Initial commit

ed_on_mnt4_298/Cargo.toml

@@ -0,0 +1,29 @@
+[package]
+name = "ark-ed-on-mnt4-298"
+version = "0.1.0"
+authors = [ "arkworks contributors" ]
+description = "A Twisted Edwards curve defined over the scalar field of the MNT4-298 curve"
+homepage = "https://arworks.rs"
+repository = "https://github.com/arkworks/algebra"
+documentation = "https://docs.rs/ark-ed-on-mnt4-298/"
+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"
+
+[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-mnt4-298 = { path = "../mnt4_298", default-features = false, features = [ "scalar_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"
+
+[features]
+default = []
+std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-mnt4-298/std" ]

ed_on_mnt4_298/src/curves/mod.rs

@@ -0,0 +1,139 @@
+use ark_ec::{
+    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
+    twisted_edwards_extended::{GroupAffine, GroupProjective},
+};
+use ark_ff::{biginteger::BigInteger320, field_new};
+
+use crate::{fq::Fq, fr::Fr};
+
+#[cfg(test)]
+mod tests;
+
+pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
+pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct EdwardsParameters;
+
+impl ModelParameters for EdwardsParameters {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+}
+
+// Many parameters need to be written down in the Montgomery residue form,
+// discussed below. Some useful numbers:
+// R for Fq: 223364648326281414938801705359223029554923725549792420683051274872200260503540791531766876
+// R for Fr: 104384076783966083500464392945960916666734135485183910065100558776489954102951241798239545
+
+impl TEModelParameters for EdwardsParameters {
+    /// COEFF_A = -1
+    /// Needs to be in the Montgomery residue form in Fq
+    /// I.e., -1 * R for Fq
+    ///     = 252557637842979910814547544293825421990201153003031094870216460866964386803867699028196261
+    #[rustfmt::skip]
+    const COEFF_A: Fq = field_new!(Fq, BigInteger320([
+        17882590928154426277u64,
+        6901912683734848330u64,
+        364575608937879866u64,
+        8740893163049517815u64,
+        2181130330288u64,
+    ]));
+
+    /// COEFF_D = 4212
+    /// Needs to be in the Montgomery residue form in Fq
+    /// I.e., 4212 * R for Fq
+    ///     = 389461279836940033614665658623660232171971995346409183754923941118154161474636585314923000
+    #[rustfmt::skip]
+    const COEFF_D: Fq = field_new!(Fq, BigInteger320([
+        8040159930071495160u64,
+        16503302848883893212u64,
+        4541498709509651666u64,
+        11429056610118256373u64,
+        3363453258354u64,
+    ]));
+
+    /// COFACTOR = 4
+    const COFACTOR: &'static [u64] = &[4];
+
+    /// COFACTOR_INV (mod r) =
+    /// 29745142885578832859584328103315528221570304936126890280067991221921526670592508030983158
+    /// Needs to be in the Montgomery residue form in Fr
+    /// I.e., 29745142885578832859584328103315528221570304936126890280067991221921526670592508030983158 * R for Fr
+    ///     = 55841162081570353734700426339805757388253838807422867796343130916044015196330318480543044
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger320([
+        6539529304383425860u64,
+        7567022062893857598u64,
+        17399624368177871129u64,
+        14575354999847441509u64,
+        482253688048u64,
+    ]));
+
+    /// Generated randomly
+    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
+
+    type MontgomeryModelParameters = EdwardsParameters;
+
+    /// Multiplication by `a` is just negation.
+    #[inline(always)]
+    fn mul_by_a(elem: &Self::BaseField) -> Self::BaseField {
+        -*elem
+    }
+}
+
+impl MontgomeryModelParameters for EdwardsParameters {
+    /// COEFF_A = 203563247015667910991582090642011229452721346107806307863040223071914240315202967004285204
+    /// Needs to be in the Montgomery residue form in Fq
+    /// I.e., 203563247015667910991582090642011229452721346107806307863040223071914240315202967004285204 * R for Fq
+    ///     = 184958108588233737086787169006685138672129232027042887479256778022373554352621152610883766
+    #[rustfmt::skip]
+    const COEFF_A: Fq = field_new!(Fq, BigInteger320([
+        13866101745789245622u64,
+        14126297534943667090u64,
+        11307578615387704385u64,
+        8263080598809044705u64,
+        1597329401399u64,
+    ]));
+    /// COEFF_B = 272359039153593414761767159011037222092403532445017207690227512667250406992205523555677931
+    /// Needs to be in the Montgomery residue form in Fq
+    //  I.e., 272359039153593414761767159011037222092403532445017207690227512667250406992205523555677931 * R for Fq
+    //      = 320157167097726084542307919580965705308273073979019302261176143711555219255114245445508756
+    #[rustfmt::skip]
+    const COEFF_B: Fq = field_new!(Fq, BigInteger320([
+        3452336036810055316u64,
+        18124271906235581187u64,
+        7868316676197606962u64,
+        9218705727289990924u64,
+        2764931259177u64,
+    ]));
+
+    type TEModelParameters = EdwardsParameters;
+}
+
+/// GENERATOR_X =
+/// 282406820114868156776872298252698015906762052916420164316497572033519876761239463633892227
+/// Needs to be in the Montgomery residue form in Fq
+/// I.e., 282406820114868156776872298252698015906762052916420164316497572033519876761239463633892227 * R for Fq
+///     = 6917556742108450905978293995070573074174231920036503115659104908111915200040057661385715
+#[rustfmt::skip]
+const GENERATOR_X: Fq = field_new!(Fq, BigInteger320([
+    797921980254612467u64,
+    14323677897559322103u64,
+    16879595040064082265u64,
+    5138786402348661261u64,
+    59741186014u64,
+]));
+
+/// GENERATOR_Y =
+/// 452667754940241021433619311795265643711152068500301853535337412655162600774122192283142703
+/// Needs to be in the Montgomery residue form in Fq
+/// I.e., 452667754940241021433619311795265643711152068500301853535337412655162600774122192283142703 * R for Fq
+///     = 411219337323952690830344109182130393590959634960952808951091963301565250764467583592890490
+#[rustfmt::skip]
+const GENERATOR_Y: Fq = field_new!(Fq, BigInteger320([
+    16522567711648317562u64,
+    4273808507945498262u64,
+    17459848913470201097u64,
+    16519670308098023011u64,
+    3551359510243u64,
+]));

ed_on_mnt4_298/src/curves/tests.rs

@@ -0,0 +1,63 @@
+use ark_ec::{AffineCurve, ProjectiveCurve};
+use ark_ff::test_rng;
+use rand::Rng;
+
+use crate::*;
+
+use ark_curve_tests::{curves::*, groups::*};
+
+#[test]
+fn test_projective_curve() {
+    curve_tests::<EdwardsProjective>();
+
+    edwards_tests::<EdwardsParameters>();
+}
+
+#[test]
+fn test_projective_group() {
+    let mut rng = test_rng();
+    let a = rng.gen();
+    let b = rng.gen();
+
+    for _i in 0..100 {
+        group_test::<EdwardsProjective>(a, b);
+    }
+}
+
+#[test]
+fn test_affine_group() {
+    let mut rng = test_rng();
+    let a: EdwardsAffine = rng.gen();
+    let b: EdwardsAffine = rng.gen();
+    for _i in 0..100 {
+        group_test::<EdwardsAffine>(a, b);
+    }
+}
+
+#[test]
+fn test_generator() {
+    let generator = EdwardsAffine::prime_subgroup_generator();
+    assert!(generator.is_on_curve());
+    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+}
+
+#[test]
+fn test_conversion() {
+    let mut rng = test_rng();
+    let a: EdwardsAffine = rng.gen();
+    let b: EdwardsAffine = rng.gen();
+    let a_b = {
+        use ark_ec::group::Group;
+        (a + &b).double().double()
+    };
+    let a_b2 = (a.into_projective() + &b.into_projective())
+        .double()
+        .double();
+    assert_eq!(a_b, a_b2.into_affine());
+    assert_eq!(a_b.into_projective(), a_b2);
+}
+
+#[test]
+fn test_montgomery_conversion() {
+    montgomery_conversion_test::<EdwardsParameters>();
+}

ed_on_mnt4_298/src/fields/fq.rs

@@ -0,0 +1 @@
+pub use ark_mnt4_298::{Fr as Fq, FrParameters as FqParameters};

ed_on_mnt4_298/src/fields/fr.rs

@@ -0,0 +1,127 @@
+use ark_ff::{
+    biginteger::BigInteger320 as BigInteger,
+    fields::{FftParameters, Fp320, Fp320Parameters, FpParameters},
+};
+
+pub type Fr = Fp320<FrParameters>;
+
+pub struct FrParameters;
+
+impl Fp320Parameters for FrParameters {}
+impl FftParameters for FrParameters {
+    type BigInt = BigInteger;
+
+    const TWO_ADICITY: u32 = 1u32;
+
+    // ROOT_OF_UNITY = GENERATOR ^ t =
+    // 118980571542315331438337312413262112886281219744507561120271964887686106682370032123932630
+    // t is defined below
+    // This number needs to be in the Montgomery residue form.
+    // I.e., write
+    // 118980571542315331438337312413262112886281219744507561120271964887686106682370032123932630
+    // * R
+    // = 14596494758349247937872919467301196219547084259323651055171406111196152579418790325693086
+    #[rustfmt::skip]
+    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
+        4913018085921565342u64,
+        18164325898792356216u64,
+        11499902056485864693u64,
+        12113224729248979119u64,
+        126057789046u64,
+    ]);
+}
+impl FpParameters for FrParameters {
+    // MODULUS = 118980571542315331438337312413262112886281219744507561120271964887686106682370032123932631
+    // Factors of MODULUS - 1:
+    //      2
+    //      5
+    //      17
+    //      47
+    //      3645289
+    //      42373926857
+    //      96404785755712297250936212793128201320333033128042968811755970858369
+    #[rustfmt::skip]
+    const MODULUS: BigInteger = BigInteger([
+        15535567651727634391u64,
+        14992835038329117496u64,
+        12879083654034347181u64,
+        16760578290609820963u64,
+        1027536270620u64,
+    ]);
+
+    const MODULUS_BITS: u32 = 296;
+
+    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
+
+    const REPR_SHAVE_BITS: u32 = 24;
+
+    // see ark-ff/src/fields/mod.rs for more information
+    // R = pow(2,320) %
+    // 118980571542315331438337312413262112886281219744507561120271964887686106682370032123932631
+    // R = 104384076783966083500464392945960916666734135485183910065100558776489954102951241798239545
+    #[rustfmt::skip]
+    const R: BigInteger = BigInteger([
+        10622549565806069049u64,
+        15275253213246312896u64,
+        1379181597548482487u64,
+        4647353561360841844u64,
+        901478481574u64
+    ]);
+
+    // R2 = R * R %
+    // 118980571542315331438337312413262112886281219744507561120271964887686106682370032123932631
+    // R2 = 64940318866745953005690402896764745514897573584912026577721076893188083397226247459368768
+    #[rustfmt::skip]
+    const R2: BigInteger = BigInteger([
+        16858329796171722560u64,
+        12060416575249219689u64,
+        17034911964548502611u64,
+        14718631438675169669u64,
+        560835539754u64
+    ]);
+
+    // INV = -(118980571542315331438337312413262112886281219744507561120271964887686106682370032123932631)^(-1) % 2^64
+    const INV: u64 = 9223688842165816345u64;
+
+    // GENERATOR = 7
+    // This number needs to be in the Montgomery residue form.
+    // I.e., write 7 * R =
+    // 16805108233870595873226876142153739349451629929242003734072122109313038626438499844081029
+    #[rustfmt::skip]
+    const GENERATOR: BigInteger = BigInteger([
+        18037929197695780229u64,
+        16969762262749485294u64,
+        6166745553471500787u64,
+        5754981480705173590u64,
+        145131747294u64,
+    ]);
+
+    // (n-1)/2 = 59490285771157665719168656206631056443140609872253780560135982443843053341185016061966315
+    #[rustfmt::skip]
+    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        7767783825863817195u64,
+        16719789556019334556u64,
+        15662913863871949398u64,
+        8380289145304910481u64,
+        513768135310u64,
+    ]);
+
+    // t = (n - 1) / 2^{TWO_ADICITY} =
+    // 59490285771157665719168656206631056443140609872253780560135982443843053341185016061966315
+    const T: BigInteger = BigInteger([
+        7767783825863817195u64,
+        16719789556019334556u64,
+        15662913863871949398u64,
+        8380289145304910481u64,
+        513768135310u64,
+    ]);
+
+    // (t-1)/2 = 29745142885578832859584328103315528221570304936126890280067991221921526670592508030983157
+    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        3883891912931908597u64,
+        8359894778009667278u64,
+        17054828968790750507u64,
+        4190144572652455240u64,
+        256884067655u64,
+    ]);
+}

ed_on_mnt4_298/src/fields/mod.rs

@@ -0,0 +1,8 @@
+pub mod fq;
+pub mod fr;
+
+pub use fq::*;
+pub use fr::*;
+
+#[cfg(all(feature = "ed_on_mnt4_298", test))]
+mod tests;

ed_on_mnt4_298/src/fields/tests.rs

@@ -0,0 +1,24 @@
+use ark_ff::test_rng;
+use rand::Rng;
+
+use crate::fields::*;
+
+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);
+    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>();
+}

ed_on_mnt4_298/src/lib.rs

@@ -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 a twisted Edwards curve whose base field is the scalar field of the
+//! curve MNT4-298. This allows defining cryptographic primitives that use elliptic curves over
+//! the scalar field of the latter curve.
+//!
+//! Curve information:
+//! * Base field: q = 475922286169261325753349249653048451545124878552823515553267735739164647307408490559963137
+//! * Scalar field: r = 118980571542315331438337312413262112886281219744507561120271964887686106682370032123932631
+//! * Valuation(q - 1, 2) = 30
+//! * Valuation(r - 1, 2) = 1
+//! * Curve equation: ax^2 + y^2 =1 + dx^2y^2, where
+//!    * a = -1
+//!    * d = 4212 mod q
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

ed_on_mnt4_298/src/mod.rs

@@ -0,0 +1,5 @@
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;