Browse Source
Add the ed25519 curve (#121)
* add ed25519 curve * changelog * curve info * fix * cleanup the script * Update ed25519/src/curves/mod.rs * Update ed25519/src/curves/mod.rs Co-authored-by: onewayfunc <onewayfunc@gmail.com>cherry-pick
Weikeng Chen
1 year ago
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GitHub
GitHub
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GPG Key ID: 4AEE18F83AFDEB23
17 changed files with 548 additions and 0 deletions
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Diff Options
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+2 -0CHANGELOG.md
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+2 -0Cargo.toml
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+30 -0ed25519/Cargo.toml
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+1 -0ed25519/LICENSE-APACHE
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+1 -0ed25519/LICENSE-MIT
-
+91 -0ed25519/scripts/fr.ipynb
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+260 -0ed25519/scripts/g1.ipynb
-
+11 -0ed25519/src/constraints/curves.rs
-
+11 -0ed25519/src/constraints/fields.rs
-
+8 -0ed25519/src/constraints/mod.rs
-
+72 -0ed25519/src/curves/mod.rs
-
+4 -0ed25519/src/curves/tests.rs
-
+7 -0ed25519/src/fields/fq.rs
-
+7 -0ed25519/src/fields/fr.rs
-
+8 -0ed25519/src/fields/mod.rs
-
+5 -0ed25519/src/fields/tests.rs
-
+28 -0ed25519/src/lib.rs
@ -0,0 +1,30 @@ |
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[package] |
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name = "ark-ed25519" |
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version = "0.3.0" |
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authors = [ "arkworks contributors" ] |
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description = "The ed25519 twisted Edwards curve" |
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homepage = "https://arkworks.rs" |
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repository = "https://github.com/arkworks-rs/curves" |
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documentation = "https://docs.rs/ark-ed25519/" |
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keywords = ["cryptography", "finite-fields", "elliptic-curves" ] |
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categories = ["cryptography"] |
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include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"] |
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license = "MIT/Apache-2.0" |
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edition = "2021" |
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|
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[dependencies] |
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ark-ff = { version = "^0.3.0", default-features = false } |
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ark-ec = { version = "^0.3.0", default-features = false } |
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ark-std = { version = "^0.3.0", default-features = false } |
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ark-r1cs-std = { version = "^0.3.0", default-features = false, optional = true } |
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|
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[dev-dependencies] |
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ark-relations = { version = "^0.3.0", default-features = false } |
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ark-serialize = { version = "^0.3.0", default-features = false } |
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ark-algebra-test-templates = { version = "^0.3.0", default-features = false } |
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ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false } |
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|
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[features] |
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default = [] |
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std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ] |
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r1cs = [ "ark-r1cs-std" ] |
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@ -0,0 +1 @@ |
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../LICENSE-APACHE |
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@ -0,0 +1 @@ |
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../LICENSE-MIT |
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@ -0,0 +1,91 @@ |
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{ |
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"cells": [ |
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{ |
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"cell_type": "code", |
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"execution_count": 1, |
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"id": "04264893", |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"r = 7237005577332262213973186563042994240857116359379907606001950938285454250989" |
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] |
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|
}, |
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|
{ |
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|
"cell_type": "code", |
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|
"execution_count": 2, |
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|
"id": "1603b293", |
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|
"metadata": {}, |
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"outputs": [ |
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|
{ |
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"data": { |
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|
"text/plain": [ |
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|
"2^2 * 3 * 11 * 198211423230930754013084525763697 * 276602624281642239937218680557139826668747" |
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] |
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}, |
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|
"execution_count": 2, |
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|
"metadata": {}, |
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"output_type": "execute_result" |
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|
} |
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], |
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"source": [ |
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"factor(r - 1)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 3, |
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|
"id": "425ceac7", |
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"metadata": {}, |
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"outputs": [ |
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{ |
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"name": "stdout", |
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|
"output_type": "stream", |
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"text": [ |
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"7237005577332262213973186563042994240857116359379907606001950938285454250988\n", |
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|
"1570463851528226261927580272323658009530148727742783848239914322803198255651\n", |
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"4908983020090465803374304318106080751443647916949975825112097080460587568629\n", |
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"7119675135705137915307919240607293966034195415655343409829245710729128040338\n", |
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|
"2975531125133123119648879457563281269120703404158613135195788908093573672641\n" |
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] |
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} |
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], |
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"source": [ |
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"gen = 2\n", |
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"print(pow(gen, (r - 1) / 2, r))\n", |
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"print(pow(gen, (r - 1) / 3, r))\n", |
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"print(pow(gen, (r - 1) / 11, r))\n", |
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"print(pow(gen, (r - 1) / 198211423230930754013084525763697, r))\n", |
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"print(pow(gen, (r - 1) / 276602624281642239937218680557139826668747, r))" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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|
"id": "f4c58ca4", |
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|
"metadata": {}, |
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|
"outputs": [], |
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"source": [] |
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|
} |
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], |
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|
"metadata": { |
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|
"kernelspec": { |
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|
"display_name": "SageMath 9.2", |
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|
"language": "sage", |
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|
"name": "sagemath" |
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|
}, |
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"language_info": { |
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|
"codemirror_mode": { |
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"name": "ipython", |
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"version": 3 |
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|
}, |
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"file_extension": ".py", |
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"mimetype": "text/x-python", |
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"name": "python", |
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"nbconvert_exporter": "python", |
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"pygments_lexer": "ipython3", |
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"version": "3.9.7" |
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} |
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}, |
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"nbformat": 4, |
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"nbformat_minor": 5 |
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} |
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@ -0,0 +1,260 @@ |
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{ |
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"cells": [ |
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|
{ |
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|
"cell_type": "code", |
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|
"execution_count": 1, |
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|
"id": "f890e69f", |
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"metadata": {}, |
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"outputs": [], |
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"source": [ |
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"q = pow(2,255) - 19" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 2, |
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"id": "d90a7f0b", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
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|
"text/plain": [ |
||||
|
"37095705934669439343138083508754565189542113879843219016388785533085940283555" |
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|
] |
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|
}, |
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|
"execution_count": 2, |
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|
"metadata": {}, |
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|
"output_type": "execute_result" |
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|
} |
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|
], |
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|
"source": [ |
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"d = ((q - 1) * (121665 * pow(121666, -1, q)) % q)\n", |
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"d" |
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] |
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}, |
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|
{ |
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|
"cell_type": "code", |
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|
"execution_count": 3, |
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|
"id": "1b2aebc5", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
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|
"text/plain": [ |
||||
|
"46316835694926478169428394003475163141307993866256225615783033603165251855960" |
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|
] |
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|
}, |
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|
"execution_count": 3, |
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|
"metadata": {}, |
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|
"output_type": "execute_result" |
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|
} |
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], |
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"source": [ |
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|
"y = 4 * pow(5, -1, q) % q\n", |
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"y" |
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] |
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}, |
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{ |
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|
"cell_type": "code", |
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|
"execution_count": 4, |
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|
"id": "aae2f8bf", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
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|
"text/plain": [ |
||||
|
"15112221349535400772501151409588531511454012693041857206046113283949847762202" |
||||
|
] |
||||
|
}, |
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|
"execution_count": 4, |
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|
"metadata": {}, |
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|
"output_type": "execute_result" |
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|
} |
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|
], |
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|
"source": [ |
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|
"x = 0x216936D3CD6E53FEC0A4E231FDD6DC5C692CC7609525A7B2C9562D608F25D51A\n", |
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|
"x" |
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|
] |
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|
}, |
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|
{ |
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|
"cell_type": "code", |
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|
"execution_count": 5, |
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|
"id": "ea9a4d90", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
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|
"text/plain": [ |
||||
|
"26187595835145689230469591415084376402084551887632582719101735842039498021991" |
||||
|
] |
||||
|
}, |
||||
|
"execution_count": 5, |
||||
|
"metadata": {}, |
||||
|
"output_type": "execute_result" |
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|
} |
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|
], |
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|
"source": [ |
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|
"x_squared = x^2 % q\n", |
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"x_squared" |
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] |
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|
}, |
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|
{ |
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|
"cell_type": "code", |
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|
"execution_count": 6, |
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|
"id": "3499c817", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
||||
|
"text/plain": [ |
||||
|
"37053468555941182535542715202780130513046395093004980492626426882532201484768" |
||||
|
] |
||||
|
}, |
||||
|
"execution_count": 6, |
||||
|
"metadata": {}, |
||||
|
"output_type": "execute_result" |
||||
|
} |
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|
], |
||||
|
"source": [ |
||||
|
"y_squared = y^2 % q\n", |
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|
"y_squared" |
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|
] |
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|
}, |
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|
{ |
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|
"cell_type": "code", |
||||
|
"execution_count": 7, |
||||
|
"id": "d9617d2d", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
||||
|
"text/plain": [ |
||||
|
"10865872720795493305073123787695754110961843205372397773524691040492703462777" |
||||
|
] |
||||
|
}, |
||||
|
"execution_count": 7, |
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|
"metadata": {}, |
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"output_type": "execute_result" |
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|
} |
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], |
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"source": [ |
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"((q - 1) * x_squared + y_squared) % q" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": 8, |
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|
"id": "ece46a74", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
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|
"text/plain": [ |
||||
|
"10865872720795493305073123787695754110961843205372397773524691040492703462777" |
||||
|
] |
||||
|
}, |
||||
|
"execution_count": 8, |
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|
"metadata": {}, |
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|
"output_type": "execute_result" |
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|
} |
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], |
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|
"source": [ |
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|
"((d * x_squared * y_squared) % q + 1) % q" |
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] |
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|
}, |
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|
{ |
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|
"cell_type": "code", |
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|
"execution_count": 9, |
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|
"id": "b430f926", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
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|
"text/plain": [ |
||||
|
"21711016731996786641919559689128982722488122124807605757398297001483711807481" |
||||
|
] |
||||
|
}, |
||||
|
"execution_count": 9, |
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|
"metadata": {}, |
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"output_type": "execute_result" |
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|
} |
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], |
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"source": [ |
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"pow(8, -1, q)" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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|
"execution_count": 10, |
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|
"id": "d8575e54", |
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|
"metadata": {}, |
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|
"outputs": [ |
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{ |
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"data": { |
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|
"text/plain": [ |
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|
"486662" |
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|
] |
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|
}, |
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|
"execution_count": 10, |
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|
"metadata": {}, |
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|
"output_type": "execute_result" |
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} |
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], |
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"source": [ |
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"A = 2 * (-1 + d) / (-1 - d)\n", |
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"A" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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|
"execution_count": 11, |
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"id": "2ee580a3", |
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|
"metadata": {}, |
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|
"outputs": [ |
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|
{ |
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|
"data": { |
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|
"text/plain": [ |
||||
|
"57896044618658097711785492504343953926634992332820282019728792003956564333285" |
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|
] |
||||
|
}, |
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|
"execution_count": 11, |
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|
"metadata": {}, |
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"output_type": "execute_result" |
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|
} |
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|
], |
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"source": [ |
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"B = 4 / (-1 - d)\n", |
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"B" |
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] |
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}, |
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{ |
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"cell_type": "code", |
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"execution_count": null, |
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|
"id": "ec089e21", |
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|
"metadata": {}, |
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|
"outputs": [], |
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|
"source": [] |
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|
} |
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|
], |
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"metadata": { |
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"kernelspec": { |
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"display_name": "SageMath 9.2", |
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"language": "sage", |
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"name": "sagemath" |
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}, |
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"language_info": { |
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"codemirror_mode": { |
||||
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"name": "ipython", |
||||
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"version": 3 |
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|
}, |
||||
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"file_extension": ".py", |
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"mimetype": "text/x-python", |
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"name": "python", |
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"nbconvert_exporter": "python", |
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|
"pygments_lexer": "ipython3", |
||||
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"version": "3.9.7" |
||||
|
} |
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|
}, |
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|
"nbformat": 4, |
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"nbformat_minor": 5 |
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} |
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@ -0,0 +1,11 @@ |
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use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;
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use crate::{constraints::FqVar, *};
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/// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
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pub type EdwardsVar = AffineVar<EdwardsParameters, FqVar>;
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#[test]
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fn test() {
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ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
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}
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@ -0,0 +1,11 @@ |
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use ark_r1cs_std::fields::fp::FpVar;
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use crate::Fq;
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/// A variable that is the R1CS equivalent of `crate::Fq`.
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pub type FqVar = FpVar<Fq>;
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|
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#[test]
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fn test() {
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ark_curve_constraint_tests::fields::field_test::<_, _, FqVar>().unwrap();
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}
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@ -0,0 +1,8 @@ |
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//! This module implements the R1CS equivalent of `ark_ed25519`.
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//! It requires a curve that embeds ed25519.
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|
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mod curves;
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mod fields;
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pub use curves::*;
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pub use fields::*;
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@ -0,0 +1,72 @@ |
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use crate::{Fq, Fr};
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use ark_ec::{
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models::CurveConfig,
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twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
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};
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use ark_ff::MontFp;
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#[cfg(test)]
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mod tests;
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pub type EdwardsAffine = Affine<EdwardsParameters>;
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pub type EdwardsProjective = Projective<EdwardsParameters>;
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#[derive(Clone, Default, PartialEq, Eq)]
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pub struct EdwardsParameters;
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impl CurveConfig for EdwardsParameters {
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type BaseField = Fq;
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type ScalarField = Fr;
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|
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/// COFACTOR = 8
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const COFACTOR: &'static [u64] = &[8];
|
||||
|
|
||||
|
/// COFACTOR_INV (mod r) =
|
||||
|
/// 2713877091499598330239944961141122840321418634767465352250731601857045344121
|
||||
|
const COFACTOR_INV: Fr =
|
||||
|
MontFp!("2713877091499598330239944961141122840321418634767465352250731601857045344121");
|
||||
|
}
|
||||
|
|
||||
|
impl TECurveConfig for EdwardsParameters {
|
||||
|
/// COEFF_A = -1
|
||||
|
const COEFF_A: Fq = MontFp!("-1");
|
||||
|
|
||||
|
/// COEFF_D = -121665 / 121666
|
||||
|
const COEFF_D: Fq =
|
||||
|
MontFp!("37095705934669439343138083508754565189542113879843219016388785533085940283555");
|
||||
|
|
||||
|
/// Standard generators from <https://neuromancer.sk/std/other/Ed25519>.
|
||||
|
const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
|
||||
|
|
||||
|
type MontCurveConfig = EdwardsParameters;
|
||||
|
|
||||
|
/// Multiplication by `a` is just negation.
|
||||
|
#[inline(always)]
|
||||
|
fn mul_by_a(elem: Self::BaseField) -> Self::BaseField {
|
||||
|
-elem
|
||||
|
}
|
||||
|
}
|
||||
|
|
||||
|
// We want to emphasize that this Montgomery curve is not Curve25519.
|
||||
|
impl MontCurveConfig for EdwardsParameters {
|
||||
|
/// COEFF_A = 486662
|
||||
|
const COEFF_A: Fq = MontFp!("486662");
|
||||
|
|
||||
|
/// COEFF_B = 57896044618658097711785492504343953926634992332820282019728792003956564333285
|
||||
|
/// This is not one, because ed25519 != curve25519
|
||||
|
const COEFF_B: Fq =
|
||||
|
MontFp!("57896044618658097711785492504343953926634992332820282019728792003956564333285");
|
||||
|
|
||||
|
type TECurveConfig = EdwardsParameters;
|
||||
|
}
|
||||
|
|
||||
|
/// GENERATOR_X =
|
||||
|
/// 15112221349535400772501151409588531511454012693041857206046113283949847762202
|
||||
|
const GENERATOR_X: Fq =
|
||||
|
MontFp!("15112221349535400772501151409588531511454012693041857206046113283949847762202");
|
||||
|
|
||||
|
/// GENERATOR_Y =
|
||||
|
/// (4/5)
|
||||
|
/// 46316835694926478169428394003475163141307993866256225615783033603165251855960
|
||||
|
const GENERATOR_Y: Fq =
|
||||
|
MontFp!("46316835694926478169428394003475163141307993866256225615783033603165251855960");
|
||||
@ -0,0 +1,4 @@ |
|||||
|
use crate::*;
|
||||
|
use ark_algebra_test_templates::*;
|
||||
|
|
||||
|
test_group!(te; EdwardsProjective; te);
|
||||
@ -0,0 +1,7 @@ |
|||||
|
use ark_ff::fields::{Fp256, MontBackend, MontConfig};
|
||||
|
|
||||
|
#[derive(MontConfig)]
|
||||
|
#[modulus = "57896044618658097711785492504343953926634992332820282019728792003956564819949"]
|
||||
|
#[generator = "2"]
|
||||
|
pub struct FqConfig;
|
||||
|
pub type Fq = Fp256<MontBackend<FqConfig, 4>>;
|
||||
@ -0,0 +1,7 @@ |
|||||
|
use ark_ff::fields::{Fp256, MontBackend, MontConfig};
|
||||
|
|
||||
|
#[derive(MontConfig)]
|
||||
|
#[modulus = "7237005577332262213973186563042994240857116359379907606001950938285454250989"]
|
||||
|
#[generator = "2"]
|
||||
|
pub struct FrConfig;
|
||||
|
pub type Fr = Fp256<MontBackend<FrConfig, 4>>;
|
||||
@ -0,0 +1,8 @@ |
|||||
|
mod fq;
|
||||
|
mod fr;
|
||||
|
|
||||
|
pub use fq::*;
|
||||
|
pub use fr::*;
|
||||
|
|
||||
|
#[cfg(test)]
|
||||
|
mod tests;
|
||||
@ -0,0 +1,5 @@ |
|||||
|
use crate::{Fq, Fr};
|
||||
|
use ark_algebra_test_templates::*;
|
||||
|
|
||||
|
test_field!(fr; Fr; mont_prime_field);
|
||||
|
test_field!(fq; Fq; mont_prime_field);
|
||||
@ -0,0 +1,28 @@ |
|||||
|
#![cfg_attr(not(feature = "std"), no_std)]
|
||||
|
#![deny(
|
||||
|
warnings,
|
||||
|
unused,
|
||||
|
future_incompatible,
|
||||
|
nonstandard_style,
|
||||
|
rust_2018_idioms
|
||||
|
)]
|
||||
|
#![forbid(unsafe_code)]
|
||||
|
|
||||
|
//! This library implements the ed25519 twisted Edwards curve.
|
||||
|
//!
|
||||
|
//! Curve information:
|
||||
|
//! * Base field: q =
|
||||
|
//! 57896044618658097711785492504343953926634992332820282019728792003956564819949
|
||||
|
//! * Scalar field: r =
|
||||
|
//! 7237005577332262213973186563042994240857116359379907606001950938285454250989
|
||||
|
//! * Curve equation: ax^2 + y^2 =1 + dx^2y^2, where
|
||||
|
//! * a = -1
|
||||
|
//! * d = -121665 / 121666
|
||||
|
|
||||
|
#[cfg(feature = "r1cs")]
|
||||
|
pub mod constraints;
|
||||
|
mod curves;
|
||||
|
mod fields;
|
||||
|
|
||||
|
pub use curves::*;
|
||||
|
pub use fields::*;
|
||||