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Add the curve25519 curve (#124)

Browse Source 
* add ed25519 curve

* changelog

* curve info

* fix

* edit

* update

* add more explanation

* Update curve25519/src/curves/mod.rs

* Update curve25519/src/curves/mod.rs

* fixed the comment

* Update curve25519/src/curves/mod.rs

Co-authored-by: onewayfunc <onewayfunc@gmail.com>
This commit is contained in:
Weikeng Chen
2022-10-29 19:55:35 -07:00
committed by GitHub
parent a7d266f73d
commit db03d405b5
17 changed files with 450 additions and 0 deletions
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30
curve25519/Cargo.toml Normal file
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[package]
name = "ark-curve25519"
version = "0.3.0"
authors = [ "arkworks contributors" ]
description = "The curve25519 Montgomery curve"
homepage = "https://arkworks.rs"
repository = "https://github.com/arkworks-rs/curves"
documentation = "https://docs.rs/ark-curve25519/"
keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
categories = ["cryptography"]
include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
license = "MIT/Apache-2.0"
edition = "2021"
[dependencies]
ark-ff = { version = "^0.3.0", default-features = false }
ark-ec = { version = "^0.3.0", default-features = false }
ark-std = { version = "^0.3.0", default-features = false }
ark-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
[dev-dependencies]
ark-relations = { version = "^0.3.0", default-features = false }
ark-serialize = { version = "^0.3.0", default-features = false }
ark-algebra-test-templates = { version = "^0.3.0", default-features = false }
ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }
[features]
default = []
std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
r1cs = [ "ark-r1cs-std" ]

1
curve25519/LICENSE-APACHE Symbolic link
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../LICENSE-APACHE

1
curve25519/LICENSE-MIT Symbolic link
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../LICENSE-MIT

91
curve25519/scripts/fr.ipynb Normal file
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "04264893",
"metadata": {},
"outputs": [],
"source": [
"r = 7237005577332262213973186563042994240857116359379907606001950938285454250989"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1603b293",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2^2 * 3 * 11 * 198211423230930754013084525763697 * 276602624281642239937218680557139826668747"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"factor(r - 1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "425ceac7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"7237005577332262213973186563042994240857116359379907606001950938285454250988\n",
"1570463851528226261927580272323658009530148727742783848239914322803198255651\n",
"4908983020090465803374304318106080751443647916949975825112097080460587568629\n",
"7119675135705137915307919240607293966034195415655343409829245710729128040338\n",
"2975531125133123119648879457563281269120703404158613135195788908093573672641\n"
]
}
],
"source": [
"gen = 2\n",
"print(pow(gen, (r - 1) / 2, r))\n",
"print(pow(gen, (r - 1) / 3, r))\n",
"print(pow(gen, (r - 1) / 11, r))\n",
"print(pow(gen, (r - 1) / 198211423230930754013084525763697, r))\n",
"print(pow(gen, (r - 1) / 276602624281642239937218680557139826668747, r))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f4c58ca4",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.2",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

162
curve25519/scripts/g1.ipynb Normal file
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "f890e69f",
"metadata": {},
"outputs": [],
"source": [
"q = pow(2,255) - 19"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d90a7f0b",
"metadata": {},
"outputs": [],
"source": [
"A = 486662\n",
"B = 1"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "1b2aebc5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"486664\n",
"486660\n"
]
}
],
"source": [
"a = (A + 2) * 1\n",
"d = (A - 2) * 1\n",
"print(a)\n",
"print(d)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "aae2f8bf",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"9"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u = 9\n",
"u"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "ea9a4d90",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"14781619447589544791020593568409986887264606134616475288964881837755586237401"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v = mod(u^3 + A * u^2 + u, q).sqrt()\n",
"v"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "95895004",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38213832894368730265794714087330135568483813637251082400757400312561599933396"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"u * pow(v, -1, q) % q"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "1134cf74",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"46316835694926478169428394003475163141307993866256225615783033603165251855960"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(u - 1) * pow(u + 1, -1, q) % q"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ec089e21",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.2",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

14
curve25519/src/constraints/curves.rs Normal file
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use ark_r1cs_std::groups::curves::twisted_edwards::{AffineVar, MontgomeryAffineVar};
use crate::{constraints::FqVar, *};
/// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
pub type EdwardsVar = AffineVar<Curve25519Config, FqVar>;
/// A variable that is the R1CS equivalent of `crate::NonZeroMontgomeryAffine`.
pub type NonZeroMontgomeryVar = MontgomeryAffineVar<Curve25519Config, FqVar>;
#[test]
fn test() {
ark_curve_constraint_tests::curves::te_test::<Curve25519Config, EdwardsVar>().unwrap();
}

11
curve25519/src/constraints/fields.rs Normal file
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use ark_r1cs_std::fields::fp::FpVar;
use crate::Fq;
/// A variable that is the R1CS equivalent of `crate::Fq`.
pub type FqVar = FpVar<Fq>;
#[test]
fn test() {
ark_curve_constraint_tests::fields::field_test::<_, _, FqVar>().unwrap();
}

8
curve25519/src/constraints/mod.rs Normal file
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//! This module implements the R1CS equivalent of `ark_curve25519`.
//! It requires a curve that embeds curve25519.
mod curves;
mod fields;
pub use curves::*;
pub use fields::*;

71
curve25519/src/curves/mod.rs Normal file
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use crate::{Fq, Fr};
use ark_ec::{
models::CurveConfig,
twisted_edwards::{Affine, MontCurveConfig, MontgomeryAffine, Projective, TECurveConfig},
};
use ark_ff::MontFp;
#[cfg(test)]
mod tests;
pub type EdwardsAffine = Affine<Curve25519Config>;
pub type EdwardsProjective = Projective<Curve25519Config>;
pub type NonZeroMontgomeryAffine = MontgomeryAffine<Curve25519Config>;
#[derive(Clone, Default, PartialEq, Eq)]
pub struct Curve25519Config;
impl CurveConfig for Curve25519Config {
type BaseField = Fq;
type ScalarField = Fr;
/// COFACTOR = 8
const COFACTOR: &'static [u64] = &[8];
/// COFACTOR_INV (mod r) =
/// 2713877091499598330239944961141122840321418634767465352250731601857045344121
const COFACTOR_INV: Fr =
MontFp!("2713877091499598330239944961141122840321418634767465352250731601857045344121");
}
// We want to emphasize that this twisted Edwards curve is not ed25519.
// Ed25519 has COEFF_A = -1 and COEFF_D = -121665 / 121666.
impl TECurveConfig for Curve25519Config {
/// COEFF_A = 486664
const COEFF_A: Fq = MontFp!("486664");
/// COEFF_D = 486660
const COEFF_D: Fq = MontFp!("486660");
/// Standard generators from <https://neuromancer.sk/std/other/Curve25519>.
/// The Montgomery form is
/// x = 0x09,
/// y = 0x20ae19a1b8a086b4e01edd2c7748d14c923d4d7e6d7c61b229e9c5a27eced3d9
/// The twisted Edwards form is
/// x = 0x547c4350219f5e19dd26a3d6668b74346a8eb726eb2396e1228cfa397ffe6bd4
/// y = 0x6666666666666666666666666666666666666666666666666666666666666658
const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
type MontCurveConfig = Curve25519Config;
}
impl MontCurveConfig for Curve25519Config {
/// COEFF_A = 486662
const COEFF_A: Fq = MontFp!("486662");
/// COEFF_B = 1
const COEFF_B: Fq = MontFp!("1");
type TECurveConfig = Curve25519Config;
}
/// GENERATOR_X =
/// 38213832894368730265794714087330135568483813637251082400757400312561599933396
const GENERATOR_X: Fq =
MontFp!("38213832894368730265794714087330135568483813637251082400757400312561599933396");
/// GENERATOR_Y =
/// (4/5)
/// 46316835694926478169428394003475163141307993866256225615783033603165251855960
const GENERATOR_Y: Fq =
MontFp!("46316835694926478169428394003475163141307993866256225615783033603165251855960");

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curve25519/src/curves/tests.rs Normal file
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use crate::*;
use ark_algebra_test_templates::*;
test_group!(te; EdwardsProjective; te);

7
curve25519/src/fields/fq.rs Normal file
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use ark_ff::fields::{Fp256, MontBackend, MontConfig};
#[derive(MontConfig)]
#[modulus = "57896044618658097711785492504343953926634992332820282019728792003956564819949"]
#[generator = "2"]
pub struct FqConfig;
pub type Fq = Fp256<MontBackend<FqConfig, 4>>;

7
curve25519/src/fields/fr.rs Normal file
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use ark_ff::fields::{Fp256, MontBackend, MontConfig};
#[derive(MontConfig)]
#[modulus = "7237005577332262213973186563042994240857116359379907606001950938285454250989"]
#[generator = "2"]
pub struct FrConfig;
pub type Fr = Fp256<MontBackend<FrConfig, 4>>;

8
curve25519/src/fields/mod.rs Normal file
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mod fq;
mod fr;
pub use fq::*;
pub use fr::*;
#[cfg(test)]
mod tests;

5
curve25519/src/fields/tests.rs Normal file
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use crate::{Fq, Fr};
use ark_algebra_test_templates::*;
test_field!(fr; Fr; mont_prime_field);
test_field!(fq; Fq; mont_prime_field);

28
curve25519/src/lib.rs Executable file
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#![cfg_attr(not(feature = "std"), no_std)]
#![deny(
warnings,
unused,
future_incompatible,
nonstandard_style,
rust_2018_idioms
)]
#![forbid(unsafe_code)]
//! This library implements the curve25519 Montgomery curve.
//!
//! Curve information:
//! * Base field: q =
//! 57896044618658097711785492504343953926634992332820282019728792003956564819949
//! * Scalar field: r =
//! 7237005577332262213973186563042994240857116359379907606001950938285454250989
//! * Curve equation: B * y^2 = x^3 + A * x^2 + x, where
//! * A = 486662
//! * B = 1
#[cfg(feature = "r1cs")]
pub mod constraints;
mod curves;
mod fields;
pub use curves::*;
pub use fields::*;