
-    const MODULUS_BITS: u32 = 761;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    // gap to 64-bit machine word
-    const REPR_SHAVE_BITS: u32 = 7;
-
-    // 2^768 % MODULUS
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        144959613005956565u64,
-        6509995272855063783u64,
-        11428286765660613342u64,
-        15738672438262922740u64,
-        17071399330169272331u64,
-        13899911246788437003u64,
-        12055474021000362245u64,
-        2545351818702954755u64,
-        8887388221587179644u64,
-        5009280847225881135u64,
-        15539704305423854047u64,
-        23071597697427581u64,
-    ]);
-
-    // R^2
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        14305184132582319705u64,
-        8868935336694416555u64,
-        9196887162930508889u64,
-        15486798265448570248u64,
-        5402985275949444416u64,
-        10893197322525159598u64,
-        3204916688966998390u64,
-        12417238192559061753u64,
-        12426306557607898622u64,
-        1305582522441154384u64,
-        10311846026977660324u64,
-        48736111365249031u64,
-    ]);
-
-    // (-1/MODULUS) % 2^64
-    const INV: u64 = 744663313386281181u64;
-
-    /// GENERATOR = 2
-    // primitive_root(MODULUS)
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        289919226011913130u64,
-        13019990545710127566u64,
-        4409829457611675068u64,
-        13030600802816293865u64,
-        15696054586628993047u64,
-        9353078419867322391u64,
-        5664203968291172875u64,
-        5090703637405909511u64,
-        17774776443174359288u64,
-        10018561694451762270u64,
-        12632664537138156478u64,
-        46143195394855163u64,
-    ]);
-
-    // (MODULUS - 1) / 2
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x7a4e800000000045,
-        0xf3489f3438000041,
-        0x0b067c577578521b,
-        0x4c508b612b33d47c,
-        0x38ee69ee39f5ff97,
-        0x4344e476897cfec8,
-        0x81e75d7f92da1182,
-        0xb83dd31c72c2748c,
-        0x29413af7c043df20,
-        0x5c930c3540e8a344,
-        0x68c3e4a0027d7f9f,
-        0x9174127dc1e705,
-    ]);
-
-    // T =
-    // 3445725192157866269698394841137828771239834456268075054756895080104811711121745868043841591644705843820432283876893306725580879560277123879674755849562650799475802549689254425186271815711798397975949850214984556421382456559534149
-    // (MODULUS - 1) / 2 ^ TWO_ADICITY
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x7a4e800000000045,
-        0xf3489f3438000041,
-        0x0b067c577578521b,
-        0x4c508b612b33d47c,
-        0x38ee69ee39f5ff97,
-        0x4344e476897cfec8,
-        0x81e75d7f92da1182,
-        0xb83dd31c72c2748c,
-        0x29413af7c043df20,
-        0x5c930c3540e8a344,
-        0x68c3e4a0027d7f9f,
-        0x9174127dc1e705,
-    ]);
-
-    // (T - 1)/2 =
-    // 1722862596078933134849197420568914385619917228134037527378447540052405855560872934021920795822352921910216141938446653362790439780138561939837377924781325399737901274844627212593135907855899198987974925107492278210691228279767074
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xbd27400000000022,
-        0xf9a44f9a1c000020,
-        0x05833e2bbabc290d,
-        0xa62845b09599ea3e,
-        0x1c7734f71cfaffcb,
-        0x21a2723b44be7f64,
-        0x40f3aebfc96d08c1,
-        0x5c1ee98e39613a46,
-        0x14a09d7be021ef90,
-        0xae49861aa07451a2,
-        0xb461f250013ebfcf,
-        0x48ba093ee0f382,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299"]
+#[generator = "2"]
+pub struct FqConfig;
+pub type Fq = Fp768<MontBackend<FqConfig, 12>>;

bw6_761/src/fields/fq3.rs

@@ -1,42 +1,27 @@
 use ark_ff::{
-    biginteger::BigInteger768 as BigInteger,
-    field_new,
-    fields::fp3::{Fp3, Fp3Parameters},
+    fields::fp3::{Fp3, Fp3Config},
+    Field, MontFp,
 };
 
 use crate::Fq;
 
-pub type Fq3 = Fp3<Fq3Parameters>;
+pub type Fq3 = Fp3<Fq3Config>;
 
-pub struct Fq3Parameters;
+pub struct Fq3Config;
 
-impl Fp3Parameters for Fq3Parameters {
+impl Fp3Config for Fq3Config {
     type Fp = Fq;
 
     /// NONRESIDUE = -4
-    // Fq3 = Fq[u]/u^3+4
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
-        0xe12e00000001e9c2,
-        0x63c1e3faa001cd69,
-        0xb1b4384fcbe29cf6,
-        0xc79630bc713d5a1d,
-        0x30127ac071851e2d,
-        0x0979f350dcd36af1,
-        0x6a66defed8b361f2,
-        0x53abac78b24d4e23,
-        0xb7ab89dede485a92,
-        0x5c3a0745675e8452,
-        0x446f17918c5f5700,
-        0xfdf24e3267fa1e,
-    ]));
+    // Fq3 = Fq\[u\]/u^3+4
+    const NONRESIDUE: Fq = MontFp!("-4");
 
     // (MODULUS^3 - 1) % 2^TWO_ADICITY == 0
     const TWO_ADICITY: u32 = 1;
 
     // (T-1)/2 with T = (MODULUS^3-1) / 2^TWO_ADICITY
     #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: &'static [u64] = &[
+    const TRACE_MINUS_ONE_DIV_TWO: &'static [u64] = &[
         0xb5e7c000000a3eac,
         0xf79b99dbf41cf4ab,
         0xe9372b1919e55ee5,
@@ -76,125 +61,28 @@ impl Fp3Parameters for Fq3Parameters {
     ];
 
     // NONRESIDUE^T % q
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = (
-        field_new!(Fq, BigInteger([
-            0xf29a000000007ab6,
-            0x8c391832e000739b,
-            0x77738a6b6870f959,
-            0xbe36179047832b03,
-            0x84f3089e56574722,
-            0xc5a3614ac0b1d984,
-            0x5c81153f4906e9fe,
-            0x4d28be3a9f55c815,
-            0xd72c1d6f77d5f5c5,
-            0x73a18e069ac04458,
-            0xf9dfaa846595555f,
-            0xd0f0a60a5be58c,
-        ])),
-        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])),
-        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])),
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
+        MontFp!("6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068298"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
     // NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0)
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
-        field_new!(Fq, BigInteger([
-            0x0202ffffffff85d5,
-            0x5a5826358fff8ce7,
-            0x9e996e43827faade,
-            0xda6aff320ee47df4,
-            0xece9cb3e1d94b80b,
-            0xc0e667a25248240b,
-            0xa74da5bfdcad3905,
-            0x2352e7fe462f2103,
-            0x7b56588008b1c87c,
-            0x45848a63e711022f,
-            0xd7a81ebb9f65a9df,
-            0x51f77ef127e87d,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x7f96b51bd840c549,
-            0xd59782096496171f,
-            0x49b046fd9ce14bbc,
-            0x4b6163bba7527a56,
-            0xef6c92fb771d59f1,
-            0x0425bedbac1dfdc7,
-            0xd3ac39de759c0ffd,
-            0x9f43ed0e063a81d0,
-            0x5bd7d20b4f9a3ce2,
-            0x0411f03c36cf5c3c,
-            0x2d658fd49661c472,
-            0x1100249ae760b93,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x67a04ae427bfb5f8,
-            0x9d32d491eb6a5cff,
-            0x43d03c1cb68051d4,
-            0x0b75ca96f69859a5,
-            0x0763497f5325ec60,
-            0x48076b5c278dd94d,
-            0x8ca3965ff91efd06,
-            0x1e6077657ea02f5d,
-            0xcdd6c153a8c37724,
-            0x28b5b634e5c22ea4,
-            0x9e01e3efd42e902c,
-            0xe3d6815769a804,
-
-        ])),
+        Fq::ONE,
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
     ];
 
     // NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0)
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
-        field_new!(Fq, BigInteger([
-            0x0202ffffffff85d5,
-            0x5a5826358fff8ce7,
-            0x9e996e43827faade,
-            0xda6aff320ee47df4,
-            0xece9cb3e1d94b80b,
-            0xc0e667a25248240b,
-            0xa74da5bfdcad3905,
-            0x2352e7fe462f2103,
-            0x7b56588008b1c87c,
-            0x45848a63e711022f,
-            0xd7a81ebb9f65a9df,
-            0x51f77ef127e87d,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x67a04ae427bfb5f8,
-            0x9d32d491eb6a5cff,
-            0x43d03c1cb68051d4,
-            0x0b75ca96f69859a5,
-            0x0763497f5325ec60,
-            0x48076b5c278dd94d,
-            0x8ca3965ff91efd06,
-            0x1e6077657ea02f5d,
-            0xcdd6c153a8c37724,
-            0x28b5b634e5c22ea4,
-            0x9e01e3efd42e902c,
-            0xe3d6815769a804,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x7f96b51bd840c549,
-            0xd59782096496171f,
-            0x49b046fd9ce14bbc,
-            0x4b6163bba7527a56,
-            0xef6c92fb771d59f1,
-            0x0425bedbac1dfdc7,
-            0xd3ac39de759c0ffd,
-            0x9f43ed0e063a81d0,
-            0x5bd7d20b4f9a3ce2,
-            0x0411f03c36cf5c3c,
-            0x2d658fd49661c472,
-            0x1100249ae760b93,
-        ])),
+        Fq::ONE,
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
     ];
 
     #[inline(always)]
-    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
-        let original = -(*fe);
-        let double = original + &original;
-        double + &double
+    fn mul_fp_by_nonresidue_in_place(fe: &mut Self::Fp) -> &mut Self::Fp {
+        fe.double_in_place().double_in_place().neg_in_place()
     }
 }

bw6_761/src/fields/fq6.rs

@@ -1,106 +1,26 @@
-use crate::{Fq, Fq3, Fq3Parameters, FQ_ONE, FQ_ZERO};
 use ark_ff::{
-    biginteger::BigInteger768 as BigInteger,
-    field_new,
-    fields::fp6_2over3::{Fp6, Fp6Parameters},
+    fields::fp6_2over3::{Fp6, Fp6Config},
+    Field, MontFp,
 };
 
-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::{Fq, Fq3, Fq3Config};
 
-pub struct Fq6Parameters;
+pub type Fq6 = Fp6<Fq6Config>;
 
-impl Fp6Parameters for Fq6Parameters {
-    type Fp3Params = Fq3Parameters;
+pub struct Fq6Config;
+
+impl Fp6Config for Fq6Config {
+    type Fp3Config = Fq3Config;
 
     /// NONRESIDUE = (0, 1, 0)
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq3 = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
-        field_new!(Fq, BigInteger([
-            0x0202ffffffff85d5,
-            0x5a5826358fff8ce7,
-            0x9e996e43827faade,
-            0xda6aff320ee47df4,
-            0xece9cb3e1d94b80b,
-            0xc0e667a25248240b,
-            0xa74da5bfdcad3905,
-            0x2352e7fe462f2103,
-            0x7b56588008b1c87c,
-            0x45848a63e711022f,
-            0xd7a81ebb9f65a9df,
-            0x51f77ef127e87d,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x8cfcb51bd8404a93,
-            0x495e69d68495a383,
-            0xd23cbc9234705263,
-            0x8d2b4c2b5fcf4f52,
-            0x6a798a5d20c612ce,
-            0x3e825d90eb6c2443,
-            0x772b249f2c9525fe,
-            0x521b2ed366e4b9bb,
-            0x84abb49bd7c4471d,
-            0x907062359c0f17e3,
-            0x3385e55030cc6f12,
-            0x3f11a3a41a2606,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x7f96b51bd840c549,
-            0xd59782096496171f,
-            0x49b046fd9ce14bbc,
-            0x4b6163bba7527a56,
-            0xef6c92fb771d59f1,
-            0x0425bedbac1dfdc7,
-            0xd3ac39de759c0ffd,
-            0x9f43ed0e063a81d0,
-            0x5bd7d20b4f9a3ce2,
-            0x0411f03c36cf5c3c,
-            0x2d658fd49661c472,
-            0x1100249ae760b93,
-        ])),
-        field_new!(Fq, BigInteger([
-            0xf29a000000007ab6,
-            0x8c391832e000739b,
-            0x77738a6b6870f959,
-            0xbe36179047832b03,
-            0x84f3089e56574722,
-            0xc5a3614ac0b1d984,
-            0x5c81153f4906e9fe,
-            0x4d28be3a9f55c815,
-            0xd72c1d6f77d5f5c5,
-            0x73a18e069ac04458,
-            0xf9dfaa846595555f,
-            0xd0f0a60a5be58c,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x67a04ae427bfb5f8,
-            0x9d32d491eb6a5cff,
-            0x43d03c1cb68051d4,
-            0x0b75ca96f69859a5,
-            0x0763497f5325ec60,
-            0x48076b5c278dd94d,
-            0x8ca3965ff91efd06,
-            0x1e6077657ea02f5d,
-            0xcdd6c153a8c37724,
-            0x28b5b634e5c22ea4,
-            0x9e01e3efd42e902c,
-            0xe3d6815769a804,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x75064ae427bf3b42,
-            0x10f9bc5f0b69e963,
-            0xcc5cb1b14e0f587b,
-            0x4d3fb306af152ea1,
-            0x827040e0fccea53d,
-            0x82640a1166dbffc8,
-            0x30228120b0181307,
-            0xd137b92adf4a6748,
-            0xf6aaa3e430ed815e,
-            0xb514282e4b01ea4b,
-            0xa422396b6e993acc,
-            0x12e5db4d0dc277,
-        ])),
+        Fq::ONE,
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775649"),
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
+        MontFp!("-1"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292651"),
     ];
 }

bw6_761/src/fields/fr.rs

@@ -1 +1 @@
-pub use ark_bls12_377::{Fq as Fr, FqParameters as FrParameters};
+pub use ark_bls12_377::{Fq as Fr, FqConfig as FrConfig};

bw6_761/src/fields/tests.rs

@@ -1,51 +1,7 @@
-use ark_ff::{test_rng, Field, PrimeField};
-use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
-use rand::Rng;
-
 use crate::*;
+use ark_algebra_test_templates::*;
 
-use ark_curve_tests::fields::*;
-
-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    let a: Fr = rng.gen();
-    let b: Fr = rng.gen();
-    field_test(a, b);
-    sqrt_field_test(a);
-    primefield_test::<Fr>();
-}
-
-#[test]
-fn test_fq() {
-    let mut rng = test_rng();
-    let a: Fq = rng.gen();
-    let b: Fq = rng.gen();
-    field_test(a, b);
-    primefield_test::<Fq>();
-    sqrt_field_test(a);
-
-    let byte_size = a.serialized_size();
-    let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
-    assert_eq!(byte_size, buffer_size);
-    field_serialization_test::<Fq>(byte_size);
-}
-
-#[test]
-fn test_fq3() {
-    let mut rng = test_rng();
-    let a: Fq3 = rng.gen();
-    let b: Fq3 = rng.gen();
-    field_test(a, b);
-    sqrt_field_test(a);
-    frobenius_test::<Fq3, _>(Fq::characteristic(), 13);
-}
-
-#[test]
-fn test_fq6() {
-    let mut rng = test_rng();
-    let a: Fq6 = rng.gen();
-    let b: Fq6 = rng.gen();
-    field_test(a, b);
-    frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
-}
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
+test_field!(fq3; Fq3);
+test_field!(fq6; Fq6);

bw6_761/src/lib.rs

@@ -8,10 +8,11 @@
 )]
 #![forbid(unsafe_code)]
 
-//! This library implements the BW6_761 curve generated in [[EG20]](https://eprint.iacr.org/2020/351).
-//! The name denotes that it is a curve generated using the Brezing--Weng method, and that
-//! its embedding degree is 6.
-//! The main feature of this curve is that the scalar field equals the base field of the BLS12_377 curve.
+//! This library implements the BW6_761 curve generated in [\[EG20\]](https://eprint.iacr.org/2020/351).
+//! The name denotes that it is a curve generated using the Brezing--Weng
+//! method, and that its embedding degree is 6.
+//! The main feature of this curve is that the scalar field equals the base
+//! field of the BLS12_377 curve.
 //!
 //! Curve information:
 //! * Base field: q = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299

cp6_782/Cargo.toml

@@ -1,29 +1,34 @@
 [package]
 name = "ark-cp6-782"
-version = "0.1.0"
+version = "0.4.0-alpha.2"
 authors = [ "arkworks contributors" ]
 description = "The CP6-782 pairing-friendly elliptic curve"
-homepage = "https://arworks.rs"
-repository = "https://github.com/arkworks/algebra"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
 documentation = "https://docs.rs/ark-cp6-782/"
-keywords = ["cryptography", "finite fields", "elliptic curves" ]
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"
 
 [dependencies]
-ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
-ark-bls12-377 = { path = "../bls12_377", default-features = false, features = [ "base_field" ] }
+ark-ff = { version = "0.4.0-alpha", default-features = false }
+ark-ec = { version = "0.4.0-alpha", default-features = false }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+ark-bls12-377 = { version = "0.4.0-alpha", path = "../bls12_377", default-features = false, features = [ "base_field" ] }
+itertools = { version = "0.10", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
 
 [dev-dependencies]
-ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
-ark-curve-tests = { path = "../curve-tests", default-features = false }
-rand = { version = "0.7", default-features = false }
-rand_xorshift = "0.2"
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }
 
 [features]
 default = []
 std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-bls12-377/std" ]
+
+[[bench]]
+name = "cp6_782"
+path = "benches/cp6_782.rs"
+harness = false

cp6_782/benches/cp6_782.rs

@@ -0,0 +1,15 @@
+use ark_algebra_bench_templates::*;
+use ark_cp6_782::{
+    fq::Fq, fq3::Fq3, fq6::Fq6, fr::Fr, g1::G1Projective as G1, g2::G2Projective as G2, CP6_782,
+};
+
+bench!(
+    Name = "CP6_782",
+    Pairing = CP6_782,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq3,
+    TargetField = Fq6,
+);

cp6_782/scripts/base_field.sage

@@ -0,0 +1,28 @@
+modulus = 22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

cp6_782/scripts/scalar_field.sage

@@ -0,0 +1,28 @@
+modulus = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)

cp6_782/src/curves/g1.rs

@@ -1,61 +1,62 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
-};
-use ark_ff::{
-    biginteger::{BigInteger384, BigInteger832},
-    field_new,
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
+    AffineRepr, CurveGroup,
 };
+use ark_ff::MontFp;
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
+use ark_std::vec::Vec;
 
 use crate::{Fq, Fr};
 
-pub type G1Affine = GroupAffine<Parameters>;
-pub type G1Projective = GroupProjective<Parameters>;
+pub type G1Affine = Affine<Config>;
+pub type G1Projective = Projective<Config>;
 
-#[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+#[derive(Clone, Debug, PartialEq, Eq, CanonicalSerialize, CanonicalDeserialize)]
+pub struct G1Prepared(pub G1Affine);
 
-impl ModelParameters for Parameters {
-    type BaseField = Fq;
-    type ScalarField = Fr;
+impl From<G1Affine> for G1Prepared {
+    fn from(other: G1Affine) -> Self {
+        G1Prepared(other)
+    }
 }
 
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 5
-    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, BigInteger832([
-        0x781c76643018bd7a,
-        0x64f3a5a4f1d1ad48,
-        0xd2f8a1eb4f72692d,
-        0xc35eb123c6ed72ca,
-        0xb58d6bcfd32de058,
-        0x841eab13b02a492c,
-        0x4b70dc5a54c487e7,
-        0x2f231a8808a74c59,
-        0x5e2915154d70b050,
-        0x8a40fa16f37a6b37,
-        0xd01980093a72c54b,
-        0xef6845c25398004c,
-        0x48,
-    ]));
+impl From<G1Projective> for G1Prepared {
+    fn from(q: G1Projective) -> Self {
+        q.into_affine().into()
+    }
+}
 
-    /// COEFF_B = 17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, BigInteger832([
-        0xec5bd271ad37429,
-        0x9db8ac843ecca28a,
-        0x94f29bcb7e01bc74,
-        0x1b0bebb77bb5af0,
-        0x75b8cef4aa27ee17,
-        0xb5767ae80812cf6b,
-        0x592fa41e377a0d8c,
-        0xb6c6deedbb52df3e,
-        0xcb1343e488737fd4,
-        0x878020734d05b5a9,
-        0x2f51354eddfa069a,
-        0x498e2ecdc545243e,
-        0x2c2,
-    ]));
+impl<'a> From<&'a G1Affine> for G1Prepared {
+    fn from(other: &'a G1Affine) -> Self {
+        G1Prepared(*other)
+    }
+}
+
+impl<'a> From<&'a G1Projective> for G1Prepared {
+    fn from(q: &'a G1Projective) -> Self {
+        q.into_affine().into()
+    }
+}
+
+impl G1Prepared {
+    pub fn is_zero(&self) -> bool {
+        self.0.is_zero()
+    }
+}
+
+impl Default for G1Prepared {
+    fn default() -> Self {
+        G1Prepared(G1Affine::generator())
+    }
+}
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Config;
+
+impl CurveConfig for Config {
+    type BaseField = Fq;
+    type ScalarField = Fr;
 
     /// COFACTOR =
     /// 86482221941698704497288378992285180119495364068003923046442785886272123124361700722982503222189455144364945735564951561028
@@ -72,55 +73,24 @@ impl SWModelParameters for Parameters {
 
     /// COFACTOR^(-1) mod r =
     /// 163276846538158998893990986356139314746223949404500031940624325017036397274793417940375498603127780919653358641788
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger384([
-        4179837108212676264,
-        15545810469293120493,
-        13202863094424182470,
-        9506285060796071546,
-        9248558385029790142,
-        87030208545296111,
-    ]));
+    const COFACTOR_INV: Fr = MontFp!("163276846538158998893990986356139314746223949404500031940624325017036397274793417940375498603127780919653358641788");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = 5
+    const COEFF_A: Fq = MontFp!("5");
+
+    /// COEFF_B = 17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414
+    const COEFF_B: Fq = MontFp!("17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414");
 
     /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 }
 
 /// G1_GENERATOR_X =
 /// 5511163824921585887915590525772884263960974614921003940645351443740084257508990841338974915037175497689287870585840954231884082785026301437744745393958283053278991955159266640440849940136976927372133743626748847559939620888818486853646
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger832([
-    0x5901480e5bc22290,
-    0x20024afcdb9bd3a9,
-    0x12dc18ff416e8138,
-    0x28c69aa0ea223e18,
-    0xafb1524a1eb7efe6,
-    0x3d5c34edc3764ca2,
-    0x736c2230c8466ce9,
-    0xacfaa04e051014f1,
-    0x5d5ff82f00ff2964,
-    0x64c13ba270a26eaf,
-    0x50e9864b56ab172e,
-    0xd8370826a322499e,
-    0x00000000000006f1,
-]));
+pub const G1_GENERATOR_X: Fq = MontFp!("5511163824921585887915590525772884263960974614921003940645351443740084257508990841338974915037175497689287870585840954231884082785026301437744745393958283053278991955159266640440849940136976927372133743626748847559939620888818486853646");
 
 /// G1_GENERATOR_Y =
 /// 7913123550914612057135582061699117755797758113868200992327595317370485234417808273674357776714522052694559358668442301647906991623400754234679697332299689255516547752391831738454121261248793568285885897998257357202903170202349380518443
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger832([
-    0x8af8b64b402e1953,
-    0xd1bbceb3a258ea51,
-    0xdca9efa3140aaa0d,
-    0x807a610058ddedb2,
-    0xeb898562fe88076c,
-    0x0e4342ca56dd8ce2,
-    0x4f5528d29f1bde9a,
-    0xf18b0c6c19feb372,
-    0x94503ac2fac9199c,
-    0xffc86a8aff08ea34,
-    0xf7b1295214735d8c,
-    0x44eda9e0f55edd10,
-    0x0000000000000ef3,
-]));
+pub const G1_GENERATOR_Y: Fq = MontFp!("7913123550914612057135582061699117755797758113868200992327595317370485234417808273674357776714522052694559358668442301647906991623400754234679697332299689255516547752391831738454121261248793568285885897998257357202903170202349380518443");

cp6_782/src/curves/g2.rs

@@ -1,71 +1,62 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
-};
-use ark_ff::{
-    biginteger::{BigInteger384, BigInteger832},
-    field_new,
+    models::CurveConfig,
+    short_weierstrass::{Affine, Projective, SWCurveConfig},
+    AffineRepr, CurveGroup,
 };
+use ark_ff::{Field, MontFp};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
+use ark_std::vec::Vec;
 
-use crate::{Fq, Fq3, Fr, FQ_ZERO};
+use crate::{Fq, Fq3, Fr};
 
-pub type G2Affine = GroupAffine<Parameters>;
-pub type G2Projective = GroupProjective<Parameters>;
+pub type G2Affine = Affine<Config>;
+pub type G2Projective = Projective<Config>;
 
-#[derive(Clone, Default, PartialEq, Eq)]
-pub struct Parameters;
+#[derive(Clone, Debug, PartialEq, Eq, CanonicalSerialize, CanonicalDeserialize)]
+pub struct G2Prepared(pub G2Affine);
 
-impl ModelParameters for Parameters {
-    type BaseField = Fq3;
-    type ScalarField = Fr;
+impl From<G2Affine> for G2Prepared {
+    fn from(other: G2Affine) -> Self {
+        G2Prepared(other)
+    }
 }
 
-impl SWModelParameters for Parameters {
-    /// COEFF_A = (0, 0, COEFF_A * TWIST^2) = (0, 0, 5)
-    #[rustfmt::skip]
-    const COEFF_A: Fq3 = field_new!(Fq3,
-        FQ_ZERO,
-        FQ_ZERO,
-        field_new!(Fq, BigInteger832([
-            0x781c76643018bd7a,
-            0x64f3a5a4f1d1ad48,
-            0xd2f8a1eb4f72692d,
-            0xc35eb123c6ed72ca,
-            0xb58d6bcfd32de058,
-            0x841eab13b02a492c,
-            0x4b70dc5a54c487e7,
-            0x2f231a8808a74c59,
-            0x5e2915154d70b050,
-            0x8a40fa16f37a6b37,
-            0xd01980093a72c54b,
-            0xef6845c25398004c,
-            0x48,
-        ])),
-    );
+impl From<G2Projective> for G2Prepared {
+    fn from(q: G2Projective) -> Self {
+        q.into_affine().into()
+    }
+}
 
-    /// COEFF_B = (G1::COEFF_B * TWIST^3, 0, 0) =
-    /// (7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612,
-    /// 0, 0)
-    #[rustfmt::skip]
-    const COEFF_B: Fq3 = field_new!(Fq3,
-        field_new!(Fq, BigInteger832([
-            0xc00a9afc5cbce615,
-            0x0260c2b730644102,
-            0x9051e955661691ec,
-            0x15f9af8514839e37,
-            0xfa62826ca407172b,
-            0x37043dc868f48874,
-            0x876b5588d132b025,
-            0x481952128335562a,
-            0x4ffa729aeddd7dcd,
-            0xe181a5dae94a399f,
-            0x671fb50145b255d8,
-            0xbc3860730482d728,
-            0x00000000000023dd,
-        ])),
-        FQ_ZERO,
-        FQ_ZERO,
-    );
+impl<'a> From<&'a G2Affine> for G2Prepared {
+    fn from(other: &'a G2Affine) -> Self {
+        G2Prepared(*other)
+    }
+}
+
+impl<'a> From<&'a G2Projective> for G2Prepared {
+    fn from(q: &'a G2Projective) -> Self {
+        q.into_affine().into()
+    }
+}
+
+impl G2Prepared {
+    pub fn is_zero(&self) -> bool {
+        self.0.is_zero()
+    }
+}
+
+impl Default for G2Prepared {
+    fn default() -> Self {
+        G2Prepared(G2Affine::generator())
+    }
+}
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Config;
+
+impl CurveConfig for Config {
+    type BaseField = Fq3;
+    type ScalarField = Fr;
 
     /// COFACTOR =
     /// 43276679045916726782882096851503554444292580777869919574700824986947162516693702667493938255647666346010819253090121562084993205202476199057555142869892665220155573207800985012241638987472334344174208389303164492698303448192856551557283997344470334833850065978668184377503856699635686872344035470027430053642178229054516302338812152178131995800255516474185251732445975837621097393375441662426280154371264547168198834382681059556891327702516519955053315674076980350109237328216856859758931256208439575383786363605925879337208599843910819433766160937121108797819223653884174994325142959644019600
@@ -106,136 +97,49 @@ impl SWModelParameters for Parameters {
 
     /// COFACTOR^(-1) mod r =
     /// 45586359457219724873147353901735745013467692594291916855200979604570630929674383405372210802279573887880950375598
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger384([
-        7373687189387546408,
-        11284009518041539892,
-        301575489693670883,
-        13203058298476577559,
-        18441611830097862156,
-        4115759498196698,
-    ]));
-
-    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const COFACTOR_INV: Fr = MontFp!("45586359457219724873147353901735745013467692594291916855200979604570630929674383405372210802279573887880950375598");
 }
 
-const G2_GENERATOR_X: Fq3 =
-    field_new!(Fq3, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
-const G2_GENERATOR_Y: Fq3 =
-    field_new!(Fq3, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
+impl SWCurveConfig for Config {
+    /// COEFF_A = (0, 0, COEFF_A * TWIST^2) = (0, 0, 5)
+    const COEFF_A: Fq3 = Fq3::new(Fq::ZERO, Fq::ZERO, MontFp!("5"));
+
+    /// COEFF_B = (G1::COEFF_B * TWIST^3, 0, 0) =
+    /// (7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612,
+    /// 0, 0)
+    const COEFF_B: Fq3 = Fq3::new(
+        MontFp!("7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612"),
+        Fq::ZERO,
+        Fq::ZERO,
+    );
+
+    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
+}
+
+const G2_GENERATOR_X: Fq3 = Fq3::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
+const G2_GENERATOR_Y: Fq3 = Fq3::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
 
 /// G2_GENERATOR_X_C0 =
 /// 13426761183630949215425595811885033211332897733228446437546263564078445562454176776915160094418980045665397361295624472103734543457352048745726512354895954850428989867542989474136256025045975283415690491751906307188562464175510373683338
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger832([
-    0x03b3fe4c8d4ecac7,
-    0x9568212677524d1e,
-    0xf5de3f2228d187c1,
-    0x7bac772e31a420ef,
-    0x0255cf59968a612b,
-    0x991d4676f6b5d605,
-    0x02dd2ae4831d29ea,
-    0xbeca7c9a62e392c2,
-    0xfc1d0633d48d2fc5,
-    0x7867813be5f7d2a1,
-    0x6f567b6617030028,
-    0xf08c9fa6ca6809df,
-    0x0000000000000de9,
-]));
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("13426761183630949215425595811885033211332897733228446437546263564078445562454176776915160094418980045665397361295624472103734543457352048745726512354895954850428989867542989474136256025045975283415690491751906307188562464175510373683338");
 
 /// G2_GENERATOR_X_C1 =
 /// 20471601555918880743198170952645906008198510944268658573129351735028343217532386920456705632337352161031960990613816401042894531220068552819818037605513359562118363589199569321421558696125646867661360498323171027455638052943806292028610
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger832([
-    0xefd1b506e5fbe05f,
-    0xad27d47a4975140c,
-    0xfa11540132dbc27a,
-    0x8dca42b6da7c4717,
-    0x66d30fd7fd76207a,
-    0xb8e4f65c68932b1d,
-    0x3b7f971e93ad14be,
-    0xf860a89f4e582f9f,
-    0x7d438aaa3986f73b,
-    0xa37ec0c18c6e106a,
-    0x9f2dfb98b5185b54,
-    0x19995e421ca939bc,
-    0x0000000000002f4f,
-]));
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("20471601555918880743198170952645906008198510944268658573129351735028343217532386920456705632337352161031960990613816401042894531220068552819818037605513359562118363589199569321421558696125646867661360498323171027455638052943806292028610");
 
 /// G2_GENERATOR_X_C2 =
 /// 3905053196875761830053608605277158152930144841844497593936739534395003062685449846381431331169369910535935138116320442345524758217411779027270883193856999691582831339845600938304719916501940381093815781408183227875600753651697934495980
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C2: Fq = field_new!(Fq, BigInteger832([
-    0xc081ed832bdf911e,
-    0xb85ff7aeebdfe7b3,
-    0x96dce6bb307b14eb,
-    0x578f7ded84bd824c,
-    0xb799305a9971d184,
-    0x0116ad33c2874b90,
-    0x862dce68efdca245,
-    0x4190947c70534c1d,
-    0x1b1aa80334248d03,
-    0xb13b07aff63fcf27,
-    0x5727687b73ab4fff,
-    0xf559a7f4eb8d180a,
-    0x0000000000002d37,
-]));
+pub const G2_GENERATOR_X_C2: Fq = MontFp!("3905053196875761830053608605277158152930144841844497593936739534395003062685449846381431331169369910535935138116320442345524758217411779027270883193856999691582831339845600938304719916501940381093815781408183227875600753651697934495980");
 
 /// G2_GENERATOR_Y_C0 =
 /// 8567517639523571619872938228644013584947463594196306323477160496987712111576624702939472765993995586889532559039169098780892505598589581147768095093536988446010255611523736706017580686335404469207486594272103717837888228343074699140243
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger832([
-    0x3f680b59e26b33d1,
-    0x720fdf65b9e15b17,
-    0x0f0b56def11247b1,
-    0x5ea05417c8a4a52c,
-    0x4ad59dc4f7c47a09,
-    0xf393e0db62107115,
-    0xde3b16404a53d2bb,
-    0xeaa74961636280e0,
-    0x2d16ccd14cf5a88c,
-    0x5667565a06187d0e,
-    0xb446fdc7565d0261,
-    0xd3ad395d6fd0faab,
-    0x0000000000000655,
-]));
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("8567517639523571619872938228644013584947463594196306323477160496987712111576624702939472765993995586889532559039169098780892505598589581147768095093536988446010255611523736706017580686335404469207486594272103717837888228343074699140243");
 
 /// G2_GENERATOR_Y_C1 =
 /// 3890537069205870914984502594450293167889863914413852788876350245583932846980126025043974070704295857226211547108005650399870458089721518559480870503159804530091559886149680718531004778697982910253701559194337987238111062202037698927752
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger832([
-    0x9e86cc63207679dd,
-    0x4e16d9a9d87c3e47,
-    0xdbee3524db80627d,
-    0x137322b87d93befc,
-    0x24a7ca2f9aae90a0,
-    0x44abea538df3e854,
-    0xc01d176c6e042eee,
-    0xf5fcc4caabc75699,
-    0x1f99972699a38960,
-    0x30d4cc8256bf963d,
-    0xa3634826edcfefff,
-    0x34f3bd0c8e5a4b38,
-    0x0000000000001d28,
-]));
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("3890537069205870914984502594450293167889863914413852788876350245583932846980126025043974070704295857226211547108005650399870458089721518559480870503159804530091559886149680718531004778697982910253701559194337987238111062202037698927752");
 
 /// G2_GENERATOR_Y_C2 =
 /// 10936269922612615564271188303104593362724754284143779051599749016735041389483971486958818324356025479751246744831831158558101688599198721653921723013062333636402617118847009085485166284126970598561393411916461254016145116183331671450721
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C2: Fq = field_new!(Fq, BigInteger832([
-    0xfc478105dedf3654,
-    0xa6fcfcfdd2710d6a,
-    0x05a68c283d5d4c65,
-    0x9fab8d94c667a679,
-    0x009b0a616ea54ff9,
-    0xf0df517bc7bc6382,
-    0xdb44338e7491f5b7,
-    0xcd192a7e53453f45,
-    0xa041a7a60982d92c,
-    0x4dd01c62bae4c7ff,
-    0x79a69a54e6b66178,
-    0xd47b0bfe832b05f8,
-    0x00000000000000ef,
-]));
+pub const G2_GENERATOR_Y_C2: Fq = MontFp!("10936269922612615564271188303104593362724754284143779051599749016735041389483971486958818324356025479751246744831831158558101688599198721653921723013062333636402617118847009085485166284126970598561393411916461254016145116183331671450721");

cp6_782/src/curves/mod.rs

@@ -1,18 +1,19 @@
-use ark_ec::{models::SWModelParameters, PairingEngine};
-use ark_ff::{
-    biginteger::BigInteger832,
-    field_new,
-    fields::{BitIteratorBE, Field, FpParameters},
-    One,
+use ark_ec::{
+    models::short_weierstrass::SWCurveConfig,
+    pairing::{MillerLoopOutput, Pairing, PairingOutput},
 };
+use ark_ff::{
+    biginteger::BigInteger832, BigInt, BitIteratorBE, CyclotomicMultSubgroup, Field, One,
+};
+use itertools::Itertools;
 
-use crate::{Fq, Fq3, Fq6, FqParameters, Fr};
+use crate::{Fq, Fq3, Fq6, Fr};
 
 pub mod g1;
-pub use self::g1::{G1Affine, G1Projective};
+pub use self::g1::{G1Affine, G1Prepared, G1Projective};
 
 pub mod g2;
-pub use self::g2::{G2Affine, G2Projective};
+pub use self::g2::{G2Affine, G2Prepared, G2Projective};
 
 #[cfg(test)]
 mod tests;
@@ -22,40 +23,40 @@ pub type GT = Fq6;
 #[derive(Copy, Clone, Debug, PartialEq, Eq)]
 pub struct CP6_782;
 
-impl PairingEngine for CP6_782 {
-    type Fr = Fr;
-    type G1Projective = G1Projective;
+impl Pairing for CP6_782 {
+    type ScalarField = Fr;
+    type BaseField = Fq;
+    type G1 = G1Projective;
     type G1Affine = G1Affine;
-    type G1Prepared = G1Affine;
-    type G2Projective = G2Projective;
+    type G1Prepared = G1Prepared;
+    type G2 = G2Projective;
     type G2Affine = G2Affine;
-    type G2Prepared = G2Affine;
-    type Fq = Fq;
-    type Fqe = Fq3;
-    type Fqk = Fq6;
+    type G2Prepared = G2Prepared;
+    type TargetField = Fq6;
 
-    fn miller_loop<'a, I>(i: I) -> Self::Fqk
-    where
-        I: IntoIterator<Item = &'a (Self::G1Prepared, Self::G2Prepared)>,
-    {
-        let mut result = Self::Fqk::one();
-        for &(ref p, ref q) in i {
-            result *= &CP6_782::ate_miller_loop(p, q);
-        }
-        result
+    fn multi_miller_loop(
+        a: impl IntoIterator<Item = impl Into<Self::G1Prepared>>,
+        b: impl IntoIterator<Item = impl Into<Self::G2Prepared>>,
+    ) -> MillerLoopOutput<Self> {
+        let mut result = Self::TargetField::one();
+        a.into_iter().zip_eq(b).for_each(|(p, q)| {
+            let (p, q) = (p.into(), q.into());
+            result *= &CP6_782::ate_miller_loop(&p, &q);
+        });
+
+        MillerLoopOutput(result)
     }
 
-    fn final_exponentiation(r: &Self::Fqk) -> Option<Self::Fqk> {
-        Some(CP6_782::final_exponentiation(r))
+    fn final_exponentiation(r: MillerLoopOutput<Self>) -> Option<PairingOutput<Self>> {
+        Some(PairingOutput(CP6_782::final_exponentiation(&r.0)))
     }
 }
 
 impl CP6_782 {
-    pub fn ate_pairing(p: &G1Affine, q: &G2Affine) -> GT {
-        CP6_782::final_exponentiation(&CP6_782::ate_miller_loop(p, q))
-    }
+    fn ate_miller_loop(p: &G1Prepared, q: &G2Prepared) -> Fq6 {
+        let p = p.0;
+        let q = q.0;
 
-    fn ate_miller_loop(p: &G1Affine, q: &G2Affine) -> Fq6 {
         let px = p.x;
         let py = p.y;
         let qx = q.x;
@@ -77,7 +78,7 @@ impl CP6_782 {
 
             let old_rx_square = old_rx.square();
             let old_rx_square_3 = old_rx_square.double() + &old_rx_square;
-            let old_rx_square_3_a = old_rx_square_3 + &g2::Parameters::COEFF_A;
+            let old_rx_square_3_a = old_rx_square_3 + &g2::Config::COEFF_A;
             let old_ry_double_inverse = old_ry.double().inverse().unwrap();
 
             let gamma = old_rx_square_3_a * &old_ry_double_inverse;
@@ -88,7 +89,7 @@ impl CP6_782 {
 
             let x = py_twist_squared;
             let y = gamma_old_rx - &old_ry - &gamma_twist_px;
-            let ell_rr_at_p = Fq6::new(x, y);
+            let ell_rr_at_p: Fq6 = Fq6::new(x, y);
 
             rx = gamma.square() - &old_rx.double();
             ry = gamma * &(old_rx - &rx) - &old_ry;
@@ -106,7 +107,7 @@ impl CP6_782 {
 
                 let x = py_twist_squared;
                 let y = gamma_qx - &qy - &gamma_twist_px;
-                let ell_rq_at_p = Fq6::new(x, y);
+                let ell_rq_at_p: Fq6 = Fq6::new(x, y);
 
                 rx = gamma.square() - &old_rx - &qx;
                 ry = gamma * &(old_rx - &rx) - &old_ry;
@@ -128,19 +129,19 @@ impl CP6_782 {
 
         // elt_q3 = elt^(q^3)
         let mut elt_q3 = elt.clone();
-        elt_q3.frobenius_map(3);
+        elt_q3.frobenius_map_in_place(3);
         // elt_q3_over_elt = elt^(q^3-1)
         let elt_q3_over_elt = elt_q3 * elt_inv;
         // alpha = elt^((q^3-1) * q)
         let mut alpha = elt_q3_over_elt.clone();
-        alpha.frobenius_map(1);
+        alpha.frobenius_map_in_place(1);
         // beta = elt^((q^3-1)*(q+1)
         alpha * &elt_q3_over_elt
     }
 
     fn final_exponentiation_last(elt: &Fq6, elt_inv: &Fq6) -> Fq6 {
         let mut elt_q = elt.clone();
-        elt_q.frobenius_map(1);
+        elt_q.frobenius_map_in_place(1);
 
         let w1_part = elt_q.cyclotomic_exp(&FINAL_EXPONENT_LAST_CHUNK_W1);
         let w0_part = if FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG {
@@ -153,14 +154,8 @@ impl CP6_782 {
     }
 }
 
-/// FQ_ZERO = 0
-pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger832([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
-
-/// FQ_ONE = 1
-pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
-
 /// TWIST = (0, 1, 0)
-pub const TWIST: Fq3 = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+pub const TWIST: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
 
 /// ATE_IS_LOOP_COUNT_NEG = false
 pub const ATE_IS_LOOP_COUNT_NEG: bool = false;
@@ -188,7 +183,7 @@ pub const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool = true;
 
 /// FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0 =
 /// 7000705447348627246181409558336018323010329260726930841638672011287206690002601216854775649561085256265269640040570922609783227469279331691880282815325569032149343779036142830666859805506518426649197067288711084398033
-pub const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger832 = BigInteger832([
+pub const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger832 = BigInt::new([
     0xb62ef36af72855d1,
     0x676b5cef49d290fa,
     0xd17fcf3c60947427,
@@ -206,7 +201,7 @@ pub const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger832 = BigInteger832([
 
 /// FINAL_EXPONENT_LAST_CHUNK_W1 =
 /// 86482221941698704497288378992285180119495364068003923046442785886272123124361700722982503222189455144364945735564951562986
-pub const FINAL_EXPONENT_LAST_CHUNK_W1: BigInteger832 = BigInteger832([
+pub const FINAL_EXPONENT_LAST_CHUNK_W1: BigInteger832 = BigInt::new([
     0x5657b9b57b942aea,
     0x84f9a65f3bd54eaf,
     0x5ea4214e35cd127,

cp6_782/src/curves/tests.rs

@@ -1,77 +1,9 @@
-use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
-use ark_ff::{test_rng, Field, One, PrimeField};
-use rand::Rng;
+use ark_algebra_test_templates::*;
+use ark_ff::Field;
 
 use crate::*;
 
-use ark_curve_tests::{curves::*, groups::*};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let sa = a.mul(s);
-    let sb = b.mul(s);
-
-    let ans1 = CP6_782::pairing(sa, b);
-    let ans2 = CP6_782::pairing(a, sb);
-    let ans3 = CP6_782::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq6::one());
-    assert_ne!(ans2, Fq6::one());
-    assert_ne!(ans3, Fq6::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq6::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq6::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq6::one());
-}
+test_group!(g1; G1Projective; sw);
+test_group!(g2; G2Projective; sw);
+test_group!(pairing_output; ark_ec::pairing::PairingOutput<CP6_782>; msm);
+test_pairing!(pairing; crate::CP6_782);

cp6_782/src/fields/fq.rs

@@ -1,166 +1,7 @@
-use ark_ff::{
-    biginteger::BigInteger832 as BigInteger,
-    fields::{FftParameters, Fp832, Fp832Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp832, MontBackend, MontConfig};
 
-pub type Fq = Fp832<FqParameters>;
-
-pub struct FqParameters;
-
-impl Fp832Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 3;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        18044746167194862600u64,
-        63590321303744709u64,
-        5009346151370959890u64,
-        2859114157767503991u64,
-        8301813204852325413u64,
-        5629414263664332594u64,
-        2637340888701394641u64,
-        17433538052687852753u64,
-        2230763098934759248u64,
-        3785382115983092023u64,
-        8895511354022222370u64,
-        15792083141709071785u64,
-        1328u64,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0xdace79b57b942ae9,
-        0x545d85c16dfd424a,
-        0xee135c065f4d26b7,
-        0x9c2f764a12c4024b,
-        0x1ad533049cfe6a39,
-        0x52a3fb77c79c1320,
-        0xab3596c8617c5792,
-        0x830c728d80f9d78b,
-        0x6a7223ee72023d07,
-        0xbc5d176b746af026,
-        0xe959283d8f526663,
-        0xc4d2263babf8941f,
-        0x3848,
-    ]);
-
-    const MODULUS_BITS: u32 = 782;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 50;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        11190988450819017841u64,
-        16170411717126802030u64,
-        2265463223430229059u64,
-        16946880912571045974u64,
-        11155248462028513229u64,
-        12855672356664541314u64,
-        8489376931127408159u64,
-        2655797810825538098u64,
-        9648483887143916718u64,
-        17514963461276738952u64,
-        16777089214204267338u64,
-        15649035958020076168u64,
-        8659u64,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        13983406830510863714u64,
-        17863856572171232656u64,
-        1698388424046564526u64,
-        1773634430448388392u64,
-        8684647957094413275u64,
-        3992637317298078843u64,
-        18420879196616862245u64,
-        3238482510270583127u64,
-        7928200707794018216u64,
-        10024831010452223910u64,
-        9613847725664942650u64,
-        15361265984156787358u64,
-        7833u64,
-    ]);
-
-    const INV: u64 = 14469047335842394791u64;
-
-    /// GENERATOR = 13
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        16669393626057438558u64,
-        1640520694378723217u64,
-        1598646156981121135u64,
-        12401834967100173388u64,
-        2356467520877704673u64,
-        14759118825104212161u64,
-        5556628239575210651u64,
-        5317520392768798654u64,
-        16398429955031064995u64,
-        3556102264904210145u64,
-        8166834915717907988u64,
-        11926665585800594452u64,
-        11716u64,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x6d673cdabdca1574,
-        0xaa2ec2e0b6fea125,
-        0xf709ae032fa6935b,
-        0xce17bb2509620125,
-        0xd6a99824e7f351c,
-        0x2951fdbbe3ce0990,
-        0xd59acb6430be2bc9,
-        0xc1863946c07cebc5,
-        0x353911f739011e83,
-        0xde2e8bb5ba357813,
-        0xf4ac941ec7a93331,
-        0x6269131dd5fc4a0f,
-        0x1c24,
-    ]);
-
-    // (T - 1)/2 =
-    // 1398117143679731058146671387906315933423474966581074036386468539227923378278626533764529938634242576261128410962740119034868607201414583335758422276643816405480145410934911750070786645716409577212967755581539567265673914343284832551598
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xadace79b57b942ae,
-        0x7545d85c16dfd424,
-        0xbee135c065f4d26b,
-        0x99c2f764a12c4024,
-        0x1ad533049cfe6a3,
-        0x252a3fb77c79c132,
-        0xbab3596c8617c579,
-        0x7830c728d80f9d78,
-        0x66a7223ee72023d0,
-        0x3bc5d176b746af02,
-        0xfe959283d8f52666,
-        0x8c4d2263babf8941,
-        0x384,
-    ]);
-
-    // T =
-    // 2796234287359462116293342775812631866846949933162148072772937078455846756557253067529059877268485152522256821925480238069737214402829166671516844553287632810960290821869823500141573291432819154425935511163079134531347828686569665103197
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x5b59cf36af72855d,
-        0xea8bb0b82dbfa849,
-        0x7dc26b80cbe9a4d6,
-        0x3385eec942588049,
-        0x35aa660939fcd47,
-        0x4a547f6ef8f38264,
-        0x7566b2d90c2f8af2,
-        0xf0618e51b01f3af1,
-        0xcd4e447dce4047a0,
-        0x778ba2ed6e8d5e04,
-        0xfd2b2507b1ea4ccc,
-        0x189a44c7757f1283,
-        0x709,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577"]
+#[generator = "13"]
+pub struct FqConfig;
+pub type Fq = Fp832<MontBackend<FqConfig, 13>>;

cp6_782/src/fields/fq3.rs

@@ -1,40 +1,24 @@
-use crate::Fq;
 use ark_ff::{
-    biginteger::BigInteger832 as BigInteger,
-    field_new,
-    fields::fp3::{Fp3, Fp3Parameters},
-    Field,
+    fields::fp3::{Fp3, Fp3Config},
+    Field, MontFp,
 };
 
-pub type Fq3 = Fp3<Fq3Parameters>;
+use crate::Fq;
 
-pub struct Fq3Parameters;
+pub type Fq3 = Fp3<Fq3Config>;
 
-impl Fp3Parameters for Fq3Parameters {
+pub struct Fq3Config;
+
+impl Fp3Config for Fq3Config {
     type Fp = Fq;
 
     /// NONRESIDUE = 13
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
-        0xe755952f4650755e,
-        0x16c44ce1331ef791,
-        0x162f8835b467306f,
-        0xac1c2b31e1062c4c,
-        0x20b3dab9a2a935e1,
-        0xccd2ec5fd01e00c1,
-        0x4d1d1bf190c8da9b,
-        0x49cba09fb0e13fbe,
-        0xe392ed2957c061a3,
-        0x3159d02b3c93d6e1,
-        0x71566d160a9f8614,
-        0xa5840728fc854414,
-        0x2dc4,
-    ]));
+    const NONRESIDUE: Fq = MontFp!("13");
 
     const TWO_ADICITY: u32 = 3;
 
     #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: &'static [u64] = &[
+    const TRACE_MINUS_ONE_DIV_TWO: &'static [u64] = &[
         0x62730e2cd2029617,
         0x660647f735cb88cf,
         0x274359d60784f69d,
@@ -74,131 +58,31 @@ impl Fp3Parameters for Fq3Parameters {
         0x2b87fda171,
     ];
 
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = (
-        field_new!(Fq, BigInteger([
-            0x59987c0ef8e31739,
-            0x59578d750d6f57dd,
-            0x9672547570dddab8,
-            0x1a1f630e1d6dbdd5,
-            0xde15f46e52d7613e,
-            0x6a1b6e4f80179926,
-            0x461ad119d93123b,
-            0x12054e3654907ed9,
-            0x85ea06b12bf811a0,
-            0xc01d53d07347f9ec,
-            0x70c424eb666c3922,
-            0x1796ce4ed605d49e,
-            0x68b,
-        ])),
-        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])),
-        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])),
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
+        MontFp!("5759691735434357221228070840130186543101559976323700017469395641639510585333061695996665166662748527158637897523704071820491869715512532675375604262649010727161924084052120196921150869218319839231115277876207074651754402338718419191428"),
+        Fq::ZERO,
+        Fq::ZERO,
     );
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
-        field_new!(Fq, BigInteger([
-            0x9b4e60b420910c71,
-            0xe068d7c83f284a6e,
-            0x1f708acc7c452c43,
-            0xeb2f6a66cca51856,
-            0x9acf675f886e9fcd,
-            0xb26885e567cc8082,
-            0x75d05357183eb61f,
-            0x24db4a09b5842a32,
-            0x85e64cf9ba4b14ae,
-            0xf311a6784358a588,
-            0xe8d431c061aecb4a,
-            0xd92c8b4aab19f288,
-            0x21d3,
-        ])),
-        field_new!(Fq, BigInteger([
-            0xe793e750fc0c0fdc,
-            0x28cd75f5634a867e,
-            0xde5e9b1261eb3c33,
-            0x68a0fb1c17595903,
-            0x19626d2c9f392e46,
-            0xc4d95794cb378b83,
-            0x54870f1f582d67c9,
-            0xf3f1a0ac4aceb56d,
-            0x811361215ea4fd47,
-            0x32cd6ee17d95bd00,
-            0x725f9881049a9c52,
-            0x5acb70be0613a307,
-            0x11bb,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x57ec31b05ef70e9c,
-            0x4b273803cb8a715d,
-            0xf0443627811cbe40,
-            0x485f10c72ec590f1,
-            0x66a35e7875569c25,
-            0xdb621dfd9498071a,
-            0xe0de3451f11039a8,
-            0x6a3f87d780a6f7eb,
-            0x637875d359122b11,
-            0x967e0211b37c8d9d,
-            0x8e255dfc2908fec6,
-            0x90da2a32facafe8f,
-            0x4b9,
-        ])),
+        Fq::ONE,
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
     ];
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
-        field_new!(Fq, BigInteger([
-            0x9b4e60b420910c71,
-            0xe068d7c83f284a6e,
-            0x1f708acc7c452c43,
-            0xeb2f6a66cca51856,
-            0x9acf675f886e9fcd,
-            0xb26885e567cc8082,
-            0x75d05357183eb61f,
-            0x24db4a09b5842a32,
-            0x85e64cf9ba4b14ae,
-            0xf311a6784358a588,
-            0xe8d431c061aecb4a,
-            0xd92c8b4aab19f288,
-            0x21d3,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x57ec31b05ef70e9c,
-            0x4b273803cb8a715d,
-            0xf0443627811cbe40,
-            0x485f10c72ec590f1,
-            0x66a35e7875569c25,
-            0xdb621dfd9498071a,
-            0xe0de3451f11039a8,
-            0x6a3f87d780a6f7eb,
-            0x637875d359122b11,
-            0x967e0211b37c8d9d,
-            0x8e255dfc2908fec6,
-            0x90da2a32facafe8f,
-            0x4b9,
-        ])),
-        field_new!(Fq, BigInteger([
-            0xe793e750fc0c0fdc,
-            0x28cd75f5634a867e,
-            0xde5e9b1261eb3c33,
-            0x68a0fb1c17595903,
-            0x19626d2c9f392e46,
-            0xc4d95794cb378b83,
-            0x54870f1f582d67c9,
-            0xf3f1a0ac4aceb56d,
-            0x811361215ea4fd47,
-            0x32cd6ee17d95bd00,
-            0x725f9881049a9c52,
-            0x5acb70be0613a307,
-            0x11bb,
-        ])),
+        Fq::ONE,
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
     ];
 
     #[inline(always)]
-    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
+    fn mul_fp_by_nonresidue_in_place(fe: &mut Self::Fp) -> &mut Self::Fp {
         let original = *fe;
-        let mut four_fe = fe.double();
-        four_fe.double_in_place();
-        let eight_fe = four_fe.double();
-        eight_fe + &four_fe + &original
+        fe.double_in_place();
+        *fe += original;
+        fe.double_in_place().double_in_place();
+        *fe += original;
+        fe
     }
 }

cp6_782/src/fields/fq6.rs

@@ -1,112 +1,26 @@
-use crate::{Fq, Fq3, Fq3Parameters, FQ_ONE, FQ_ZERO};
 use ark_ff::{
-    biginteger::BigInteger832 as BigInteger,
-    field_new,
-    fields::fp6_2over3::{Fp6, Fp6Parameters},
+    fields::fp6_2over3::{Fp6, Fp6Config},
+    Field, MontFp,
 };
 
-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::{Fq, Fq3, Fq3Config};
 
-pub struct Fq6Parameters;
+pub type Fq6 = Fp6<Fq6Config>;
 
-impl Fp6Parameters for Fq6Parameters {
-    type Fp3Params = Fq3Parameters;
+pub struct Fq6Config;
+
+impl Fp6Config for Fq6Config {
+    type Fp3Config = Fq3Config;
 
     /// NONRESIDUE = (0, 1, 0).
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq3 = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
 
-    #[rustfmt::skip]
     const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
-        field_new!(Fq, BigInteger([
-            0x9b4e60b420910c71,
-            0xe068d7c83f284a6e,
-            0x1f708acc7c452c43,
-            0xeb2f6a66cca51856,
-            0x9acf675f886e9fcd,
-            0xb26885e567cc8082,
-            0x75d05357183eb61f,
-            0x24db4a09b5842a32,
-            0x85e64cf9ba4b14ae,
-            0xf311a6784358a588,
-            0xe8d431c061aecb4a,
-            0xd92c8b4aab19f288,
-            0x21d3,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x82e248051c9d1c4d,
-            0x9364dbda272d0ed,
-            0xfdcf25dede306877,
-            0x53d06582e3fe7159,
-            0xb431d48c27a7ce14,
-            0x7741dd7a33040c05,
-            0xca576276706c1de9,
-            0x18cceab60052df9f,
-            0x6f9ae1b18f011f6,
-            0x25df1559c0ee6289,
-            0x5b33ca416649679d,
-            0x33f7fc08b12d9590,
-            0x338f,
-        ])),
-        field_new!(Fq, BigInteger([
-            0xe793e750fc0c0fdc,
-            0x28cd75f5634a867e,
-            0xde5e9b1261eb3c33,
-            0x68a0fb1c17595903,
-            0x19626d2c9f392e46,
-            0xc4d95794cb378b83,
-            0x54870f1f582d67c9,
-            0xf3f1a0ac4aceb56d,
-            0x811361215ea4fd47,
-            0x32cd6ee17d95bd00,
-            0x725f9881049a9c52,
-            0x5acb70be0613a307,
-            0x11bb,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x3f8019015b031e78,
-            0x73f4adf92ed4f7dc,
-            0xcea2d139e307fa73,
-            0xb1000be3461ee9f5,
-            0x8005cba5148fca6b,
-            0xa03b75925fcf929d,
-            0x35654371493da172,
-            0x5e312883cb75ad59,
-            0xe48bd6f4b7b72859,
-            0xc94b70f331124a9d,
-            0x84f67d2da39b18,
-            0xeba59af100dea197,
-            0x1674,
-        ])),
-        field_new!(Fq, BigInteger([
-            0x57ec31b05ef70e9c,
-            0x4b273803cb8a715d,
-            0xf0443627811cbe40,
-            0x485f10c72ec590f1,
-            0x66a35e7875569c25,
-            0xdb621dfd9498071a,
-            0xe0de3451f11039a8,
-            0x6a3f87d780a6f7eb,
-            0x637875d359122b11,
-            0x967e0211b37c8d9d,
-            0x8e255dfc2908fec6,
-            0x90da2a32facafe8f,
-            0x4b9,
-        ])),
-        field_new!(Fq, BigInteger([
-            0xf33a92647f881b0d,
-            0x2b900fcc0ab2bbcb,
-            0xfb4c0f3fd61ea84,
-            0x338e7b2dfb6aa948,
-            0x172c5d7fdc53bf3,
-            0x8dcaa3e2fc64879d,
-            0x56ae87a9094eefc8,
-            0x8f1ad1e1362b221e,
-            0xe95ec2cd135d3fbf,
-            0x898fa889f6d53325,
-            0x76f98fbc8ab7ca11,
-            0x6a06b57da5e4f118,
-            0x268d,
-        ])),
+        Fq::ONE,
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756862"),
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
+        MontFp!("22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825576"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068716"),
     ];
 }

cp6_782/src/fields/fr.rs

@@ -1 +1 @@
-pub use ark_bls12_377::{Fq as Fr, FqParameters as FrParameters};
+pub use ark_bls12_377::{Fq as Fr, FqConfig as FrConfig};

cp6_782/src/fields/mod.rs

@@ -10,5 +10,5 @@ pub use self::fq3::*;
 pub mod fq6;
 pub use self::fq6::*;
 
-#[cfg(all(feature = "cp6_782", test))]
+#[cfg(test)]
 mod tests;