Merge branch 'master' into releases

CHANGELOG.md

@@ -22,7 +22,8 @@
 - [\#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.
-
+- [\#141](https://github.com/arkworks-rs/curves/pull/103) Faster cofactor clearing for BLS12-377.
+- [\#138](https://github.com/arkworks-rs/curves/pull/138) Implement WB Hash-to-Curve for bls12-381 and bls12-377
 
 ### Bug fixes
 

Cargo.toml

@@ -31,6 +31,8 @@ members = [
     "vesta",
 
     "secp256k1",
+    "secp256r1",
+    "secp384r1",
     "secq256k1",
     
     "curve25519",

bls12_377/Cargo.toml

@@ -24,6 +24,7 @@ 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 }
+sha2 = { version = "0.10", default-features = false }
 
 [features]
 default = [ "curve" ]

bls12_377/src/curves/g1.rs

@@ -1,15 +1,24 @@
-use ark_ec::models::{
-    short_weierstrass::{Affine as SWAffine, SWCurveConfig},
-    twisted_edwards::{
-        Affine as TEAffine, MontCurveConfig, Projective as TEProjective, TECurveConfig,
+use ark_ec::{
+    bls12,
+    bls12::Bls12Config,
+    hashing::curve_maps::wb::{IsogenyMap, WBConfig},
+    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 ark_ff::{Field, MontFp, PrimeField, Zero};
+use ark_std::{ops::Neg, One};
 
+use super::g1_swu_iso::{SwuIsoConfig, ISOGENY_MAP_TO_G1};
 use crate::{Fq, Fr};
 
+pub type G1Affine = bls12::G1Affine<crate::Config>;
+pub type G1Projective = bls12::G1Projective<crate::Config>;
+
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Config;
 
@@ -39,6 +48,20 @@ impl SWCurveConfig for Config {
     fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
+
+    #[inline]
+    fn clear_cofactor(p: &G1SWAffine) -> G1SWAffine {
+        // Using the effective cofactor.
+        //
+        // It is enough to multiply by (x - 1), instead of (x - 1)^2 / 3
+        let h_eff = x_minus_one().into_bigint();
+        <Config as SWCurveConfig>::mul_affine(p, h_eff.as_ref()).into()
+    }
+}
+
+fn x_minus_one() -> Fr {
+    const X: Fr = Fr::from_sign_and_limbs(!crate::Config::X_IS_NEGATIVE, crate::Config::X);
+    X - Fr::one()
 }
 
 pub type G1SWAffine = SWAffine<Config>;
@@ -158,6 +181,12 @@ pub const G1_GENERATOR_X: Fq = MontFp!("8193799937315096423993825557346594823998
 /// 241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030
 pub const G1_GENERATOR_Y: Fq = MontFp!("241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030");
 
+impl WBConfig for Config {
+    type IsogenousCurve = SwuIsoConfig;
+
+    const ISOGENY_MAP: IsogenyMap<'static, Self::IsogenousCurve, Self> = ISOGENY_MAP_TO_G1;
+}
+
 // The generator for twisted Edward form is the same SW generator converted into
 // the normalized TE form (TE2).
 //``` sage
@@ -209,3 +238,34 @@ pub const TE_GENERATOR_X: Fq = MontFp!("7122256953170913722937026889632370569028
 /// TE_GENERATOR_Y =
 /// 6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235
 pub const TE_GENERATOR_Y: Fq = MontFp!("6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235");
+
+#[cfg(test)]
+mod test {
+
+    use super::*;
+    use crate::g1;
+    use ark_std::{rand::Rng, UniformRand};
+
+    fn sample_unchecked() -> SWAffine<g1::Config> {
+        let mut rng = ark_std::test_rng();
+        loop {
+            let x = Fq::rand(&mut rng);
+            let greatest = rng.gen();
+
+            if let Some(p) = SWAffine::get_point_from_x_unchecked(x, greatest) {
+                return p;
+            }
+        }
+    }
+
+    #[test]
+    fn test_cofactor_clearing() {
+        const SAMPLES: usize = 100;
+        for _ in 0..SAMPLES {
+            let p: SWAffine<g1::Config> = sample_unchecked();
+            let p = <Config as SWCurveConfig>::clear_cofactor(&p);
+            assert!(p.is_on_curve());
+            assert!(p.is_in_correct_subgroup_assuming_on_curve());
+        }
+    }
+}

bls12_377/src/curves/g1_swu_iso.rs

@@ -0,0 +1,107 @@
+use ark_ec::{
+    hashing::curve_maps::{swu::SWUConfig, wb::IsogenyMap},
+    models::{
+        short_weierstrass::{Affine, SWCurveConfig},
+        CurveConfig,
+    },
+};
+
+use ark_ff::MontFp;
+
+use crate::{g1, Fq, Fr};
+
+type G1Affine = Affine<SwuIsoConfig>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct SwuIsoConfig;
+
+impl CurveConfig for SwuIsoConfig {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = (x - 1)^2 / 3  = iso_G1.domain().order() /
+    /// 8444461749428370424248824938781546531375899335154063827935233455917409239041
+    //  30631250834960419227450344600217059328
+    const COFACTOR: &'static [u64] = &[0x0, 0x170b5d4430000000];
+
+    /// COFACTOR_INV = COFACTOR^{-1} mod r
+    /// = 5285428838741532253824584287042945485047145357130994810877
+    const COFACTOR_INV: Fr = MontFp!("5285428838741532253824584287042945485047145357130994810877");
+}
+
+// sage: iso_G1
+// Isogeny of degree 2 from Elliptic Curve defined by y^2 = x^3 +
+// 258664426012969092796408009721202742408018065645352501567204841856062976176281513834280849065051431927238430294002*
+// x + 22 over Finite Field of size
+// 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+// to Elliptic Curve defined by y^2 = x^3 + 1 over Finite Field of size
+// 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+
+impl SWCurveConfig for SwuIsoConfig {
+    /// COEFF_A
+    const COEFF_A: Fq = MontFp!("258664426012969092796408009721202742408018065645352501567204841856062976176281513834280849065051431927238430294002");
+
+    /// COEFF_B
+    const COEFF_B: Fq = MontFp!("22");
+
+    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
+}
+
+// sage: G1_gen  = iso_G1.domain().random_point()
+// sage: G1_gen = 30631250834960419227450344600217059328* G1_gen
+// sage: G1_gen.order() ==
+// 8444461749428370424248824938781546531375899335154063827935233455917409239041
+// True
+// sage: G1_gen
+// (183898640136580512316530045470998831691790391453237259434516336279447756609241220664846162561503820562316877867830 : 69018534046895515891776145953191511526693172354818719412306559690461416836925400134233128432719372819569406562974 : 1)
+/// G1_GENERATOR_X =
+/// 183898640136580512316530045470998831691790391453237259434516336279447756609241220664846162561503820562316877867830
+pub const G1_GENERATOR_X: Fq = MontFp!("183898640136580512316530045470998831691790391453237259434516336279447756609241220664846162561503820562316877867830");
+
+/// G1_GENERATOR_Y =
+/// 69018534046895515891776145953191511526693172354818719412306559690461416836925400134233128432719372819569406562974
+pub const G1_GENERATOR_Y: Fq = MontFp!("69018534046895515891776145953191511526693172354818719412306559690461416836925400134233128432719372819569406562974");
+
+impl SWUConfig for SwuIsoConfig {
+    const ZETA: Fq = MontFp!("-11"); // arbitatry primitive root of unity (element)
+}
+
+pub const ISOGENY_MAP_TO_G1 : IsogenyMap<'_, SwuIsoConfig, g1::Config, > = IsogenyMap {
+    x_map_numerator : &[
+        MontFp!("193998319509726820447277314072485610595876362210707887456279225959507476652652651634192264150953923683470146535424"), 
+        MontFp!("40474824132456359704279181570318738632422647360355249739068643631356267969150730939906729705473"), 
+        MontFp!("193998319509726820507989550271170150152295134566185995404913197000040351261255617081226666104680020093330241093633"),
+    ],
+
+    x_map_denominator : &[
+        MontFp!("161899296529825438817116726281274954529690589441420998956274574525425071876602923759626918821892"), 
+        MontFp!("1"),
+    ],
+
+    y_map_numerator : &[
+        MontFp!("193998319509726820507989550271170150152295134566185995404913197000040351261255617081226666104680020093330241093631"), 
+        MontFp!("32333053251621136903112182208573040583096119983059602439070460434672245065050016464457115901761911040205276577794"), 
+        MontFp!("129332213006484547066038603046131306324615528732935438218576102373893108782773376834518846023512776472080255287298"), 
+        MontFp!("226331372761347957259321141983031841844344323660550327972398729833380409804798219928097777122126690108885281275905"),
+    ],
+
+    y_map_denominator : &[
+        MontFp!("258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458169"), 
+        MontFp!("971395779178952632902700357687649727178143536648525993737647447152550431259617542557761512931340"), 
+        MontFp!("485697889589476316451350178843824863589071768324262996868823723576275215629808771278880756465676"), 
+        MontFp!("1"),
+    ],
+};
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_gen() {
+        let gen: G1Affine = SwuIsoConfig::GENERATOR;
+        assert!(gen.is_on_curve());
+        assert!(gen.is_in_correct_subgroup_assuming_on_curve());
+    }
+}

bls12_377/src/curves/g2.rs

@@ -1,12 +1,22 @@
 use ark_ec::{
-    models::{short_weierstrass::SWCurveConfig, CurveConfig},
-    short_weierstrass::Affine,
+    bls12,
+    bls12::Bls12Config,
+    hashing::curve_maps::wb::{IsogenyMap, WBConfig},
+    models::CurveConfig,
+    short_weierstrass::{Affine, Projective, SWCurveConfig},
+    AffineRepr, CurveGroup, Group,
 };
+
 use ark_ff::{Field, MontFp, Zero};
+use ark_std::ops::Neg;
+
+use crate::*;
+
+use super::g2_swu_iso::{SwuIsoConfig, ISOGENY_MAP_TO_G2};
 
-use crate::{g1, Fq, Fq2, Fr};
+pub type G2Affine = bls12::G2Affine<crate::Config>;
+pub type G2Projective = bls12::G2Projective<crate::Config>;
 
-pub type G2Affine = Affine<Config>;
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Config;
 
@@ -56,6 +66,36 @@ impl SWCurveConfig for Config {
     fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
+
+    #[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)
+
+        let x: &'static [u64] = crate::Config::X;
+        let p_projective = p.into_group();
+
+        // [x]P
+        let x_p = Config::mul_affine(p, x);
+        // 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;
+        tmp += &psi_p;
+
+        // tmp2 = [x^2]P + [x]ψ(P)
+        let mut tmp2: Projective<Config> = tmp;
+        tmp2 = tmp2.mul_bigint(x);
+
+        // add up all the terms
+        psi2_p2 += tmp2;
+        psi2_p2 -= x_p;
+        psi2_p2 += &-psi_p;
+        (psi2_p2 - p_projective).into_affine()
+    }
 }
 
 pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
@@ -76,3 +116,124 @@ pub const G2_GENERATOR_Y_C0: Fq = MontFp!("6316029476829207320938136194393519890
 /// G2_GENERATOR_Y_C1 =
 /// 149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491
 pub const G2_GENERATOR_Y_C1: Fq = MontFp!("149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491");
+
+// PSI_X = u^((p-1)/3)
+const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = Fq2::new(
+    MontFp!(
+        "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"
+    ),
+    Fq::ZERO,
+);
+
+// PSI_Y = u^((p-1)/2)
+const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = Fq2::new(
+    MontFp!(
+        "216465761340224619389371505802605247630151569547285782856803747159100223055385581585702401816380679166954762214499"),
+        Fq::ZERO,
+    );
+
+// PSI_2_X = u^((p^2 - 1)/3)
+const DOUBLE_P_POWER_ENDOMORPHISM_COEFF_0: Fq2 = Fq2::new(
+        MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+        Fq::ZERO
+    );
+
+/// psi(x,y) is the untwist-Frobenius-twist endomorhism on E'(Fq2)
+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 + 1/u.
+    //    To map a point (x, y) in E' to (s, t) in E,
+    //    one set s = x * (u ^ (1/3)), t = y * (u ^ (1/2)),
+    //    because E: y^2 = x^3 + 1.
+    // 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) ^ (1/3)), y' = t' / ((u) ^ (1/2)).
+    //
+    // To sum up, it maps
+    // (x,y) -> (x^p * (u ^ ((p-1)/3)), y^p * (u ^ ((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);
+
+    res.x *= P_POWER_ENDOMORPHISM_COEFF_0;
+    res.y *= P_POWER_ENDOMORPHISM_COEFF_1;
+
+    res
+}
+
+/// For a p-power endomorphism psi(P), compute psi(psi(P))
+fn double_p_power_endomorphism(p: &Projective<Config>) -> Projective<Config> {
+    // p_power_endomorphism(&p_power_endomorphism(&p.into_affine())).into()
+    let mut res = *p;
+
+    res.x *= DOUBLE_P_POWER_ENDOMORPHISM_COEFF_0;
+    // u^((p^2 - 1)/2) == -1
+    res.y = res.y.neg();
+
+    res
+}
+
+impl WBConfig for Config {
+    type IsogenousCurve = SwuIsoConfig;
+
+    const ISOGENY_MAP: IsogenyMap<'static, Self::IsogenousCurve, Self> = ISOGENY_MAP_TO_G2;
+}
+
+#[cfg(test)]
+mod test {
+
+    use super::*;
+    use ark_std::{rand::Rng, UniformRand};
+
+    fn sample_unchecked() -> Affine<g2::Config> {
+        let mut rng = ark_std::test_rng();
+        loop {
+            let x1 = Fq::rand(&mut rng);
+            let x2 = Fq::rand(&mut rng);
+            let greatest = rng.gen();
+            let x = Fq2::new(x1, x2);
+
+            if let Some(p) = Affine::get_point_from_x_unchecked(x, greatest) {
+                return p;
+            }
+        }
+    }
+
+    #[test]
+    fn test_psi_2() {
+        let p = sample_unchecked();
+        let psi_p = p_power_endomorphism(&p);
+        let psi2_p_composed = p_power_endomorphism(&psi_p);
+        let psi2_p_optimised = double_p_power_endomorphism(&p.into());
+
+        assert_eq!(psi2_p_composed, psi2_p_optimised);
+    }
+
+    #[test]
+    fn test_cofactor_clearing() {
+        let h_eff = &[
+            0x1e34800000000000,
+            0xcf664765b0000003,
+            0x8e8e73ad8a538800,
+            0x78ba279637388559,
+            0xb85860aaaad29276,
+            0xf7ee7c4b03103b45,
+            0x8f6ade35a5c7d769,
+            0xa951764c46f4edd2,
+            0x53648d3d9502abfb,
+            0x1f60243677e306,
+        ];
+        const SAMPLES: usize = 10;
+        for _ in 0..SAMPLES {
+            let p: Affine<g2::Config> = sample_unchecked();
+            let optimised = p.clear_cofactor();
+            let naive = g2::Config::mul_affine(&p, h_eff);
+            assert_eq!(optimised.into_group(), naive);
+            assert!(optimised.is_on_curve());
+            assert!(optimised.is_in_correct_subgroup_assuming_on_curve());
+        }
+    }
+}

bls12_377/src/curves/g2_swu_iso.rs

@@ -0,0 +1,457 @@
+use ark_ec::{
+    hashing::curve_maps::{swu::SWUConfig, wb::IsogenyMap},
+    models::{
+        short_weierstrass::{Affine, SWCurveConfig},
+        CurveConfig,
+    },
+};
+use ark_ff::MontFp;
+
+use crate::{g2, Fq2, Fr};
+
+type G2Affine = Affine<SwuIsoConfig>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct SwuIsoConfig;
+
+impl CurveConfig for SwuIsoConfig {
+    type BaseField = Fq2;
+    type ScalarField = Fr;
+
+    /// COFACTOR =
+    /// 7923214915284317143930293550643874566881017850177945424769256759165301436616933228209277966774092486467289478618404761412630691835764674559376407658497
+    /// same as the original g2 curve
+    /// sage: iso_G2.domain().order() == iso_G2.codomain().order()
+    /// True
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        0x0000000000000001,
+        0x452217cc90000000,
+        0xa0f3622fba094800,
+        0xd693e8c36676bd09,
+        0x8c505634fae2e189,
+        0xfbb36b00e1dcc40c,
+        0xddd88d99a6f6a829,
+        0x26ba558ae9562a,
+    ];
+
+    /// COFACTOR_INV = COFACTOR^{-1} mod r
+    /// = 6764900296503390671038341982857278410319949526107311149686707033187604810669
+    const COFACTOR_INV: Fr =
+        MontFp!("6764900296503390671038341982857278410319949526107311149686707033187604810669");
+}
+
+// sage: E2p = iso_G2.domain()
+// sage: r = 8444461749428370424248824938781546531375899335154063827935233455917409239041
+// sage: E2p.order()/r
+// 7923214915284317143930293550643874566881017850177945424769256759165301436616933228209277966774092486467289478618404761412630691835764674559376407658497
+// sage: E2p
+// Elliptic Curve defined by y^2 = x^3 +
+// (69357795553467368835766998649443114298653120475771922004522583893765862042427351483161253261358624703462995261783*
+// X2+203567575243095400658685394654545117908398249146024925306257919445062693445414588103741379252427065422417496933054)*
+// x + (806998283981877041862626354975415285020485827233942100233224759047656510577433749137260740227904569833498998565*
+// X2+249039961697346248294162904170316935273494032138504221215795383014884687447192317932476994472315647695087734549420)
+// over Finite Field in X2 of size
+// 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177^2
+impl SWCurveConfig for SwuIsoConfig {
+    /// COEFF_A =
+    #[rustfmt::skip]
+    const COEFF_A: Fq2 = Fq2::new(
+                                    MontFp!("203567575243095400658685394654545117908398249146024925306257919445062693445414588103741379252427065422417496933054"),
+                                    MontFp!("69357795553467368835766998649443114298653120475771922004522583893765862042427351483161253261358624703462995261783"),
+    );
+
+    /// COEFF_B =
+    #[rustfmt::skip]
+    const COEFF_B: Fq2 = Fq2::new(
+        MontFp!("249039961697346248294162904170316935273494032138504221215795383014884687447192317932476994472315647695087734549420"),
+        MontFp!("806998283981877041862626354975415285020485827233942100233224759047656510577433749137260740227904569833498998565"),
+    );
+
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
+}
+
+const G2_GENERATOR_X: Fq2 = Fq2::new(
+    MontFp!("44471777796618567688228760095584248343372454885978087674329841655595593880133139294404651664057692271364857231527"),
+    MontFp!("152209914092745808277594956866181055187624831129109767937025242463317365117655129123148193049673425418513926319001"),
+);
+const G2_GENERATOR_Y: Fq2 = Fq2::new(
+        MontFp!("115206687171448860889110309021279060303629519187879257051215751573842462972180856243991157572371972099444077110343"),
+MontFp!("191377956145194479040228903677940355038998863371661730030204479850936075480341608934735952709786495341106477933498"),
+);
+
+impl SWUConfig for SwuIsoConfig {
+    // sage: F2.primitive_element()
+    // X2 + 12
+    const ZETA: Fq2 = Fq2::new(MontFp!("12"), MontFp!("1")); // arbitatry primitive root of unity (element)
+}
+pub const ISOGENY_MAP_TO_G2  : IsogenyMap<'_, SwuIsoConfig, g2::Config> = IsogenyMap {
+    x_map_numerator : &[
+        Fq2::new(
+                   MontFp!("165752316658948679552567650341600213993620343632797226373648182250196112194084163699689918190990441453209217107673"), 
+                   MontFp!("172182978063994664796636281648715261218877265445686511820228400278128135165425091257965367402286789184662480399420")), 
+        Fq2::new(
+                   MontFp!("49078863819486020728803126419770411403544927967564775122533948145670810135602221046611632159195633125363688522753"), 
+                   MontFp!("133330677606878026253733532636681674371349711466687180056118155523679405609126901243884039337337134962627419965345")), 
+        Fq2::new(
+                   MontFp!("88440326308038176392218244342168484162310820452393341528824316035047758188693394849605113877264996124652991932266"), 
+                   MontFp!("26460985441766134300772651139298255538590921173641559533448371120006177647448359485069994828122162245692248966113")), 
+        Fq2::new(
+                   MontFp!("240831597672798022181780196442988629902557797416422752447288392631352072879531084668083129009311685341499602842359"), 
+                   MontFp!("124795068789978952575783920730487695370136831800946532752608526840944057283524691812795315973894625798220920082767")), 
+        Fq2::new(
+                   MontFp!("231856156439094824000656216233999389240375109059054378946071472571709648546048606758615235778059505184730503731408"), 
+                   MontFp!("134026238756820071135251263743482298414233385640297868129438877114735051445009051866011097877494554014116371908672")), 
+        Fq2::new(
+                   MontFp!("161628978970526519329329822295337582413127505041035400390544637404697415598883543152357105789965717470570494458589"), 
+                   MontFp!("116602947282570158568911982642223012726308726836613908383578383334370050655181609483409110122767402070015216413338")), 
+        Fq2::new(
+                   MontFp!("231615170079008089001496386178968115998492752668752266579314749799030868007672086089822600816657899022828734321418"), 
+                   MontFp!("141639542381992520856560441410242716791591163086143661904501184306161835850893036003163803884002896297253767009574")), 
+        Fq2::new(
+                   MontFp!("96957224446676123824350918241672464825735454895610578698586352322390662445273628285471423071856275085141118045105"), 
+                   MontFp!("97587419381711441517698658129839468394457401157021696651597713140291602428957555768352336399994179660880524139808")), 
+        Fq2::new(
+                   MontFp!("18662780664429933771192510151421557554668611953190652639195940454142648933454488952361465779870877163142807899993"), 
+                   MontFp!("55517007457989983858891530398020104232682844055600438506715652841000901588962918721851719951820185832313468320365")), 
+        Fq2::new(
+                   MontFp!("188864327416940344326229259749844123042825201085435432627935318423081174922012610651352346391417830722940140585036"), 
+                   MontFp!("233542978062801907184831603532041452683131033894029390005010898310417350737942550513935694209129350870817277172583")), 
+        Fq2::new(
+                   MontFp!("33702103741469458207888758659069786556456463428431771947788685622778743201883736580054112022350187936628758294279"), 
+                   MontFp!("7531651998638745138624528632013700806848273210661661935097722938692087106885113623803921367479582718152259987647")), 
+        Fq2::new(
+                   MontFp!("129405180560592211762572081137246817341681076084973348177153469170177032429929182033872985192027066614650754524309"), 
+                   MontFp!("71494892585734577638768956295356005795556178117525317604450863442514001295461407965931789120761632296953990284809")), 
+        Fq2::new(
+                   MontFp!("121805396188033590038927712795579559087103093135515082191363074395734682090746320669474388875423586929711608364404"), 
+                   MontFp!("75932324143801627944771670190157701465835368459121478812142087933983158148741884038298732552979549182443318608554")), 
+        Fq2::new(
+                   MontFp!("205121513164720886728676669276499362266139599046368626660027529707299170205603076104821498121463983514654737906998"), 
+                   MontFp!("168051662766288660516992486993594951443897767271245608184500932350745292043277998040372769419920145370014740823389")), 
+        Fq2::new(
+                   MontFp!("224387508661509885922784938707800296916307265709615639996851552571542396031861010679067114387017955365668256976459"), 
+                   MontFp!("139097554917981907719834170888130444861465074977932740823078016609751284491153969166862091045221603146530147099779")), 
+        Fq2::new(
+                   MontFp!("142477190388553987083175296028785369398580520754966744245694134692905987471896623788336582063245356609279657681007"), 
+                   MontFp!("140302880976816076816721836344737338071783799730513599397010923016385668972882234545823525686327074617973208860421")), 
+        Fq2::new(
+                   MontFp!("205538184807792915395400814312734290381492118179294333381188081024280220461983210331268164749465891791515156713363"), 
+                   MontFp!("13030331252003455924520111292282390143014750833628314421882396445822808054003584720817672388894671968339344750750")), 
+        Fq2::new(
+                   MontFp!("139197805910452438551419010260519164074855817417063470117576949912038778696248952069759607969690314639425179841530"), 
+                   MontFp!("134745690770497208213126494241047670387239583870118646766457825646403640347226342104549240830903829682059982326727")), 
+        Fq2::new(
+                   MontFp!("46999088780962505530452862218145506822520603893157196954987630663398814970386085186714696215299498862118704356116"), 
+                   MontFp!("239220883081126775212690475926873251881459118214247205003758844846022330659109168499739536107988232402392010148915")), 
+        Fq2::new(
+                   MontFp!("137461512605659170682300574841422927080299499340556631216517745531687218204749421916211266297116812992348911035943"), 
+                   MontFp!("126932856673577834557989832150639712812952235385146245135235966945536973066700604316981524138335070494135486842267")), 
+        Fq2::new(
+                   MontFp!("57815299880375466472857931022912171296473275308202666945592250229771936329503691945881925004852905385160277065937"), 
+                   MontFp!("207900273391847649346738694548609379565855077833395139615718913929125517933139374225345876078131155102796477330196")), 
+        Fq2::new(
+                   MontFp!("182397511129719455005407008314265069548677727690813781407770284951663734172103638427690475141072553074575221965383"), 
+                   MontFp!("225121846650282460844501132545123914298308844633699320249517374760159461135641190512758348530493533776082794775238")), 
+        Fq2::new(
+                   MontFp!("42757221749971324771094873984161893488770713619971906650868412147150411626107692517374735631529074208182971223761"), 
+                   MontFp!("111424637101855455933266154646364284011426845669269128135151076357862608862363255550023430066507374024948118755170")), 
+        Fq2::new(
+                   MontFp!("257686488674545770403807165703608491821700153538449954828958424244540050698630649531963334687249831352703307010320"), 
+                   MontFp!("0")),
+    ],
+
+    x_map_denominator : &[
+        Fq2::new(
+                   MontFp!("196537929755540830130458921156910352741196129560556501635658595085779576490417628044619830744899117989899096675116"), 
+                   MontFp!("106967816747202586221026040614608875779671819314280336591550617355334247302203894951925800601923998790402234025494")), 
+        Fq2::new(
+                   MontFp!("73314120416427646620569455169905724114883313094893949291513517502168861559767103394033744003864213510722887906274"), 
+                   MontFp!("38999017135204040984255776995893429123212353273299706702441986090800506456890730978953545316903022073202240280957")), 
+        Fq2::new(
+                   MontFp!("133779461364688439286044255858523747234865723284672664672066362220940987786797573428234566651244275384657571315397"), 
+                   MontFp!("154931903368935230733381648548242132592387960818255334523314635613616976204585469590179605887364646535250639335453")), 
+        Fq2::new(
+                   MontFp!("247957910140234524214324761874381439955705875777136703199106095643204254634304448830280410483013931961038942096519"), 
+                   MontFp!("214943806307523271117409515396321303330984956986022871981067208079182219051826091487389512723678609613943324945884")), 
+        Fq2::new(
+                   MontFp!("11697862001088266121450094179739500241088837734277696824118211258364151630931186792937914301859707394679202145393"), 
+                   MontFp!("95980723944521770226526824868742386994509079773043937452565624851192578861364669763702851513923262074687274763858")), 
+        Fq2::new(
+                   MontFp!("168096269708683796856556357930292925811554548435612382636199127159818409693729567946366892866365435246772528367031"), 
+                   MontFp!("99720174640078175171062115168656883367851695095484071724968247253018133737453004325770034298778522431209097310502")), 
+        Fq2::new(
+                   MontFp!("33059404918884325948584592996172619413923041143099424466021368531149134447772287601175965141235934645074697267050"), 
+                   MontFp!("10757428905957703588038877674336794621171834192483169256644941002565404396356505770991807551250572677872221995215")), 
+        Fq2::new(
+                   MontFp!("142027935684179419855710336591935481541662612521926997142809731189880364304749483394981554800161483370077741056896"), 
+                   MontFp!("1943403947563275150997369785095274118967148389261968103605246462390957897712088493386683316483490223770940902453")), 
+        Fq2::new(
+                   MontFp!("200535851812830711305923885193456283997079838967145939474743725430895019937175928830731575175640901984178880783011"), 
+                   MontFp!("73874168720549156282270730246833500558176745413797996774310087510749148634278604002052708223696920208907646881989")), 
+        Fq2::new(
+                   MontFp!("220384543328043309613139993483671702409123249316603413540407457441864555087013622511692877380446192851630287225413"), 
+                   MontFp!("39000405073743042346296304484168728185850505353133307908773204457381817815206498660334035187329579833299098854925")), 
+        Fq2::new(
+                   MontFp!("219195224293908756855578672234544437367397890301565855376597788842679778002659222115121213889017072727428356719234"), 
+                   MontFp!("247894577734607804564008327202067464850944943412136922154651844411293409127507835027401641672218158657943826643185")), 
+        Fq2::new(
+                   MontFp!("146699001487357489560227247646638441970227213145065178169054120124066032784405371946823057532199624317631250110158"), 
+                   MontFp!("196336324454181158449524835117699225596467237400207491815838252818724619960701247377784788803043096102210425517795")), 
+        Fq2::new(
+                   MontFp!("155939253194251956164424003889230633804182501306742152137449150503013281009623802843490858570697615902305132709111"), 
+                   MontFp!("172261303485740204844677209985093962119870302741179905216184157502752680126595180139007438892219460422745105017475")), 
+        Fq2::new(
+                   MontFp!("137972103666241533333852948884443545062916813938500094392929132716673981519930321922556812217620174550912349461419"), 
+                   MontFp!("47600282095791674213992406796226738606147801920837771594412659335039656256887529097801732359033209329929517773020")), 
+        Fq2::new(
+                   MontFp!("135098057022357227608956235549944366234286127511416070373827898662879730495316177891045223676768538262860577751087"), 
+                   MontFp!("218641591773893348322227471378547165043111820723080862748702228639502320411481947789769811366015509814793754417785")), 
+        Fq2::new(
+                   MontFp!("228687493726193558146661770435566220015197012398911029567178581932152080915557441338298274247922585720118620741642"), 
+                   MontFp!("48223421552324743764826987807666420223567068651197810526658625431719723647078135623842652870214605734395702563953")), 
+        Fq2::new(
+                   MontFp!("82401683815523491481199527201592079745651015539510634295850130611233688561451492330603949648060220533354045095181"), 
+                   MontFp!("159070381032762485827712709726121404273458384870681735035622289092845201234785949112608113110663482448286550123895")), 
+        Fq2::new(
+                   MontFp!("61539107135026562717413992304341045078777699607129438878970720148394005607774781361280841945254066290447512808860"), 
+                   MontFp!("258564647705165711537697112631909171171984598885182416737094411313452565619624851452883996847677936536536427515609")), 
+        Fq2::new(
+                   MontFp!("219867891253233227579149075701158020315633373195728794672342716359369374905471205886891783929214978430681990036959"), 
+                   MontFp!("40524381030862708561992431051313657250449208728762250622105264621614810013551839533882876237430311293361821844681")), 
+        Fq2::new(
+                   MontFp!("88800087516399959501800534486349824688877578947555023348699585957763763180753947498274724426567091309571649023166"), 
+                   MontFp!("122245180850560437899129167839042992977076962956306963014567407897293197200681367630073717776421484831646532593850")), 
+        Fq2::new(
+                   MontFp!("69204740140688189359361744597982172008615446130082862488352885921056331761951244674105352971861180999345144984246"), 
+                   MontFp!("38216467720351249271557670250657907497353617320059247139049052120842234439257669911851800147147313339669901995490")), 
+        Fq2::new(
+                   MontFp!("114765242606519624982400506165904237893471895287563151339459173837887003905317760268941880935997925302483810508170"), 
+                   MontFp!("226808321937551848279625259185874129283473963677740840941191767963773773116795416044456897499248110949601850478751")), 
+        Fq2::new(
+                   MontFp!("1"), 
+                   MontFp!("0")),
+    ],
+
+    y_map_numerator : &[
+        Fq2::new(
+                   MontFp!("243169287995837894205750503657473181252400776697661357268613577074201794943537027717771587727860769419520957117060"), 
+                   MontFp!("154445371651863854130996979206021232172872232688365227537444264835087932826365764405635125797374865965304745730822")), 
+        Fq2::new(
+                   MontFp!("109149004424675517113489432756837393820953128532207867425106578478986226345054217066591849467433110788215195319750"), 
+                   MontFp!("30408441237651674477115309504276625429344634933425091999725383701660094027885762738289460271315609173544614563248")), 
+        Fq2::new(
+                   MontFp!("8414285408102090292522571401032945098403423241877066651551931468973120658567171350501434823318074450118610388181"), 
+                   MontFp!("226047422399128874433860903177676209375847937545805175562415311468986239012130226120019081492247088609694678876810")), 
+        Fq2::new(
+                   MontFp!("228308803559737454633222698485074629499383737811342884536963429506633258142551503400414163815852158951494613610809"), 
+                   MontFp!("220909287290837789818195731110558629271153823543746871132117978761339034747123501189473420274677281822601971748563")), 
+        Fq2::new(
+                   MontFp!("116623955280658732717402646061913268461869836841204913444259922610012147799771656282704605878638711580234302879520"), 
+                   MontFp!("251345693404812657374633929641944735274020119374936409701199723189056283828393555325905238148261248120379910778583")), 
+        Fq2::new(
+                   MontFp!("142632909729670553826438094523500302011158161959746397893981306350515911350319381478896794266740222044724793183031"), 
+                   MontFp!("135097007131619291616144192105571840182910366835929043414300810591005223344182310684819863256436016908585466099814")), 
+        Fq2::new(
+                   MontFp!("159262246805999098136860288248138175456624792734939305704793543040582454889431805248352849370505960249829264037333"), 
+                   MontFp!("256411146327954053251262434650444473133439725697572806395735688747939610541453396276159230618136278790246160635595")), 
+        Fq2::new(
+                   MontFp!("106675525854808944323662773997719159035717496275254424840883415090817949089664218352587480756720528552217297479523"), 
+                   MontFp!("142202207982399429498494980946602932891398916434890751210930378360132151108127041093945093575972538591541631204396")), 
+        Fq2::new(
+                   MontFp!("115853993705912938985758922127173369175321347209545356726288637524744651943071927137158115778405271676616612170666"), 
+                   MontFp!("188439202506521797668192307957766105517906171778775206324453830870041256388075168650527562921934698697140423464142")), 
+        Fq2::new(
+                   MontFp!("199891426461397900698689228549412057991574595606781836622700872746783962617889812808189413859146835266670353365164"), 
+                   MontFp!("123487321384490387195094801639396482206262484603737596281845841408384878196277195829349272799617445074531384638014")), 
+        Fq2::new(
+                   MontFp!("203453160391122297114764634999687500867096029894782931052056493086745424054313508850135956093450854351511962568248"), 
+                   MontFp!("3933321808920817665892338621688661599151270488240879901971434149901647580182088988848276352998263499828820719486")), 
+        Fq2::new(
+                   MontFp!("216229669548325266866202681779047392389311278655704899819569794547799955366773265486059541504823551138048188296915"), 
+                   MontFp!("41448968894064940344019909320065089603789758666259308674991068396259424208998703895462327945020441899649105710894")), 
+        Fq2::new(
+                   MontFp!("202678826482051686554967485240375873611017127444692775767942717540980994219310434688309713205309853725035377739266"), 
+                   MontFp!("48778316120483961415587198479185523835826749642473845435889717611018677968038563827240090688089889339896065735651")), 
+        Fq2::new(
+                   MontFp!("43364741387169348753014627410136368149262698966106150910900756728904165177527487078077667350512959263803465594111"), 
+                   MontFp!("61944739699039529393579599024212698483276675572994284564132452254474389809816373777333943401872462638231436446348")), 
+        Fq2::new(
+                   MontFp!("1902545032251691771730077590223241149624964994150687591044314892275508885163105731414463515832696686914784357054"), 
+                   MontFp!("67221897212365550931740188657735915316732820967428518278153545138481072202717711417949297443415145931349647354864")), 
+        Fq2::new(
+                   MontFp!("232464396645736057215489125286424902556417590819993013568149210848680788030572385843387291711255018198764185991688"), 
+                   MontFp!("41800154023275681622180037448850007404785328883356603798952195956734186941687720006035939799906615555216990599152")), 
+        Fq2::new(
+                   MontFp!("187038260664272653235271156369560372695631446985830424056061915935191103410794701043280599214000281588074544657045"), 
+                   MontFp!("38290302770763423573829549940707041833171456153861823771988991461936307395626028842226881832323571911777783325552")), 
+        Fq2::new(
+                   MontFp!("8193038016485856982946817225511231096542148907426451941320763511467909442967073658628847889502238964737537651732"), 
+                   MontFp!("9418692556935347898382092734571186686450013671235254851703843297990915553970523788207837029694342875454233715193")), 
+        Fq2::new(
+                   MontFp!("134073844001083825421215848942909782702386338984309026786345170296027964134133613977422644522116018820345983847098"), 
+                   MontFp!("153830492090479629579603390014414329445124716355506854714467139884353350218676155251380590350715220577136073627555")), 
+        Fq2::new(
+                   MontFp!("24894203921911934571199160858232802417038583022586807490232139245280305064770051397858560092019807972764914216208"), 
+                   MontFp!("120208242722200714489749801697072499732825359039071841003310452443348308205795253556381720202955786470886397257982")), 
+        Fq2::new(
+                   MontFp!("190392008574458975806418600277835706985376229847531539152452591238358119216217627352637258288556199770365835067627"), 
+                   MontFp!("236947842470057836630333692287445445381482585314120394670322793497639860754696181540315462907276465780536189751938")), 
+        Fq2::new(
+                   MontFp!("128014602802339573117431114877417430852771121268703430430938496966993823548956133449208721198231566864014207876438"), 
+                   MontFp!("76313913933214383311039506294052736258824720597935452573279680967713148986901401959316819572744945391130691484709")), 
+        Fq2::new(
+                   MontFp!("25945524144868616798377005434321968607597029473408456417628770501736226577600936996306306386148517051252174176056"), 
+                   MontFp!("93302878136439028547402102681387844515310157832968167882878653011659204369510932686206718073261314562836132094987")), 
+        Fq2::new(
+                   MontFp!("89345438915485267000169594163110872264018138861479961667441187849751112704236404111089533981719810422892295971197"), 
+                   MontFp!("225199447663521472758596124691205483139271667363437613911741821442536429098852529066869544898685674003162780468715")), 
+        Fq2::new(
+                   MontFp!("133226465537371725791207823007732608016851433266603356824246032571600774858733596680855277271698121233692296984412"), 
+                   MontFp!("214026235442364760645768878901893433888530027239186932434340221483611429797860448445573321733516533800376783586849")), 
+        Fq2::new(
+                   MontFp!("209865017468509971341642462085093919192185569139223034709204939485243056860760867821924437786503336074163109167043"), 
+                   MontFp!("219490420378012040044597900078465204875085141304274262719756064241884227366143829466191943246131284770521917871841")), 
+        Fq2::new(
+                   MontFp!("107794270350250727824303719264349327362253764840855494366195678657690526275364378542854833701549538802096418248084"), 
+                   MontFp!("214497132288922282410470995366492104127705853917251639956391350188219443322307620708083843529019036699996096662829")), 
+        Fq2::new(
+                   MontFp!("216436913923048926393371382639334167145590308917722616640273699755872914758105310937706004925121569777096571773501"), 
+                   MontFp!("14821532235517245029225575994881495294340097494060025842437989195232333244802578196149414170959605497405878582540")), 
+        Fq2::new(
+                   MontFp!("149340524242957423974772893433814190392014381473852786295383636551096665463613496468840974015807625484823068784839"), 
+                   MontFp!("92602205576740019970555092291786069878442230185393269119060098961688837594116147683652993589116622567477525635445")), 
+        Fq2::new(
+                   MontFp!("187289608720372854303118076618428364941868395899689208696722069999084187290922488892094161492110977423619035272649"), 
+                   MontFp!("138246251209835932037747211155451146889753321830881007441732932302281412878493276648902633332871835811473542877960")), 
+        Fq2::new(
+                   MontFp!("165653628641840315664303139225783620502451401675361521932235743336920154286645843675719999005591028855021909439672"), 
+                   MontFp!("221484407095875062109245088271905042727631591858266177514520864715688286361376419124935364810076972840743950061836")), 
+        Fq2::new(
+                   MontFp!("133980604703672698089766182661998480874540278232523164821108522954758888202993741126021280431373622479768313949356"), 
+                   MontFp!("38886256490758184304393553179653915986060051480245869194662478974097783410818598716423697164666847852998235320966")), 
+        Fq2::new(
+                   MontFp!("8411654157888762354868203383638678565276209861191964793314989111047210939710084789719415109438273538021505111510"), 
+                   MontFp!("187207294428708203829145346569036650547801585764458185253951079008883539428999915118458145884040644479498579194069")), 
+        Fq2::new(
+                   MontFp!("191144230647045707590184821948778479495825928592047153194222027257046414968351470170933284561757547536684715232224"), 
+                   MontFp!("0")),
+    ],
+
+    y_map_denominator : &[
+        Fq2::new(
+                   MontFp!("177304823246185962354212404236288831041380791662214394697399928748373114098169675564032904690251242875327747673679"), 
+                   MontFp!("234106598974619695004693596968258258794247055108931498762994964636371479098512727352039267846913406623802246782945")), 
+        Fq2::new(
+                   MontFp!("255874157960252694683645508260848371559149621054025374393554376526882940742514793344046680765937904153005134511200"), 
+                   MontFp!("19068358873460915055376626440913257473060029137260026174266944920186136734103362122730468957229595374427187617425")), 
+        Fq2::new(
+                   MontFp!("83946178094995839681455048029661822915614318352963730526672352524233381944447759416757234629624830143848209247040"), 
+                   MontFp!("36167189440196390196320129647971031300455228428629866775570898825049060037811108115927676106354625467897211624573")), 
+        Fq2::new(
+                   MontFp!("214137118009637944275213937166601531498145257806838837034827533674793291112410824873653425491233537265355337125438"), 
+                   MontFp!("75310151275642225944994533227518963961512910025529659163648069668626195571780520556481029340507362571133885889206")), 
+        Fq2::new(
+                   MontFp!("107140053800026140817203074526089346919722280052456645787788712045148531978814339001150298053597504647766497707422"), 
+                   MontFp!("114397460921328140828185121166450637136573513025702964340164304518654108540682577087979875141067314446917571826582")), 
+        Fq2::new(
+                   MontFp!("42398151340378868438123040588425908782227436520374323184618125390984068793920538080412999034838310511981244418952"), 
+                   MontFp!("82194329196840936158921467961561828669469444994699107543787160001285217807552090667641931153824104285439311091477")), 
+        Fq2::new(
+                   MontFp!("32044478312863504453978511975839237915357713065285858656377527520925624222082496835678894223326750023304346513708"), 
+                   MontFp!("224732340440722096332247540469311391766792864305974461767563394934556509366444399113606207665094042937608880394380")), 
+        Fq2::new(
+                   MontFp!("53290030879673160724264978063216325707183784347799183367929912851157629196486013218134779085284663628473135140615"), 
+                   MontFp!("42967590874964323361920860309631969474991176192252393149421408476343364383848642144439727879920981862569415477634")), 
+        Fq2::new(
+                   MontFp!("250488593850017034090300371968459931740406675270099747930030660805939980644430804509506597720682995099971419762057"), 
+                   MontFp!("131736273443849165304852712527070616520885505701320868662058330388440710419459541866884603770735894010610491333882")), 
+        Fq2::new(
+                   MontFp!("251064692215092635541196206457923985861467397867989080397969990645886126152674833092283559946890888232618697517884"), 
+                   MontFp!("171430383391121065822039978510482289343958135960126315509375831831735263180943544895493884988847947752888720502133")), 
+        Fq2::new(
+                   MontFp!("255810123836950778051032251049468471118744836441263107437005316697409810175422976454215094737538073112171964000966"), 
+                   MontFp!("78363344687446114757879143124020926645520829625790622079288990711202726499291972408305265373741655103522048633806")), 
+        Fq2::new(
+                   MontFp!("94953611600133917480746113251669332369937157892937924494319507354263981756523698288726321437604686331762128114942"), 
+                   MontFp!("224037954053161681052577381077631881138732983068288196649494577229506443999757164090758954620762136536790092765707")), 
+        Fq2::new(
+                   MontFp!("18177910449767953614338723180992575758462819793657888834925741153507922227776503487306285172452430778418239589878"), 
+                   MontFp!("55976309667093193926953058482403983650044130588205371047077237394269232758375928755579870418413040530924659710422")), 
+        Fq2::new(
+                   MontFp!("108398849957050915959578499238335172000970311919637037913625633347326921657585237193100994767528244599176367431882"), 
+                   MontFp!("204809230842263072415312635210643987712012160534293694062738501600937603588267937911969298058204043106501986725326")), 
+        Fq2::new(
+                   MontFp!("40836628940164991036725499428168139451294386215534361893839871958837737306822281294361671587764896498700322394958"), 
+                   MontFp!("119396884503349014053839666170414789560955868303656326650021743484252346209353246139311353657707899076368015332219")), 
+        Fq2::new(
+                   MontFp!("57449149099548285338146473529383255206310079371370663992648410210841833627207062160011080280732475904935527767063"), 
+                   MontFp!("53213606042373287683153647684084583002441527525177758051678463570615020765660540938870067881706148841340293404257")), 
+        Fq2::new(
+                   MontFp!("136011650568921952309089811450436645471254909718073766303847394446918967077385999380499048535832357755732371368738"), 
+                   MontFp!("167478505497067957490757520193067128323382872103395718848436244112857102765738573826312783708349214669979612036158")), 
+        Fq2::new(
+                   MontFp!("124201488690791095020042847186337439989685011854729481246272047846908500431421470344897520044190299684207452017073"), 
+                   MontFp!("206045464105062318563700338460670926332476051084269665075012377410704353049241671458557389593362582538704238377616")), 
+        Fq2::new(
+                   MontFp!("141307886851791570111930048284226290849958071383456038631306928334570275405889250568493573543543795501685612269615"), 
+                   MontFp!("33695298953151791677564491610276872092952551110021466172491397823758283921068636555353240048692541883780027233962")), 
+        Fq2::new(
+                   MontFp!("248265339860070148327157063205450906034372346050742532250909040050681913704941472496789561564874787781299103889328"), 
+                   MontFp!("246735083688655178976599901436968434779493759990448799231310864308891009496294971885106650388027197609829556319894")), 
+        Fq2::new(
+                   MontFp!("242374981274128257174433646391488180576863913259197526647513270422870835725158808599624055920155693832356361192562"), 
+                   MontFp!("228823832066259533984346839854456963456061412139464585495219844904598927917971403987214543635705786807302526573779")), 
+        Fq2::new(
+                   MontFp!("252218794556637183364789705825049189219556217519670190016584589877973440046635828866291293002549365274213665103495"), 
+                   MontFp!("246226868929550107779875102413192686259972538740042993595504829761267272514998892312681511407413880843390092913913")), 
+        Fq2::new(
+                   MontFp!("194440756770673250653849096711805826346541581797630354589253365569405779009028682866443842541588052010949210024484"), 
+                   MontFp!("75265817091612360444217709043194311507703596250641164601263089234422086318666070167810083868284770450890779266774")), 
+        Fq2::new(
+                   MontFp!("30126025128311053094362231518416999154688680759401769180563223025361877725315179695978985780460875616652938854146"), 
+                   MontFp!("53390417057360854696711134553867053334956120915983753729596602193155006833056717338565729257476036879055975910097")), 
+        Fq2::new(
+                   MontFp!("101332532133743769759178027285109552486478973958553103055307446365529747250973790438239230671819476569086244438727"), 
+                   MontFp!("148745905560783494991892238622790396213255789465409808038709750840775025617296316699696997331989504328034553213894")), 
+        Fq2::new(
+                   MontFp!("64805743514968884017432304617184871899075979363892814607985017391426869625002757534871594116135107848421987411961"), 
+                   MontFp!("6046324386958113626500748531301314307229746408846776295678625368971798823548167403538529285882066298168231669149")), 
+        Fq2::new(
+                   MontFp!("42585898388361518080924198789209195881860509830112816215046001795045034138585747974649960102171072364466234418812"), 
+                   MontFp!("132695208880203057798268960407754614753345990251279710979596670783892175104478291787481794529190706739877760089560")), 
+        Fq2::new(
+                   MontFp!("212862020601301354783026588297306531610140885387724836359356800753780855161155144746080869191538655229274242914307"), 
+                   MontFp!("157598266513011182093451150345114371606842593014102635902061162138398777778450012845089379844999350325670077782200")), 
+        Fq2::new(
+                   MontFp!("4121090928751590306336774011079865996138664888804166805010515676212588791761189056383637824656513752764121888675"), 
+                   MontFp!("183219245849642047090141657656072708461001592401873575143115550847958265143529306190408825011434780265059908079650")), 
+        Fq2::new(
+                   MontFp!("79081485025787885179619178550309706744599846607596447880706626420512740963985633088538634502003788677250834958908"), 
+                   MontFp!("183808890703436998546164599111050972902808423546263572335175957576564587842514119276068990911067829699066843757937")), 
+        Fq2::new(
+                   MontFp!("212106075999882114389916784897163150756429321557076536924307653148222968665985018997130331497354557069316538670523"), 
+                   MontFp!("6765896997590927451499527318422027932088882822980873934837948553969718709492787823596776070132570199077127482065")), 
+        Fq2::new(
+                   MontFp!("234716866510887739589745422464313597883163631119309437461957606368046054279070563732715561665778636277317684644515"), 
+                   MontFp!("97451989647642778641795555357790293895920858058713680518946629728091416392679362160653023502048556793761866531581")), 
+        Fq2::new(
+                   MontFp!("172147863909779437473600759248856356840207842931344727009188760756830505857976640403412821403996887953725715762255"), 
+                   MontFp!("210880269899843225414111521931364427157014189139153931141845520612300425501022712679200902179085486362182614989038")), 
+        Fq2::new(
+                   MontFp!("1"), 
+                   MontFp!("0")),
+    ],
+};
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_gen() {
+        let gen: G2Affine = SwuIsoConfig::GENERATOR;
+        assert!(gen.is_on_curve());
+        assert!(gen.is_in_correct_subgroup_assuming_on_curve());
+    }
+}

bls12_377/src/curves/mod.rs

@@ -8,6 +8,9 @@ use crate::*;
 pub mod g1;
 pub mod g2;
 
+mod g1_swu_iso;
+mod g2_swu_iso;
+
 #[cfg(test)]
 mod tests;
 

bls12_377/src/curves/tests.rs

@@ -1,7 +0,0 @@
-use crate::{Bls12_377, G1Projective, G2Projective};
-use ark_algebra_test_templates::*;
-
-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/curves/tests/BLS12377G1_XMD-SHA-256_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x40",
+  "Z": "0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508bffffffffff6",
+  "ciphersuite": "BLS12377G1_XMD:SHA-256_SSWU_RO_",
+  "curve": "BLS12-377 G1",
+  "dst": "QUUX-V01-CS02-with-BLS12377G1_XMD:SHA-256_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
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+        "y": "0x017c05a4f658399a64f5028b1c5d8a928f6a955bf28525d906592b9e6aabdad838102c6b1b4a9108898931fa42ef0cdf"
+      },
+      "Q0": {
+        "x": "0x00e10a1e6c2853d3416288652f6cda34fd2363c993f4c4fdebb38f185855fd17fdae6f8b35f6586abf39b746e14c0297",
+        "y": "0x0132b86c328a4c52e82db1a43257ca0cb5a8f8e2546b92a854117ab26cf6607e9d8c207854d8597426c6987ebca42d97"
+      },
+      "Q1": {
+        "x": "0x005648e0f6aa7131780c1ae8d396bdac0dc8e76426b8a2adf6b0dee3a0f80b7152343332a9c2ad5c83113b8956fe2685",
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+      },
+      "msg": "",
+      "u": [
+        "0x00e91c93755d4dce58b4277d109ca11cb178e160d0209f0b97c0ef0a9d03206bdb93498faaaba98969d4a50f91d8fed3",
+        "0x01442032ceae5c549af8f3222a0b9fafe5ef19a001ab399c2ddbb9f7dd59671150a067bd104604bc7d7fb9b909a2b276"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x015756bc7b5a8140577878f75009f8a0009bf1820719354863a52057d0758b27ff7d843e177fc618146edec267d1510f",
+        "y": "0x013b4be1db30d04593dc965b804044c2f92e366543f32377463a0deeddf7ddaa0e62e843d5590e948e5a0d9af2b917cd"
+      },
+      "Q0": {
+        "x": "0x01029fe43eca43ce7adca5d31a84b66b28fc00de3adcddd393c3ad1bd993e24cf70a9dd99b8233d2a657536943cc5000",
+        "y": "0x0011e54e8956bfbfdd17dab8b91e571a49ef5c5c7a5b3c00f9ecb045c39c6f59e3c60c3cc0d290c0e5effde15672ce8f"
+      },
+      "Q1": {
+        "x": "0x009e6c4f23e3590fb40b0a622a3cda01addda2a4ebd860ba4d87615c299f87e02c190035e593e6b80b18282d37168f3a",
+        "y": "0x0090c6fac6f33662a3b50631e367b087e144315a4400bbfbcea7c16366cba865893c85bfa79d82cad31954925363219b"
+      },
+      "msg": "abc",
+      "u": [
+        "0x00cf409921dcdce7de4b3541144bbb5c41592a95278af448bb6f6287e5a71b71c8148a03b8f98cf6e654b2a93bf89c5b",
+        "0x00bccdefe8cbec53dad21b03a0d1f05e1e4c401a7f20ff349043ff1afe8074ea4edb457a2181d6388a41be08445f1099"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x01a6d66a21a28362895c867fa2a65e5e54fd85171a0a8327faec0f7272dd5fbfeaafb311d7e83c85dfabbc790fb8031f",
+        "y": "0x01183a9c2d97c91c06cb090e69cfdf0e89e92baa780b8e3c5e1d92488d3a2422896c4ab808ab099f0b4d9203c7499147"
+      },
+      "Q0": {
+        "x": "0x017397c57e444777264e21318d6e0096779eccafd05f7a95a87acad1f8730fe7fe9e1d1dbf1ddf11539515596ad71861",
+        "y": "0x01660b0335de45c1d4e7edc3b1230bbedaf598cc3943ce854fc2d86d84080486c4b0f325dbcbef0212b99ee3d0994f58"
+      },
+      "Q1": {
+        "x": "0x00cfcc6e7987859db4156bd643a7ac69357f0fa86c6fec36e039b2822001c90fd852c4afa98a5dcb00e65280299520ed",
+        "y": "0x01823e2bce6d7769163f6646e6d80944572a6c473d7760b0b55911697437e7bedbc6674a4cf55850d03bc238128e9479"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x019061c2817582abc25c57a58f08f5239bd8d0eb1980d2b911e38131a779e0991c5a5662eb8a6aad8ce0bbc0cdfb67b8",
+        "0x003d673f221f321f652ad6baac32fd04ad1c06a2c03e4974f752e9b87f5fe222b120e853c7a7c767255adda229c71a49"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x009574af6ebc91ea9e337178cbd5c83ecb9d42fed22b3272c3e50b1840c5089fe5bec9808eaaba8a06ced26a30b82747",
+        "y": "0x00ccbad45957f1d493c1859e325c27dca3c63ac49177a1b2a9b5e22e14fd23845a638214e85506f46260db2827e2869a"
+      },
+      "Q0": {
+        "x": "0x00a4721db398949969915611e7a65cc43d167bc9c6b11fa69e871663aac40266a4a01ae64ac380dcce313f9975fe8f2b",
+        "y": "0x002123e943b9a1943d7a57e69e30c84c9bcebc96905b920365f2fc5a4af2f9c42bc1c7c5660d3b10de8c8b1381b8163c"
+      },
+      "Q1": {
+        "x": "0x00860490ade9e09cbf22a1f32cfe14bd1e82721b73a244d1e3e03a38ea45b0332dca194a5f43bbc8e9bc6319399a0a13",
+        "y": "0x00279ad50592f1a5b92430020566b2bca7837bef7fe0f8e08d456962b7ff6a25b4839863baa4a9659bee69af343d8ed9"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x000ec0c5ca9fd63019bd1f989f8b054b29a0a1833a0e3078031da7bb6446de321ddd6ba40a7cb9dfc70afca8bac538ff",
+        "0x000e110ff18deec2d60a2dfc92642fdebd6d70712114a6310e1f3eadf56e608a05058d378413fdb819c8274437f0d440"
+      ]
+    },
+    {
+      "P": {
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+        "y": "0x01a9529726f7d9994634d1d02c1ab474e2b9c20f2cb0cfec7e566ea033f40438548e737c43d4e7d1cb2fb75bf7686533"
+      },
+      "Q0": {
+        "x": "0x003ca77f5b09d595550a258c0480381569c8ed1caf4bf69e3c8a530d1d910d3ee941a53f6abc452219aa79f22734e61c",
+        "y": "0x004d376f45eb23e03be43ea5c1e00f9290d800d01ff0141c8faa8d1b0bd88c2ee8f3bb8c7ce17ddfe21633ec2b223780"
+      },
+      "Q1": {
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+        "y": "0x00346cb1d6116a329e755b913f5d2d9c7f5405b21e8e400853791ffaefc18a1b1aa8610bbbd4961fe112aa78d1859a40"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x00d5ca54c4622a2f8ec71843ce327959689ae7ff37e7509a88212b3b852e213cbef248471eac50bfdbca3c9ce733d8e8",
+        "0x00b91b02d867e03924593529ae87f35a2adf317a87209bed9c91d5c886e801191676a272422454c7d9692b8368b02e21"
+      ]
+    }
+  ]
+}

bls12_377/src/curves/tests/BLS12377G2_XMD-SHA-256_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x40",
+  "Z": "0xc,0x1",
+  "ciphersuite": "BLS12377G2_XMD:SHA-256_SSWU_RO_",
+  "curve": "BLS12-377 G2",
+  "dst": "QUUX-V01-CS02-with-BLS12377G2_XMD:SHA-256_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x2",
+    "p": "0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x012988d49df0158335f268551a0121a3fd5509580e675ed2e26f66ffb8ec1089b9db4a69bd19db25f7cae34619b8542a,0x0060eecba902692a7f95900c6501ea3f6e6f52b2e951586f60c9f31585c4fb63cb5486d155df4bc394a872f6e0bc3eea",
+        "y": "0x00e07c09af8c992a920bdfcdba4db43b542c5799258f2a01897d5a0c621db77c29f02ca2afa99d78dad2abdd4e180d89,0x00020a02b4d45959b67af782b737915298c203dada50f9d4941ada19ea7e986e91a83cb33d01af449dc540244b418561"
+      },
+      "Q0": {
+        "x": "0x0040618d422085e035e06f0333349c4630b7e47d96c45b803db208243cfe176cc9b89710c0ac9b6c25387772b0253de9,0x016e1c02056c1c0d179c0225b37845f1ea7fdeede136d731b2365248003829bee421b65f64b43c579ad9b30469d6cdd1",
+        "y": "0x0011e6e3019b9c453e3b930a091fb514b082e0353dbd58185d8e9211ec33d036c7c1d535ba020ad2b5cf584aab23fcf0,0x014063792b5a789670e1f75fd996a22fa9174888dd315fdb8b4597bdd7572edbb145817b933a0f79c467dabf473ed98c"
+      },
+      "Q1": {
+        "x": "0x00d0ec3127b58d178301f9f63be6932d2bf84a71fc79e50004efe7d13ab9ebd80cb7a958a369a1061e5aeb5365d657d2,0x00a69c72d1855528334e08529d9d304d39326e5670943f2fa3d57f32b4e1ce215a7df744bff01574e5ef35826e61cdef",
+        "y": "0x0158d9d3ea783058becfbde70cf6215c53a9afd702308c551c5d8b02e00240e20ff93d2d4515d3033b92d44b76f063fa,0x0111257e46569bdb27e1c54c51b57a0aef5c5b287e28205b6b08bb585087774993895c2886dcc500c98fc3af92f114dd"
+      },
+      "msg": "",
+      "u": [
+        "0x00bad459056ed98adf92ddc87a4b9970b8ce50e5c1d811f72a5631f0ee41eeba11bdc1fcbf135ab259f7be9dbf44c3f4,0x018d496adfe469a57596f015eebd869b7bed74083c573bb4b9d40a471e082517e5b744dac07eb67dac975bb8411766c6",
+        "0x0022395aab1038ade247f4b17deb81f4b00cabc04ad532fd3ac580ddbfcb44b3cb9d1d1976b09de603a0a228e713ae7d,0x01a366c20f9c2c1bc6b766e25856a85967a104d616680f4a79d97745c224fdadff08940f11ae0b26ea96f656f28b5e78"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x001346f07170e2ed45d08def787101795af173163239e7a1ee3297fd4e2b4fb6d76380058612e745a62a6fa6186744b7,0x00977c6b055e2b80e68afb986a05870294628464393619a2d92a698abcbc8927fe9729b4b72daac63e7f0c76ef711992",
+        "y": "0x016896c5571627fb322a371c57528f98131c51b1dc4ceb2be384610dc3f1a224236febd2c501bcea4d387a3c0c7b4e1c,0x007a86495cf20600a5d066b91a726df0b7d67f8758d7ed3fedb797d8772805c52eba9a7bd4661d37932f855b05f19892"
+      },
+      "Q0": {
+        "x": "0x00af89668bbc75ea1818bde76c0d126f516356b5b4da3f06603a0c4af5c68e44e8984ce185b756287b9aead31fc54c4c,0x0013b1d55b0cf613f54d056541daea78edc693750cb992564a9a7861e66f26b3cd4da71a30295dea0e40f0809847a030",
+        "y": "0x0127448b51269ac893ef00a585646b14371c0af69cafafaf3176e663f4e033b29a85e332116d8d9a3bfc8d1873730866,0x009a3aad06b68199b2e66fc1dafe20dcc5af8dd740be98fe7db529b424f098ae27759d7613f1942e9b1602664868c17b"
+      },
+      "Q1": {
+        "x": "0x009fc985f056445b2f6156a8021faff087f9b8d4690653346ca74b4420589fdbe511491fec0c535b52d521c1bb4be400,0x00f920679bd77a0d50d624513cf2296e4565f57dc3d7a578ddb19bfa60f05de1d5954ce247979fbc6501af72cd62e334",
+        "y": "0x0164c6cd007aba3e295df8310a2da71ef40022cec7a2e51dcab9f3850795ac823c7bb65082a88199d7c378b0ac4e9257,0x0028633591401d7da706fcb4a4da6f8999a7aff7b167bb96fd92511dca61f62f4b4e0be3213f0d68841a110b39c5a685"
+      },
+      "msg": "abc",
+      "u": [
+        "0x014a48b15756981016043ea1be11e30a728877c090f3beb8bd56cdadeb98792c0f47246c99c92c6a6d9b4f2ccef6d09f,0x01445002d867fb15a2d50311d23ace363b27befbe88d5feecababd66082e6b056d306f7f9dec8d3f4dfb1b2314963cec",
+        "0x001559a97f7639b2b5122e90b51a35c6714903b15cdab56bbe16eac4f8a0bd1514b412867f46f6948362c6f29d88c9fb,0x015556fa42d21cb9c6af6de63f6fbfcd6cae7c788e1b74c978f9c2ad1aae724912ff47bd4bab7d77c2af68b9c45b8c49"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x00dceaed928808d01aff4fc8c762d8cda12cc7ba1f6e721887606ee40ed0df1186f8cde71550636425de7b5ec0137fca,0x0166a7280c74d1bb3f0fd8c48aae30b855ba1a59a1dc309fb743f44b958ee721f1c273ee9ccc17e5ae931d566cf93671",
+        "y": "0x003125c58959ccbbca6e456a531833720d87dd039068ec1c4dbeab97230db643c71fb47e6be54eda3a470f452f3d6b1c,0x00d070fa5ebd18f6af02f65102b74cc379af99ab9d2b797a316c736bda39fb209bdaee9b59877cd0925c9d0949d91b0a"
+      },
+      "Q0": {
+        "x": "0x013c8c7d3aa93cb082f1b83edfd76a44a17aba8253a4b0a183b679b9e4d85e1e9653145b4947320187e99825d1846149,0x014e9afc495733168d15ebddd8d5177563e2b33a584a9993cef5536a1bba557590f37fc79651825cdf7bb6516ab54a88",
+        "y": "0x008a53b0d7d5a96b9fb7a15c60374028f1ab06c6545c69cfbb6ad7320e3933c64bb13b5139009ae7fb4dc0d29a1eacbd,0x0081a61008d4e7204c4a0268c1b4a369d142f4cfbfc8ee794d9653d89dc42d9b27e208ae0f11167d7eadfb56c7d4d1da"
+      },
+      "Q1": {
+        "x": "0x0062e543539c61cbfeb512fd1ec5f58bedec3ecc8bfec05de8043bfa92fec6fd7a671c9d3c9b0f86278ec6fbf4ae02a6,0x00f9402ce08a6d603d17d45dbaeda0babc9188a7837dba10c4aaad3e4dba9b5208b8df01d0635c30cb913ab16d9d23dc",
+        "y": "0x001c23bb7a1789b4afb3d896e497e8c9d5d4018721ac1303836265bd3d54e7eaa5f63ba45fa8e3776642fa27f049d792,0x00cd3bf5161c9ac44a3a490beb0e12c91de09706c4c86b369da263ee63560e84c30ba0ebd72536fa7f874539f2d590b1"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x014058fb0e66728eb352ca096e0ff6534512d1b8da4391b192da08e1d45d86064c92f01568889b13318cc3ad8144190a,0x004f706e3d9a2a46f32f2953cb7a305d092ffb332f085d6ff4ec063d24686c8917a9036e0699c7dcf48f884f1e47ab2e",
+        "0x00cf38b24a429230e04edbaf3b759aacfd37dc8dcc9b297b65b1b9705858f4d3bffee8b10324be05d7e4a18bcc4cd863,0x00c478b8e924194155ae97dd29ed2374cf8e207049e32bfb1519ead43702d49f22208ce12b058e7ff31ae7866f05959e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x00cdb3038598c178025dbaf99dcd440d99c2b38d5b8041893d67002e7c6bab93beaff51439845d06c63f6ddd7c5c401e,0x011d2a48f51437628dd6508f6bbb306da621acadf14fbe9e8f47ddf1915beea1e4e3286319c172a32742d7faa45a5b7f",
+        "y": "0x00cac5a0278869557095a63c6a7203468a71d58ad123aaa82f72381cd94250c01479ea8cbe643a8341678679305bc01d,0x01a91041b5c1406e643b44d4564babe6f2bdf5fa3c1620419fb6cdb4ba294f1494a33fc829784cc14cbc8066c5310a87"
+      },
+      "Q0": {
+        "x": "0x012f22361e00eb23ffe9082f1b4bf4822553cd42c8367588e5329fa166efdcf09c53e0e0b5f06e2a610f42c6b278050c,0x01aade240952b9e4db24fd88e0b0552904b3cb8bab3e4cfbaf2a5c35da48127ef75d1348d76225e8fb896c62766902b5",
+        "y": "0x00f205ed12fd5bdeac9a95349e8383ab854dd59690992b6240357652246388e3224ddfa5ce06de195dfe4e9dc2c5a901,0x01203782b3fa65de7ab229eafae08b4ea9bae437e195491b03fab30ddce83881a0b940b33f0f3e7bd7feca2c76e139d6"
+      },
+      "Q1": {
+        "x": "0x0171cca78371628178ecc12072e263eda9725524b5de48e340ccc8514897834b81cf36466ef7e2473f88aca8830fd0c7,0x017273b33c0259339fac166bf927a66da0a6b40b751048a0093bb4e5d37c35f2a7318e393d4aaef61435ad4471603662",
+        "y": "0x008fe7352facf00e07a74b1315db5b308827577c53a950607fe25974039598f017ed7cc054c1d279dd4957a19435d16d,0x0083382ba5e521808254bf1e058dd663336bf591c564d15a0df71791c4124c2ab38baee90d1d4435f4d6c3967df0f9ef"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x017afe7f987942b49e66831d61b785992f3172b2387f55e97863062e81734b0001bd64ed508d6721956741688dc9af0b,0x00631bcf5d854071890838210f50dfa1359da5ff4694255b7cd6ed630e4c6dfca746c69a9c5f3d76ee3cceae20bb355b",
+        "0x00b1fc859bd156b84a8b95d503db388a604c7a05ead79f8cd08cb21b677f3bd77143d8334ff51ddbc77ebf670b7839fa,0x00df8ed5ad61dced6490d9b58585fa3803f04f0b7d4efee366296339e634201c6f8924c8c3794c45685f49c6f974cf7e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x00bc60ec05a3e54f000d07e4ef4d86c9f5bbc8d17aae021f547615a1c89a374bb47fdd25aa488ce8ad6e4b45483cf70f,0x00dac74d2a7d021f868b1ba53075fbb5d8b44fa709ba1b94d904d18cd79373bf23e277ca808bc70b64bd47fa877e81aa",
+        "y": "0x010dc70c8b009d9013768bef31ebf18db9ae405fbbdebf7cb8ced20d10ef633e66e3c2301e233e375e75c972f9dc11f1,0x0040e8b8abcd97f7bb841fb35655830456be9b0e931db9dbd40307ce7380b53351d22557ca29204b55eb7298cc3b1e0a"
+      },
+      "Q0": {
+        "x": "0x01891e447beb5b70294a6f5f7e0230faed4b3119353bf55ad2afa86cc266359350c07d1eb974389a67533c07f15d506b,0x0164482864c5fabe4716cc80bfd8776a8037d87dd141058737c5cf407aa39ec76b78564621637edb6c2ef6b8921d72c9",
+        "y": "0x003b6cffeb0e47c6bd294263d38fb8908707502415d850d06b524a61e1de100d8a768996c6cb8c8d67b8e88cd3dcb4d7,0x008ac2f1ea197c81aab704952b808f0cb418d63df22b39d5b88c000c40890200934e8695aac7345e3da11493d76c4231"
+      },
+      "Q1": {
+        "x": "0x00f507c2c5090a0e1d5c8e8db72e168c461cb99cbab2f9672934a3a2d92b81501553fce7bc3da3d53fc487dfe7512dd0,0x004d70e612013e7b66829a9d3e7d0f8a865fa3cddb794ce30e3b145d4287e4eca91977889f0a6a3837089c34c4ca035e",
+        "y": "0x0055eb01ee257e72fc09d0cb36162af8d98bbb9cad244715cfd63dc30e66ff452d6f4519c418654b4110eabcdf701f76,0x00a20ce3bdb4d1da6b8047caf4b7c2285265021dff3b1c1a760badef8d5b108aff67a13d964218711613330b3f0c3344"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x011c761e1ea0285445d16b6982d2c58b8ac14ac32dcecd59a76d652c86adacb8643fabc49f6340a9bbb85220ae3272db,0x00a340146d9af76164b2aac1026bb445b0f4a9d8d65725c2b26051c905b40146548056e0828590573efb151312ed97de",
+        "0x000edd1a63bc707aef87eed2bd7bf933247a697404d4ed1abebf8db4670cf14c9ebf6b138c642be96bc7fa9616284e7a,0x00521fae4b02b3a025c08bbeb2c4783786f82816b7f4c8d496f4715906a3b1085cd48d9d2b58588c138ae4757e220a91"
+      ]
+    }
+  ]
+}

bls12_377/src/curves/tests/mod.rs

@@ -0,0 +1,57 @@
+use crate::{Bls12_377, G1Projective, G2Projective};
+use ark_algebra_test_templates::*;
+
+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);
+test_h2c!(g1_h2c; "./src/curves/tests"; "BLS12377G1"; crate::g1::Config; crate::Fq; crate::Fq; 1);
+test_h2c!(g2_hc2; "./src/curves/tests"; "BLS12377G2"; crate::g2::Config; crate::Fq2; crate::Fq; 2);
+
+#[cfg(test)]
+mod test {
+    use ark_ec::{
+        hashing::{
+            curve_maps::wb::{WBConfig, WBMap},
+            map_to_curve_hasher::MapToCurveBasedHasher,
+            HashToCurve,
+        },
+        short_weierstrass::Projective,
+    };
+    use ark_ff::field_hashers::DefaultFieldHasher;
+    use ark_std::Zero;
+
+    /// make a simple hash
+    fn wb_hash_arbitrary_string_to_curve<WBCurve: WBConfig>() {
+        use sha2::Sha256;
+        let test_wb_to_curve_hasher = MapToCurveBasedHasher::<
+            Projective<WBCurve>,
+            DefaultFieldHasher<Sha256, 128>,
+            WBMap<WBCurve>,
+        >::new(&[1])
+        .unwrap();
+
+        let hash_result = test_wb_to_curve_hasher.hash(b"if you stick a Babel fish in your ear you can instantly understand anything said to you in any form of language.").expect("fail to hash the string to curve");
+
+        assert!(
+            hash_result.x != WBCurve::BaseField::zero()
+                && hash_result.y != WBCurve::BaseField::zero(),
+            "we assume that not both a and b coefficienst are zero for the test curve"
+        );
+
+        assert!(
+            hash_result.is_on_curve(),
+            "hash results into a point off the curve"
+        );
+    }
+
+    #[test]
+    fn wb_hash_arbitrary_string_to_g1() {
+        wb_hash_arbitrary_string_to_curve::<crate::g1::Config>();
+    }
+
+    #[test]
+    fn wb_hash_arbitrary_string_to_g2() {
+        wb_hash_arbitrary_string_to_curve::<crate::g2::Config>();
+    }
+}

bls12_381/Cargo.toml

@@ -13,14 +13,14 @@ license = "MIT/Apache-2.0"
 edition = "2021"
 
 [dependencies]
-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 }
+ark-ff = { version="^0.4.0-alpha", default-features = false }
+ark-ec = { version="^0.4.0-alpha" }
+ark-std = { version = "^0.4.0-alpha", default-features = false }
+ark-serialize = { version = "^0.4.0-alpha", default-features = false }
 
 [dev-dependencies]
-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-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]

bls12_381/src/curves/g1.rs

@@ -1,7 +1,7 @@
-use crate::*;
 use ark_ec::{
     bls12,
     bls12::Bls12Config,
+    hashing::curve_maps::wb::{IsogenyMap, WBConfig},
     models::CurveConfig,
     short_weierstrass::{Affine, SWCurveConfig},
     AffineRepr, Group,
@@ -10,8 +10,12 @@ 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,
+use super::g1_swu_iso;
+use crate::{
+    util::{
+        read_g1_compressed, read_g1_uncompressed, serialize_fq, EncodingFlags, G1_SERIALIZED_SIZE,
+    },
+    Fq, Fr,
 };
 
 pub type G1Affine = bls12::G1Affine<crate::Config>;
@@ -143,6 +147,14 @@ fn one_minus_x() -> Fr {
     Fr::one() - X
 }
 
+// Parameters from the [IETF draft v16, section E.2](https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-11-isogeny-map-for-bls12-381).
+impl WBConfig for Config {
+    type IsogenousCurve = g1_swu_iso::SwuIsoConfig;
+
+    const ISOGENY_MAP: IsogenyMap<'static, Self::IsogenousCurve, Self> =
+        g1_swu_iso::ISOGENY_MAP_TO_G1;
+}
+
 /// G1_GENERATOR_X =
 /// 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
 pub const G1_GENERATOR_X: Fq = MontFp!("3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");
@@ -167,6 +179,7 @@ pub fn endomorphism(p: &Affine) -> Affine {
 mod test {
 
     use super::*;
+    use crate::g1;
     use ark_std::{rand::Rng, UniformRand};
 
     fn sample_unchecked() -> Affine<g1::Config> {

bls12_381/src/curves/g1_swu_iso.rs

@@ -0,0 +1,140 @@
+use crate::{g1, Fq, Fr};
+use ark_ec::{
+    hashing::curve_maps::{swu::SWUConfig, wb::IsogenyMap},
+    models::{
+        short_weierstrass::{Affine, SWCurveConfig},
+        CurveConfig,
+    },
+};
+use ark_ff::MontFp;
+
+type G1Affine = Affine<SwuIsoConfig>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct SwuIsoConfig;
+
+impl CurveConfig for SwuIsoConfig {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = (x - 1)^2 / 3  = 76329603384216526031706109802092473003
+    const COFACTOR: &'static [u64] = &[0x8c00aaab0000aaab, 0x396c8c005555e156];
+
+    /// COFACTOR_INV = COFACTOR^{-1} mod r
+    /// = 52435875175126190458656871551744051925719901746859129887267498875565241663483
+    const COFACTOR_INV: Fr =
+        MontFp!("52435875175126190458656871551744051925719901746859129887267498875565241663483");
+}
+
+// https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/
+// Hashing to Elliptic Curves
+// 8.8.1.  BLS12-381 G1
+// BLS12381G1_XMD:SHA-256_SSWU_RO_ is defined as follows:
+// * E': y'^2 = x'^3 + A' * x' + B', where
+//      -  A' = 0x144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1d
+//      -  B' = 0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0
+//      -  A' = 12190336318893619529228877361869031420615612348429846051986726275283378313155663745811710833465465981901188123677
+//      -  B' = 2906670324641927570491258158026293881577086121416628140204402091718288198173574630967936031029026176254968826637280
+//  * Z: 11
+impl SWCurveConfig for SwuIsoConfig {
+    const COEFF_A: Fq = MontFp!("12190336318893619529228877361869031420615612348429846051986726275283378313155663745811710833465465981901188123677");
+
+    #[rustfmt::skip]
+    const COEFF_B: Fq = MontFp!("2906670324641927570491258158026293881577086121416628140204402091718288198173574630967936031029026176254968826637280");
+
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
+}
+
+/// Lexicographically smallest, valid x-coordinate of a point P on the curve
+/// (with its corresponding y) multiplied by the cofactor. P_x = 2
+/// P_y = 658522096176515125667361255350269797307718222519385801637008089782287711363858559738763090642304321670226247205569
+/// P = E(P_x, P_y)
+/// G = P * COFACTOR
+const G1_GENERATOR_X: Fq = MontFp!("1677416608493238977774703213729589714082762656433187746258164626835771660734158898989765932111853529350617333597651");
+const G1_GENERATOR_Y: Fq = MontFp!("1405098061573104639413728190240719229571583960971553962991897960445246185035342568402755187331334546673157015627211");
+
+impl SWUConfig for SwuIsoConfig {
+    // ZETA = 0xb as per the IETF draft.
+    const ZETA: Fq = MontFp!("11");
+}
+
+pub const ISOGENY_MAP_TO_G1 : IsogenyMap<'_, SwuIsoConfig, g1::Config, > = IsogenyMap {
+    x_map_numerator : &[
+        MontFp!("2712959285290305970661081772124144179193819192423276218370281158706191519995889425075952244140278856085036081760695"),
+        MontFp!("3564859427549639835253027846704205725951033235539816243131874237388832081954622352624080767121604606753339903542203"),
+        MontFp!("2051387046688339481714726479723076305756384619135044672831882917686431912682625619320120082313093891743187631791280"),
+        MontFp!("3612713941521031012780325893181011392520079402153354595775735142359240110423346445050803899623018402874731133626465"),
+        MontFp!("2247053637822768981792833880270996398470828564809439728372634811976089874056583714987807553397615562273407692740057"),
+        MontFp!("3415427104483187489859740871640064348492611444552862448295571438270821994900526625562705192993481400731539293415811"),
+        MontFp!("2067521456483432583860405634125513059912765526223015704616050604591207046392807563217109432457129564962571408764292"),
+        MontFp!("3650721292069012982822225637849018828271936405382082649291891245623305084633066170122780668657208923883092359301262"),
+        MontFp!("1239271775787030039269460763652455868148971086016832054354147730155061349388626624328773377658494412538595239256855"),
+        MontFp!("3479374185711034293956731583912244564891370843071137483962415222733470401948838363051960066766720884717833231600798"),
+        MontFp!("2492756312273161536685660027440158956721981129429869601638362407515627529461742974364729223659746272460004902959995"),
+        MontFp!("1058488477413994682556770863004536636444795456512795473806825292198091015005841418695586811009326456605062948114985"),
+    ],
+
+    x_map_denominator : &[
+        MontFp!("1353092447850172218905095041059784486169131709710991428415161466575141675351394082965234118340787683181925558786844"),
+        MontFp!("2822220997908397120956501031591772354860004534930174057793539372552395729721474912921980407622851861692773516917759"),
+        MontFp!("1717937747208385987946072944131378949849282930538642983149296304709633281382731764122371874602115081850953846504985"),
+        MontFp!("501624051089734157816582944025690868317536915684467868346388760435016044027032505306995281054569109955275640941784"),
+        MontFp!("3025903087998593826923738290305187197829899948335370692927241015584233559365859980023579293766193297662657497834014"),
+        MontFp!("2224140216975189437834161136818943039444741035168992629437640302964164227138031844090123490881551522278632040105125"),
+        MontFp!("1146414465848284837484508420047674663876992808692209238763293935905506532411661921697047880549716175045414621825594"),
+        MontFp!("3179090966864399634396993677377903383656908036827452986467581478509513058347781039562481806409014718357094150199902"),
+        MontFp!("1549317016540628014674302140786462938410429359529923207442151939696344988707002602944342203885692366490121021806145"),
+        MontFp!("1442797143427491432630626390066422021593505165588630398337491100088557278058060064930663878153124164818522816175370"),
+        MontFp!("1"),
+    ],
+
+    y_map_numerator : &[
+        MontFp!("1393399195776646641963150658816615410692049723305861307490980409834842911816308830479576739332720113414154429643571"),
+        MontFp!("2968610969752762946134106091152102846225411740689724909058016729455736597929366401532929068084731548131227395540630"),
+        MontFp!("122933100683284845219599644396874530871261396084070222155796123161881094323788483360414289333111221370374027338230"),
+        MontFp!("303251954782077855462083823228569901064301365507057490567314302006681283228886645653148231378803311079384246777035"),
+        MontFp!("1353972356724735644398279028378555627591260676383150667237975415318226973994509601413730187583692624416197017403099"),
+        MontFp!("3443977503653895028417260979421240655844034880950251104724609885224259484262346958661845148165419691583810082940400"),
+        MontFp!("718493410301850496156792713845282235942975872282052335612908458061560958159410402177452633054233549648465863759602"),
+        MontFp!("1466864076415884313141727877156167508644960317046160398342634861648153052436926062434809922037623519108138661903145"),
+        MontFp!("1536886493137106337339531461344158973554574987550750910027365237255347020572858445054025958480906372033954157667719"),
+        MontFp!("2171468288973248519912068884667133903101171670397991979582205855298465414047741472281361964966463442016062407908400"),
+        MontFp!("3915937073730221072189646057898966011292434045388986394373682715266664498392389619761133407846638689998746172899634"),
+        MontFp!("3802409194827407598156407709510350851173404795262202653149767739163117554648574333789388883640862266596657730112910"),
+        MontFp!("1707589313757812493102695021134258021969283151093981498394095062397393499601961942449581422761005023512037430861560"),
+        MontFp!("349697005987545415860583335313370109325490073856352967581197273584891698473628451945217286148025358795756956811571"),
+        MontFp!("885704436476567581377743161796735879083481447641210566405057346859953524538988296201011389016649354976986251207243"),
+        MontFp!("3370924952219000111210625390420697640496067348723987858345031683392215988129398381698161406651860675722373763741188"),
+    ],
+
+    y_map_denominator : &[
+        MontFp!("3396434800020507717552209507749485772788165484415495716688989613875369612529138640646200921379825018840894888371137"),
+        MontFp!("3907278185868397906991868466757978732688957419873771881240086730384895060595583602347317992689443299391009456758845"),
+        MontFp!("854914566454823955479427412036002165304466268547334760894270240966182605542146252771872707010378658178126128834546"),
+        MontFp!("3496628876382137961119423566187258795236027183112131017519536056628828830323846696121917502443333849318934945158166"),
+        MontFp!("1828256966233331991927609917644344011503610008134915752990581590799656305331275863706710232159635159092657073225757"),
+        MontFp!("1362317127649143894542621413133849052553333099883364300946623208643344298804722863920546222860227051989127113848748"),
+        MontFp!("3443845896188810583748698342858554856823966611538932245284665132724280883115455093457486044009395063504744802318172"),
+        MontFp!("3484671274283470572728732863557945897902920439975203610275006103818288159899345245633896492713412187296754791689945"),
+        MontFp!("3755735109429418587065437067067640634211015783636675372165599470771975919172394156249639331555277748466603540045130"),
+        MontFp!("3459661102222301807083870307127272890283709299202626530836335779816726101522661683404130556379097384249447658110805"),
+        MontFp!("742483168411032072323733249644347333168432665415341249073150659015707795549260947228694495111018381111866512337576"),
+        MontFp!("1662231279858095762833829698537304807741442669992646287950513237989158777254081548205552083108208170765474149568658"),
+        MontFp!("1668238650112823419388205992952852912407572045257706138925379268508860023191233729074751042562151098884528280913356"),
+        MontFp!("369162719928976119195087327055926326601627748362769544198813069133429557026740823593067700396825489145575282378487"),
+        MontFp!("2164195715141237148945939585099633032390257748382945597506236650132835917087090097395995817229686247227784224263055"),
+        MontFp!("1"),
+    ],
+};
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_gen() {
+        let gen: G1Affine = SwuIsoConfig::GENERATOR;
+        assert!(gen.is_on_curve());
+        assert!(gen.is_in_correct_subgroup_assuming_on_curve());
+    }
+}

bls12_381/src/curves/g2.rs

@@ -3,6 +3,7 @@ use ark_std::ops::Neg;
 use ark_ec::{
     bls12,
     bls12::Bls12Config,
+    hashing::curve_maps::wb::{IsogenyMap, WBConfig},
     models::CurveConfig,
     short_weierstrass::{Affine, Projective, SWCurveConfig},
     AffineRepr, CurveGroup, Group,
@@ -10,7 +11,10 @@ use ark_ec::{
 use ark_ff::{Field, MontFp, Zero};
 use ark_serialize::{Compress, SerializationError};
 
-use super::util::{serialize_fq, EncodingFlags, G2_SERIALIZED_SIZE};
+use super::{
+    g2_swu_iso,
+    util::{serialize_fq, EncodingFlags, G2_SERIALIZED_SIZE},
+};
 use crate::{
     util::{read_g2_compressed, read_g2_uncompressed},
     *,
@@ -200,11 +204,8 @@ pub const G2_GENERATOR_Y_C0: Fq = MontFp!("1985150602287291935568054521177171638
 /// 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582
 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(
+const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = Fq2::new(
     Fq::ZERO,
     MontFp!(
                 "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"
@@ -212,28 +213,30 @@ pub const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = Fq2::new(
 );
 
 // PSI_Y = 1/(u+1)^((p-1)/2)
-pub const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = Fq2::new(
+const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = Fq2::new(
     MontFp!(
                 "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
     MontFp!(
-                "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257")
+       "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257")
 );
 
-pub const DOUBLE_P_POWER_ENDOMORPHISM: Fq2 = Fq2::new(
+// PSI_2_X = (u+1)^((1-p^2)/3)
+const DOUBLE_P_POWER_ENDOMORPHISM_COEFF_0: Fq2 = Fq2::new(
     MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
     Fq::ZERO
 );
 
-pub fn p_power_endomorphism(p: &Affine<Config>) -> Affine<Config> {
+/// psi(P) is the untwist-Frobenius-twist endomorhism on E'(Fq2)
+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)),
+    //    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)).
+    //    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)))
@@ -252,20 +255,52 @@ pub fn p_power_endomorphism(p: &Affine) -> Affine {
 }
 
 /// For a p-power endomorphism psi(P), compute psi(psi(P))
-pub fn double_p_power_endomorphism(p: &Projective<Config>) -> Projective<Config> {
+fn double_p_power_endomorphism(p: &Projective<Config>) -> Projective<Config> {
     let mut res = *p;
 
-    res.x *= DOUBLE_P_POWER_ENDOMORPHISM;
+    res.x *= DOUBLE_P_POWER_ENDOMORPHISM_COEFF_0;
     res.y = res.y.neg();
 
     res
 }
 
+// Parametres from the [IETF draft v16, section E.3](https://www.ietf.org/archive/id/draft-irtf-cfrg-hash-to-curve-16.html#name-3-isogeny-map-for-bls12-381).
+impl WBConfig for Config {
+    type IsogenousCurve = g2_swu_iso::SwuIsoConfig;
+
+    const ISOGENY_MAP: IsogenyMap<'static, Self::IsogenousCurve, Self> =
+        g2_swu_iso::ISOGENY_MAP_TO_G2;
+}
+
 #[cfg(test)]
 mod test {
 
     use super::*;
-    use ark_std::UniformRand;
+    use ark_std::{rand::Rng, UniformRand};
+
+    fn sample_unchecked() -> Affine<g2::Config> {
+        let mut rng = ark_std::test_rng();
+        loop {
+            let x1 = Fq::rand(&mut rng);
+            let x2 = Fq::rand(&mut rng);
+            let greatest = rng.gen();
+            let x = Fq2::new(x1, x2);
+
+            if let Some(p) = Affine::get_point_from_x_unchecked(x, greatest) {
+                return p;
+            }
+        }
+    }
+
+    #[test]
+    fn test_psi_2() {
+        let p = sample_unchecked();
+        let psi_p = p_power_endomorphism(&p);
+        let psi2_p_composed = p_power_endomorphism(&psi_p);
+        let psi2_p_optimised = double_p_power_endomorphism(&p.into());
+
+        assert_eq!(psi2_p_composed, psi2_p_optimised);
+    }
 
     #[test]
     fn test_cofactor_clearing() {
@@ -284,13 +319,14 @@ mod test {
             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 p: Affine<g2::Config> = sample_unchecked();
+            let optimised = p.clear_cofactor();
             let naive = g2::Config::mul_affine(&p, h_eff);
-            assert_eq!(optimised, naive);
+            assert_eq!(optimised.into_group(), naive);
+            assert!(optimised.is_on_curve());
+            assert!(optimised.is_in_correct_subgroup_assuming_on_curve());
         }
     }
 }

bls12_381/src/curves/g2_swu_iso.rs

@@ -0,0 +1,151 @@
+use crate::*;
+
+use ark_ec::{
+    hashing::curve_maps::{swu::SWUConfig, wb::IsogenyMap},
+    models::{
+        short_weierstrass::{Affine, SWCurveConfig},
+        CurveConfig,
+    },
+};
+use ark_ff::MontFp;
+
+type G2Affine = Affine<SwuIsoConfig>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct SwuIsoConfig;
+
+impl CurveConfig for SwuIsoConfig {
+    type BaseField = Fq2;
+    type ScalarField = Fr;
+
+    /// Cofactors of g2_iso and g2 are the same.
+    /// COFACTOR = (x^8 - 4 x^7 + 5 x^6) - (4 x^4 + 6 x^3 - 4 x^2 - 4 x + 13) //
+    /// 9
+    /// = 3055023339312683442009997531931215042144660192541881426676640329822676041829718840265074273592599778478322728390416166612858038233783720963550777062779109
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        0xcf1c38e31c7238e5,
+        0x1616ec6e786f0c70,
+        0x21537e293a6691ae,
+        0xa628f1cb4d9e82ef,
+        0xa68a205b2e5a7ddf,
+        0xcd91de4547085aba,
+        0x91d50792876a202,
+        0x5d543a95414e7f1,
+    ];
+
+    /// COFACTOR_INV = COFACTOR^{-1} mod r
+    /// 26652489039290660355457965112010883481355318854675681319708643586776743290055
+    const COFACTOR_INV: Fr =
+        MontFp!("26652489039290660355457965112010883481355318854675681319708643586776743290055");
+}
+
+// https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/
+// Hashing to Elliptic Curves
+// 8.8.2.  BLS12-381 G2
+//   * E': y'^2 = x'^3 + A' * x' + B', where
+//
+//      - A' = 240 * I
+//
+//      - B' = 1012 * (1 + I)
+//
+//   * Z: -(2 + I)
+impl SWCurveConfig for SwuIsoConfig {
+    /// COEFF_A = 240 * I
+    const COEFF_A: Fq2 = Fq2::new(MontFp!("0"), MontFp!("240"));
+
+    /// COEFF_B = 1012 + 1012 * I
+    const COEFF_B: Fq2 = Fq2::new(MontFp!("1012"), MontFp!("1012"));
+
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
+}
+
+/// Lexicographically smallest, valid x-coordinate of a point P on the curve
+/// (with its corresponding y) multiplied by the cofactor. P_x = 1
+/// P_y = 1199519624119946820355795551601605892701128025883245860600494152840508171012839086684258857614063467038089173303263 + 2721622435888802346851223931977585460571674503470326381323808470905804676865417627238564067834747838523978879375704 * I
+/// P = E(P_x, P_y)
+/// G = P * COFACTOR
+const G2_GENERATOR_X: Fq2 = Fq2::new(
+    MontFp!("2595569946714414516067015540153643524656442638788025933727967960306287756885400469291119095920626560658971252184199"),
+    MontFp!("1037079738597573406765355774006601850633656296583542639082316151670128374872040593053087014315526494961765370307992")
+);
+const G2_GENERATOR_Y: Fq2 = Fq2::new(
+    MontFp!("3927929472994661655038722055497331445175131868678630546921475383290711810401295661250673209427965906654429357114487"),
+    MontFp!("3300326318345570015758639333209189167876318321385223785506096497597561910823001330832964776707374262378602791224889")
+);
+
+impl SWUConfig for SwuIsoConfig {
+    // ZETA = -(2 + u) as per IETF draft.
+    const ZETA: Fq2 = Fq2::new(MontFp!("-2"), MontFp!("-1"));
+}
+
+pub const ISOGENY_MAP_TO_G2  : IsogenyMap<'_, SwuIsoConfig, g2::Config> = IsogenyMap {
+    x_map_numerator: &[
+        Fq2::new(
+                   MontFp!("889424345604814976315064405719089812568196182208668418962679585805340366775741747653930584250892369786198727235542"),
+                   MontFp!("889424345604814976315064405719089812568196182208668418962679585805340366775741747653930584250892369786198727235542")), 
+        Fq2::new(
+                   MontFp!("0"),
+                   MontFp!("2668273036814444928945193217157269437704588546626005256888038757416021100327225242961791752752677109358596181706522")),
+        Fq2::new(
+                   MontFp!("2668273036814444928945193217157269437704588546626005256888038757416021100327225242961791752752677109358596181706526"),
+                   MontFp!("1334136518407222464472596608578634718852294273313002628444019378708010550163612621480895876376338554679298090853261")), 
+        Fq2::new(
+                   MontFp!("3557697382419259905260257622876359250272784728834673675850718343221361467102966990615722337003569479144794908942033"), 
+                   MontFp!("0")),
+    ],
+
+    x_map_denominator:  &[
+        Fq2::new(
+                   MontFp!("0"), 
+                   MontFp!("4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559715")), 
+        Fq2::new(
+                   MontFp!("12"), 
+                   MontFp!("4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559775")), 
+        Fq2::new(
+                   MontFp!("1"), 
+                   MontFp!("0")),
+    ],
+
+    y_map_numerator: &[
+        Fq2::new(
+                   MontFp!("3261222600550988246488569487636662646083386001431784202863158481286248011511053074731078808919938689216061999863558"),
+                   MontFp!("3261222600550988246488569487636662646083386001431784202863158481286248011511053074731078808919938689216061999863558")),
+        Fq2::new(
+                   MontFp!("0"),
+                   MontFp!("889424345604814976315064405719089812568196182208668418962679585805340366775741747653930584250892369786198727235518")),
+        Fq2::new(
+                   MontFp!("2668273036814444928945193217157269437704588546626005256888038757416021100327225242961791752752677109358596181706524"),
+                   MontFp!("1334136518407222464472596608578634718852294273313002628444019378708010550163612621480895876376338554679298090853263")),
+        Fq2::new(
+                   MontFp!("2816510427748580758331037284777117739799287910327449993381818688383577828123182200904113516794492504322962636245776"),
+                   MontFp!("0")),
+    ],
+
+    y_map_denominator: &[
+        Fq2::new(
+                   MontFp!("4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559355"),
+                   MontFp!("4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559355")),
+        Fq2::new(
+                   MontFp!("0"),
+                   MontFp!("4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559571")),
+        Fq2::new(
+                   MontFp!("18"),
+                   MontFp!("4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559769")),
+        Fq2::new(
+                   MontFp!("1"),
+                   MontFp!("0")),
+    ],
+};
+
+#[cfg(test)]
+mod test {
+    use super::*;
+
+    #[test]
+    fn test_gen() {
+        let gen: G2Affine = curves::g2_swu_iso::SwuIsoConfig::GENERATOR;
+        assert!(gen.is_on_curve());
+        assert!(gen.is_in_correct_subgroup_assuming_on_curve());
+    }
+}

bls12_381/src/curves/mod.rs

@@ -6,6 +6,9 @@ pub mod g1;
 pub mod g2;
 pub(crate) mod util;
 
+mod g1_swu_iso;
+mod g2_swu_iso;
+
 #[cfg(test)]
 mod tests;
 

bls12_381/src/curves/tests/BLS12381G1_XMD-SHA-256_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x40",
+  "Z": "0xb",
+  "ciphersuite": "BLS12381G1_XMD:SHA-256_SSWU_RO_",
+  "curve": "BLS12-381 G1",
+  "dst": "QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x1",
+    "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x052926add2207b76ca4fa57a8734416c8dc95e24501772c814278700eed6d1e4e8cf62d9c09db0fac349612b759e79a1",
+        "y": "0x08ba738453bfed09cb546dbb0783dbb3a5f1f566ed67bb6be0e8c67e2e81a4cc68ee29813bb7994998f3eae0c9c6a265"
+      },
+      "Q0": {
+        "x": "0x11a3cce7e1d90975990066b2f2643b9540fa40d6137780df4e753a8054d07580db3b7f1f03396333d4a359d1fe3766fe",
+        "y": "0x0eeaf6d794e479e270da10fdaf768db4c96b650a74518fc67b04b03927754bac66f3ac720404f339ecdcc028afa091b7"
+      },
+      "Q1": {
+        "x": "0x160003aaf1632b13396dbad518effa00fff532f604de1a7fc2082ff4cb0afa2d63b2c32da1bef2bf6c5ca62dc6b72f9c",
+        "y": "0x0d8bb2d14e20cf9f6036152ed386d79189415b6d015a20133acb4e019139b94e9c146aaad5817f866c95d609a361735e"
+      },
+      "msg": "",
+      "u": [
+        "0x0ba14bd907ad64a016293ee7c2d276b8eae71f25a4b941eece7b0d89f17f75cb3ae5438a614fb61d6835ad59f29c564f",
+        "0x019b9bd7979f12657976de2884c7cce192b82c177c80e0ec604436a7f538d231552f0d96d9f7babe5fa3b19b3ff25ac9"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x03567bc5ef9c690c2ab2ecdf6a96ef1c139cc0b2f284dca0a9a7943388a49a3aee664ba5379a7655d3c68900be2f6903",
+        "y": "0x0b9c15f3fe6e5cf4211f346271d7b01c8f3b28be689c8429c85b67af215533311f0b8dfaaa154fa6b88176c229f2885d"
+      },
+      "Q0": {
+        "x": "0x125435adce8e1cbd1c803e7123f45392dc6e326d292499c2c45c5865985fd74fe8f042ecdeeec5ecac80680d04317d80",
+        "y": "0x0e8828948c989126595ee30e4f7c931cbd6f4570735624fd25aef2fa41d3f79cfb4b4ee7b7e55a8ce013af2a5ba20bf2"
+      },
+      "Q1": {
+        "x": "0x11def93719829ecda3b46aa8c31fc3ac9c34b428982b898369608e4f042babee6c77ab9218aad5c87ba785481eff8ae4",
+        "y": "0x0007c9cef122ccf2efd233d6eb9bfc680aa276652b0661f4f820a653cec1db7ff69899f8e52b8e92b025a12c822a6ce6"
+      },
+      "msg": "abc",
+      "u": [
+        "0x0d921c33f2bad966478a03ca35d05719bdf92d347557ea166e5bba579eea9b83e9afa5c088573c2281410369fbd32951",
+        "0x003574a00b109ada2f26a37a91f9d1e740dffd8d69ec0c35e1e9f4652c7dba61123e9dd2e76c655d956e2b3462611139"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x11e0b079dea29a68f0383ee94fed1b940995272407e3bb916bbf268c263ddd57a6a27200a784cbc248e84f357ce82d98",
+        "y": "0x03a87ae2caf14e8ee52e51fa2ed8eefe80f02457004ba4d486d6aa1f517c0889501dc7413753f9599b099ebcbbd2d709"
+      },
+      "Q0": {
+        "x": "0x08834484878c217682f6d09a4b51444802fdba3d7f2df9903a0ddadb92130ebbfa807fffa0eabf257d7b48272410afff",
+        "y": "0x0b318f7ecf77f45a0f038e62d7098221d2dbbca2a394164e2e3fe953dc714ac2cde412d8f2d7f0c03b259e6795a2508e"
+      },
+      "Q1": {
+        "x": "0x158418ed6b27e2549f05531a8281b5822b31c3bf3144277fbb977f8d6e2694fedceb7011b3c2b192f23e2a44b2bd106e",
+        "y": "0x1879074f344471fac5f839e2b4920789643c075792bec5af4282c73f7941cda5aa77b00085eb10e206171b9787c4169f"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x062d1865eb80ebfa73dcfc45db1ad4266b9f3a93219976a3790ab8d52d3e5f1e62f3b01795e36834b17b70e7b76246d4",
+        "0x0cdc3e2f271f29c4ff75020857ce6c5d36008c9b48385ea2f2bf6f96f428a3deb798aa033cd482d1cdc8b30178b08e3a"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x15f68eaa693b95ccb85215dc65fa81038d69629f70aeee0d0f677cf22285e7bf58d7cb86eefe8f2e9bc3f8cb84fac488",
+        "y": "0x1807a1d50c29f430b8cafc4f8638dfeeadf51211e1602a5f184443076715f91bb90a48ba1e370edce6ae1062f5e6dd38"
+      },
+      "Q0": {
+        "x": "0x0cbd7f84ad2c99643fea7a7ac8f52d63d66cefa06d9a56148e58b984b3dd25e1f41ff47154543343949c64f88d48a710",
+        "y": "0x052c00e4ed52d000d94881a5638ae9274d3efc8bc77bc0e5c650de04a000b2c334a9e80b85282a00f3148dfdface0865"
+      },
+      "Q1": {
+        "x": "0x06493fb68f0d513af08be0372f849436a787e7b701ae31cb964d968021d6ba6bd7d26a38aaa5a68e8c21a6b17dc8b579",
+        "y": "0x02e98f2ccf5802b05ffaac7c20018bc0c0b2fd580216c4aa2275d2909dc0c92d0d0bdc979226adeb57a29933536b6bb4"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x010476f6a060453c0b1ad0b628f3e57c23039ee16eea5e71bb87c3b5419b1255dc0e5883322e563b84a29543823c0e86",
+        "0x0b1a912064fb0554b180e07af7e787f1f883a0470759c03c1b6509eb8ce980d1670305ae7b928226bb58fdc0a419f46e"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x082aabae8b7dedb0e78aeb619ad3bfd9277a2f77ba7fad20ef6aabdc6c31d19ba5a6d12283553294c1825c4b3ca2dcfe",
+        "y": "0x05b84ae5a942248eea39e1d91030458c40153f3b654ab7872d779ad1e942856a20c438e8d99bc8abfbf74729ce1f7ac8"
+      },
+      "Q0": {
+        "x": "0x0cf97e6dbd0947857f3e578231d07b309c622ade08f2c08b32ff372bd90db19467b2563cc997d4407968d4ac80e154f8",
+        "y": "0x127f0cddf2613058101a5701f4cb9d0861fd6c2a1b8e0afe194fccf586a3201a53874a2761a9ab6d7220c68661a35ab3"
+      },
+      "Q1": {
+        "x": "0x092f1acfa62b05f95884c6791fba989bbe58044ee6355d100973bf9553ade52b47929264e6ae770fb264582d8dce512a",
+        "y": "0x028e6d0169a72cfedb737be45db6c401d3adfb12c58c619c82b93a5dfcccef12290de530b0480575ddc8397cda0bbebf"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x0a8ffa7447f6be1c5a2ea4b959c9454b431e29ccc0802bc052413a9c5b4f9aac67a93431bd480d15be1e057c8a08e8c6",
+        "0x05d487032f602c90fa7625dbafe0f4a49ef4a6b0b33d7bb349ff4cf5410d297fd6241876e3e77b651cfc8191e40a68b7"
+      ]
+    }
+  ]
+}

bls12_381/src/curves/tests/BLS12381G2_XMD-SHA-256_SSWU_RO_.json

@@ -0,0 +1,115 @@
+{
+  "L": "0x40",
+  "Z": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9,0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa",
+  "ciphersuite": "BLS12381G2_XMD:SHA-256_SSWU_RO_",
+  "curve": "BLS12-381 G2",
+  "dst": "QUUX-V01-CS02-with-BLS12381G2_XMD:SHA-256_SSWU_RO_",
+  "expand": "XMD",
+  "field": {
+    "m": "0x2",
+    "p": "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
+  },
+  "hash": "sha256",
+  "k": "0x80",
+  "map": {
+    "name": "SSWU"
+  },
+  "randomOracle": true,
+  "vectors": [
+    {
+      "P": {
+        "x": "0x0141ebfbdca40eb85b87142e130ab689c673cf60f1a3e98d69335266f30d9b8d4ac44c1038e9dcdd5393faf5c41fb78a,0x05cb8437535e20ecffaef7752baddf98034139c38452458baeefab379ba13dff5bf5dd71b72418717047f5b0f37da03d",
+        "y": "0x0503921d7f6a12805e72940b963c0cf3471c7b2a524950ca195d11062ee75ec076daf2d4bc358c4b190c0c98064fdd92,0x12424ac32561493f3fe3c260708a12b7c620e7be00099a974e259ddc7d1f6395c3c811cdd19f1e8dbf3e9ecfdcbab8d6"
+      },
+      "Q0": {
+        "x": "0x019ad3fc9c72425a998d7ab1ea0e646a1f6093444fc6965f1cad5a3195a7b1e099c050d57f45e3fa191cc6d75ed7458c,0x171c88b0b0efb5eb2b88913a9e74fe111a4f68867b59db252ce5868af4d1254bfab77ebde5d61cd1a86fb2fe4a5a1c1d",
+        "y": "0x0ba10604e62bdd9eeeb4156652066167b72c8d743b050fb4c1016c31b505129374f76e03fa127d6a156213576910fef3,0x0eb22c7a543d3d376e9716a49b72e79a89c9bfe9feee8533ed931cbb5373dde1fbcd7411d8052e02693654f71e15410a"
+      },
+      "Q1": {
+        "x": "0x113d2b9cd4bd98aee53470b27abc658d91b47a78a51584f3d4b950677cfb8a3e99c24222c406128c91296ef6b45608be,0x13855912321c5cb793e9d1e88f6f8d342d49c0b0dbac613ee9e17e3c0b3c97dfbb5a49cc3fb45102fdbaf65e0efe2632",
+        "y": "0x0fd3def0b7574a1d801be44fde617162aa2e89da47f464317d9bb5abc3a7071763ce74180883ad7ad9a723a9afafcdca,0x056f617902b3c0d0f78a9a8cbda43a26b65f602f8786540b9469b060db7b38417915b413ca65f875c130bebfaa59790c"
+      },
+      "msg": "",
+      "u": [
+        "0x03dbc2cce174e91ba93cbb08f26b917f98194a2ea08d1cce75b2b9cc9f21689d80bd79b594a613d0a68eb807dfdc1cf8,0x05a2acec64114845711a54199ea339abd125ba38253b70a92c876df10598bd1986b739cad67961eb94f7076511b3b39a",
+        "0x02f99798e8a5acdeed60d7e18e9120521ba1f47ec090984662846bc825de191b5b7641148c0dbc237726a334473eee94,0x145a81e418d4010cc027a68f14391b30074e89e60ee7a22f87217b2f6eb0c4b94c9115b436e6fa4607e95a98de30a435"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x02c2d18e033b960562aae3cab37a27ce00d80ccd5ba4b7fe0e7a210245129dbec7780ccc7954725f4168aff2787776e6,0x139cddbccdc5e91b9623efd38c49f81a6f83f175e80b06fc374de9eb4b41dfe4ca3a230ed250fbe3a2acf73a41177fd8",
+        "y": "0x1787327b68159716a37440985269cf584bcb1e621d3a7202be6ea05c4cfe244aeb197642555a0645fb87bf7466b2ba48,0x00aa65dae3c8d732d10ecd2c50f8a1baf3001578f71c694e03866e9f3d49ac1e1ce70dd94a733534f106d4cec0eddd16"
+      },
+      "Q0": {
+        "x": "0x12b2e525281b5f4d2276954e84ac4f42cf4e13b6ac4228624e17760faf94ce5706d53f0ca1952f1c5ef75239aeed55ad,0x05d8a724db78e570e34100c0bc4a5fa84ad5839359b40398151f37cff5a51de945c563463c9efbdda569850ee5a53e77",
+        "y": "0x02eacdc556d0bdb5d18d22f23dcb086dd106cad713777c7e6407943edbe0b3d1efe391eedf11e977fac55f9b94f2489c,0x04bbe48bfd5814648d0b9e30f0717b34015d45a861425fabc1ee06fdfce36384ae2c808185e693ae97dcde118f34de41"
+      },
+      "Q1": {
+        "x": "0x19f18cc5ec0c2f055e47c802acc3b0e40c337256a208001dde14b25afced146f37ea3d3ce16834c78175b3ed61f3c537,0x15b0dadc256a258b4c68ea43605dffa6d312eef215c19e6474b3e101d33b661dfee43b51abbf96fee68fc6043ac56a58",
+        "y": "0x05e47c1781286e61c7ade887512bd9c2cb9f640d3be9cf87ea0bad24bd0ebfe946497b48a581ab6c7d4ca74b5147287f,0x19f98db2f4a1fcdf56a9ced7b320ea9deecf57c8e59236b0dc21f6ee7229aa9705ce9ac7fe7a31c72edca0d92370c096"
+      },
+      "msg": "abc",
+      "u": [
+        "0x15f7c0aa8f6b296ab5ff9c2c7581ade64f4ee6f1bf18f55179ff44a2cf355fa53dd2a2158c5ecb17d7c52f63e7195771,0x01c8067bf4c0ba709aa8b9abc3d1cef589a4758e09ef53732d670fd8739a7274e111ba2fcaa71b3d33df2a3a0c8529dd",
+        "0x187111d5e088b6b9acfdfad078c4dacf72dcd17ca17c82be35e79f8c372a693f60a033b461d81b025864a0ad051a06e4,0x08b852331c96ed983e497ebc6dee9b75e373d923b729194af8e72a051ea586f3538a6ebb1e80881a082fa2b24df9f566"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x121982811d2491fde9ba7ed31ef9ca474f0e1501297f68c298e9f4c0028add35aea8bb83d53c08cfc007c1e005723cd0,0x190d119345b94fbd15497bcba94ecf7db2cbfd1e1fe7da034d26cbba169fb3968288b3fafb265f9ebd380512a71c3f2c",
+        "y": "0x05571a0f8d3c08d094576981f4a3b8eda0a8e771fcdcc8ecceaf1356a6acf17574518acb506e435b639353c2e14827c8,0x0bb5e7572275c567462d91807de765611490205a941a5a6af3b1691bfe596c31225d3aabdf15faff860cb4ef17c7c3be"
+      },
+      "Q0": {
+        "x": "0x0f48f1ea1318ddb713697708f7327781fb39718971d72a9245b9731faaca4dbaa7cca433d6c434a820c28b18e20ea208,0x06051467c8f85da5ba2540974758f7a1e0239a5981de441fdd87680a995649c211054869c50edbac1f3a86c561ba3162",
+        "y": "0x168b3d6df80069dbbedb714d41b32961ad064c227355e1ce5fac8e105de5e49d77f0c64867f3834848f152497eb76333,0x134e0e8331cee8cb12f9c2d0742714ed9eee78a84d634c9a95f6a7391b37125ed48bfc6e90bf3546e99930ff67cc97bc"
+      },
+      "Q1": {
+        "x": "0x004fd03968cd1c99a0dd84551f44c206c84dcbdb78076c5bfee24e89a92c8508b52b88b68a92258403cbe1ea2da3495f,0x1674338ea298281b636b2eb0fe593008d03171195fd6dcd4531e8a1ed1f02a72da238a17a635de307d7d24aa2d969a47",
+        "y": "0x0dc7fa13fff6b12558419e0a1e94bfc3cfaf67238009991c5f24ee94b632c3d09e27eca329989aee348a67b50d5e236c,0x169585e164c131103d85324f2d7747b23b91d66ae5d947c449c8194a347969fc6bbd967729768da485ba71868df8aed2"
+      },
+      "msg": "abcdef0123456789",
+      "u": [
+        "0x0313d9325081b415bfd4e5364efaef392ecf69b087496973b229303e1816d2080971470f7da112c4eb43053130b785e1,0x062f84cb21ed89406890c051a0e8b9cf6c575cf6e8e18ecf63ba86826b0ae02548d83b483b79e48512b82a6c0686df8f",
+        "0x1739123845406baa7be5c5dc74492051b6d42504de008c635f3535bb831d478a341420e67dcc7b46b2e8cba5379cca97,0x01897665d9cb5db16a27657760bbea7951f67ad68f8d55f7113f24ba6ddd82caef240a9bfa627972279974894701d975"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x19a84dd7248a1066f737cc34502ee5555bd3c19f2ecdb3c7d9e24dc65d4e25e50d83f0f77105e955d78f4762d33c17da,0x0934aba516a52d8ae479939a91998299c76d39cc0c035cd18813bec433f587e2d7a4fef038260eef0cef4d02aae3eb91",
+        "y": "0x14f81cd421617428bc3b9fe25afbb751d934a00493524bc4e065635b0555084dd54679df1536101b2c979c0152d09192,0x09bcccfa036b4847c9950780733633f13619994394c23ff0b32fa6b795844f4a0673e20282d07bc69641cee04f5e5662"
+      },
+      "Q0": {
+        "x": "0x09eccbc53df677f0e5814e3f86e41e146422834854a224bf5a83a50e4cc0a77bfc56718e8166ad180f53526ea9194b57,0x0c3633943f91daee715277bd644fba585168a72f96ded64fc5a384cce4ec884a4c3c30f08e09cd2129335dc8f67840ec",
+        "y": "0x0eb6186a0457d5b12d132902d4468bfeb7315d83320b6c32f1c875f344efcba979952b4aa418589cb01af712f98cc555,0x119e3cf167e69eb16c1c7830e8df88856d48be12e3ff0a40791a5cd2f7221311d4bf13b1847f371f467357b3f3c0b4c7"
+      },
+      "Q1": {
+        "x": "0x0eb3aabc1ddfce17ff18455fcc7167d15ce6b60ddc9eb9b59f8d40ab49420d35558686293d046fc1e42f864b7f60e381,0x198bdfb19d7441ebcca61e8ff774b29d17da16547d2c10c273227a635cacea3f16826322ae85717630f0867539b5ed8b",
+        "y": "0x0aaf1dee3adf3ed4c80e481c09b57ea4c705e1b8d25b897f0ceeec3990748716575f92abff22a1c8f4582aff7b872d52,0x0d058d9061ed27d4259848a06c96c5ca68921a5d269b078650c882cb3c2bd424a8702b7a6ee4e0ead9982baf6843e924"
+      },
+      "msg": "q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq",
+      "u": [
+        "0x025820cefc7d06fd38de7d8e370e0da8a52498be9b53cba9927b2ef5c6de1e12e12f188bbc7bc923864883c57e49e253,0x034147b77ce337a52e5948f66db0bab47a8d038e712123bb381899b6ab5ad20f02805601e6104c29df18c254b8618c7b",
+        "0x0930315cae1f9a6017c3f0c8f2314baa130e1cf13f6532bff0a8a1790cd70af918088c3db94bda214e896e1543629795,0x10c4df2cacf67ea3cb3108b00d4cbd0b3968031ebc8eac4b1ebcefe84d6b715fde66bef0219951ece29d1facc8a520ef"
+      ]
+    },
+    {
+      "P": {
+        "x": "0x01a6ba2f9a11fa5598b2d8ace0fbe0a0eacb65deceb476fbbcb64fd24557c2f4b18ecfc5663e54ae16a84f5ab7f62534,0x11fca2ff525572795a801eed17eb12785887c7b63fb77a42be46ce4a34131d71f7a73e95fee3f812aea3de78b4d01569",
+        "y": "0x0b6798718c8aed24bc19cb27f866f1c9effcdbf92397ad6448b5c9db90d2b9da6cbabf48adc1adf59a1a28344e79d57e,0x03a47f8e6d1763ba0cad63d6114c0accbef65707825a511b251a660a9b3994249ae4e63fac38b23da0c398689ee2ab52"
+      },
+      "Q0": {
+        "x": "0x17cadf8d04a1a170f8347d42856526a24cc466cb2ddfd506cff01191666b7f944e31244d662c904de5440516a2b09004,0x0d13ba91f2a8b0051cf3279ea0ee63a9f19bc9cb8bfcc7d78b3cbd8cc4fc43ba726774b28038213acf2b0095391c523e",
+        "y": "0x17ef19497d6d9246fa94d35575c0f8d06ee02f21a284dbeaa78768cb1e25abd564e3381de87bda26acd04f41181610c5,0x12c3c913ba4ed03c24f0721a81a6be7430f2971ffca8fd1729aafe496bb725807531b44b34b59b3ae5495e5a2dcbd5c8"
+      },
+      "Q1": {
+        "x": "0x16ec57b7fe04c71dfe34fb5ad84dbce5a2dbbd6ee085f1d8cd17f45e8868976fc3c51ad9eeda682c7869024d24579bfd,0x13103f7aace1ae1420d208a537f7d3a9679c287208026e4e3439ab8cd534c12856284d95e27f5e1f33eec2ce656533b0",
+        "y": "0x0958b2c4c2c10fcef5a6c59b9e92c4a67b0fae3e2e0f1b6b5edad9c940b8f3524ba9ebbc3f2ceb3cfe377655b3163bd7,0x0ccb594ed8bd14ca64ed9cb4e0aba221be540f25dd0d6ba15a4a4be5d67bcf35df7853b2d8dad3ba245f1ea3697f66aa"
+      },
+      "msg": "a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+      "u": [
+        "0x190b513da3e66fc9a3587b78c76d1d132b1152174d0b83e3c1114066392579a45824c5fa17649ab89299ddd4bda54935,0x12ab625b0fe0ebd1367fe9fac57bb1168891846039b4216b9d94007b674de2d79126870e88aeef54b2ec717a887dcf39",
+        "0x0e6a42010cf435fb5bacc156a585e1ea3294cc81d0ceb81924d95040298380b164f702275892cedd81b62de3aba3f6b5,0x117d9a0defc57a33ed208428cb84e54c85a6840e7648480ae428838989d25d97a0af8e3255be62b25c2a85630d2dddd8"
+      ]
+    }
+  ]
+}

bls12_381/src/curves/tests/mod.rs

@@ -10,6 +10,8 @@ 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_h2c!(g1_h2c; "./src/curves/tests"; "BLS12381G1"; crate::g1::Config; crate::Fq; crate::Fq; 1);
+test_h2c!(g2_hc2; "./src/curves/tests"; "BLS12381G2"; crate::g2::Config; crate::Fq2; crate::Fq; 2);
 
 #[test]
 fn test_g1_endomorphism_beta() {

bls12_381/src/fields/fq.rs

@@ -7,3 +7,6 @@ use ark_ff::fields::{Fp384, MontBackend, MontConfig};
 #[small_subgroup_power = "2"]
 pub struct FqConfig;
 pub type Fq = Fp384<MontBackend<FqConfig, 6>>;
+
+pub const FQ_ONE: Fq = ark_ff::MontFp!("1");
+pub const FQ_ZERO: Fq = ark_ff::MontFp!("0");

secp256k1/src/curves/mod.rs

@@ -43,10 +43,12 @@ impl SWCurveConfig for Config {
     }
 }
 
-/// G_GENERATOR_X = 55066263022277343669578718895168534326250603453777594175500187360389116729240
+/// G_GENERATOR_X =
+/// 55066263022277343669578718895168534326250603453777594175500187360389116729240
 pub const G_GENERATOR_X: Fq =
     MontFp!("55066263022277343669578718895168534326250603453777594175500187360389116729240");
 
-/// G_GENERATOR_Y = 32670510020758816978083085130507043184471273380659243275938904335757337482424
+/// G_GENERATOR_Y =
+/// 32670510020758816978083085130507043184471273380659243275938904335757337482424
 pub const G_GENERATOR_Y: Fq =
     MontFp!("32670510020758816978083085130507043184471273380659243275938904335757337482424");

secp256r1/Cargo.toml

@@ -0,0 +1,30 @@
+[package]
+name = "ark-secp256r1"
+version = "0.4.0-alpha"
+authors = [ "arkworks contributors" ]
+description = "The secp256r1 curve"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
+documentation = "https://docs.rs/ark-secp256r1/"
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+categories = ["cryptography"]
+include = ["Cargo.toml", "src", "LICENSE-APACHE", "LICENSE-MIT"]
+license = "MIT/Apache-2.0"
+edition = "2021"
+
+[dependencies]
+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-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-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" ]

secp256r1/LICENSE-APACHE

@@ -0,0 +1 @@
+../LICENSE-APACHE

secp256r1/LICENSE-MIT

@@ -0,0 +1 @@
+../LICENSE-MIT

secp256r1/src/constraints/curves.rs

@@ -0,0 +1,10 @@
+use crate::{constraints::FqVar, *};
+use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;
+
+/// A group element in the secp256r1 curve.
+pub type GVar = ProjectiveVar<Config, FqVar>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::curves::sw_test::<Config, GVar>().unwrap();
+}

secp256r1/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 FqVar = FpVar<Fq>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::fields::field_test::<_, _, FqVar>().unwrap();
+}

secp256r1/src/constraints/mod.rs

@@ -0,0 +1,7 @@
+//! This module implements the R1CS equivalent of `ark_secp256r1`.
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

secp256r1/src/curves/mod.rs

@@ -0,0 +1,50 @@
+use ark_ec::{
+    models::CurveConfig,
+    short_weierstrass::{self as sw, SWCurveConfig},
+};
+use ark_ff::{Field, MontFp};
+
+use crate::{fq::Fq, fr::Fr};
+
+#[cfg(test)]
+mod tests;
+
+pub type Affine = sw::Affine<Config>;
+pub type Projective = sw::Projective<Config>;
+
+#[derive(Copy, Clone, Default, PartialEq, Eq)]
+pub struct Config;
+
+impl CurveConfig for Config {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = 1
+    const COFACTOR: &'static [u64] = &[0x1];
+
+    /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr =  Fr::ONE;
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = -3
+    const COEFF_A: Fq = MontFp!("-3");
+
+    /// COEFF_B = 41058363725152142129326129780047268409114441015993725554835256314039467401291
+    const COEFF_B: Fq =
+        MontFp!("41058363725152142129326129780047268409114441015993725554835256314039467401291");
+
+    /// GENERATOR = (G_GENERATOR_X, G_GENERATOR_Y)
+    const GENERATOR: Affine = Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
+}
+
+/// G_GENERATOR_X =
+/// 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296
+pub const G_GENERATOR_X: Fq =
+    MontFp!("48439561293906451759052585252797914202762949526041747995844080717082404635286");
+
+/// G_GENERATOR_Y =
+/// 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
+pub const G_GENERATOR_Y: Fq =
+    MontFp!("36134250956749795798585127919587881956611106672985015071877198253568414405109");

secp256r1/src/curves/tests.rs

@@ -0,0 +1,4 @@
+use crate::Projective;
+use ark_algebra_test_templates::*;
+
+test_group!(g1; Projective; sw);

secp256r1/src/fields/fq.rs

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "115792089210356248762697446949407573530086143415290314195533631308867097853951"]
+#[generator = "2"]
+pub struct FqConfig;
+pub type Fq = Fp256<MontBackend<FqConfig, 4>>;

secp256r1/src/fields/fr.rs

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "115792089210356248762697446949407573529996955224135760342422259061068512044369"]
+#[generator = "11"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;

secp256r1/src/fields/mod.rs

@@ -0,0 +1,8 @@
+pub mod fq;
+pub use self::fq::*;
+
+pub mod fr;
+pub use self::fr::*;
+
+#[cfg(test)]
+mod tests;

secp256r1/src/fields/tests.rs

@@ -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);

secp256r1/src/lib.rs

@@ -0,0 +1,29 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the secp256r1 curve.
+//! Source: <https://neuromancer.sk/std/secg/secp256r1>
+//!
+//! Curve information:
+//! * Base field: q =
+//!   0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
+//! * Scalar field: r =
+//!   0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
+//! * a = -3
+//! * b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
+//! * Curve equation: y^2 = x^3 + ax + b
+
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

secp384r1/Cargo.toml

@@ -0,0 +1,30 @@
+[package]
+name = "ark-secp384r1"
+version = "0.4.0-alpha"
+authors = [ "arkworks contributors" ]
+description = "The secp384r1 curve"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
+documentation = "https://docs.rs/ark-secp384r1/"
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+categories = ["cryptography"]
+include = ["Cargo.toml", "src", "LICENSE-APACHE", "LICENSE-MIT"]
+license = "MIT/Apache-2.0"
+edition = "2021"
+
+[dependencies]
+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-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-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" ]

secp384r1/LICENSE-APACHE

@@ -0,0 +1 @@
+../LICENSE-APACHE

secp384r1/LICENSE-MIT

@@ -0,0 +1 @@
+../LICENSE-MIT

secp384r1/src/constraints/curves.rs

@@ -0,0 +1,10 @@
+use crate::{constraints::FqVar, *};
+use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;
+
+/// A group element in the secp384r1 curve.
+pub type GVar = ProjectiveVar<Config, FqVar>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::curves::sw_test::<Config, GVar>().unwrap();
+}

secp384r1/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 FqVar = FpVar<Fq>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::fields::field_test::<_, _, FqVar>().unwrap();
+}

secp384r1/src/constraints/mod.rs

@@ -0,0 +1,7 @@
+//! This module implements the R1CS equivalent of `ark_secp384r1`.
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

secp384r1/src/curves/mod.rs

@@ -0,0 +1,50 @@
+use ark_ec::{
+    models::CurveConfig,
+    short_weierstrass::{self as sw, SWCurveConfig},
+};
+use ark_ff::{Field, MontFp};
+
+use crate::{fq::Fq, fr::Fr};
+
+#[cfg(test)]
+mod tests;
+
+pub type Affine = sw::Affine<Config>;
+pub type Projective = sw::Projective<Config>;
+
+#[derive(Copy, Clone, Default, PartialEq, Eq)]
+pub struct Config;
+
+impl CurveConfig for Config {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = 1
+    const COFACTOR: &'static [u64] = &[0x1];
+
+    /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr =  Fr::ONE;
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = -3
+    const COEFF_A: Fq = MontFp!("-3");
+
+    /// COEFF_B = 27580193559959705877849011840389048093056905856361568521428707301988689241309860865136260764883745107765439761230575
+    const COEFF_B: Fq =
+        MontFp!("27580193559959705877849011840389048093056905856361568521428707301988689241309860865136260764883745107765439761230575");
+
+    /// GENERATOR = (G_GENERATOR_X, G_GENERATOR_Y)
+    const GENERATOR: Affine = Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
+}
+
+/// G_GENERATOR_X =
+/// 26247035095799689268623156744566981891852923491109213387815615900925518854738050089022388053975719786650872476732087
+pub const G_GENERATOR_X: Fq =
+    MontFp!("26247035095799689268623156744566981891852923491109213387815615900925518854738050089022388053975719786650872476732087");
+
+/// G_GENERATOR_Y =
+/// 8325710961489029985546751289520108179287853048861315594709205902480503199884419224438643760392947333078086511627871
+pub const G_GENERATOR_Y: Fq =
+    MontFp!("8325710961489029985546751289520108179287853048861315594709205902480503199884419224438643760392947333078086511627871");

secp384r1/src/curves/tests.rs

@@ -0,0 +1,4 @@
+use crate::Projective;
+use ark_algebra_test_templates::*;
+
+test_group!(g1; Projective; sw);

secp384r1/src/fields/fq.rs

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319"]
+#[generator = "2"]
+pub struct FqConfig;
+pub type Fq = Fp384<MontBackend<FqConfig, 6>>;

secp384r1/src/fields/fr.rs

@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643"]
+#[generator = "2"]
+pub struct FrConfig;
+pub type Fr = Fp384<MontBackend<FrConfig, 6>>;

secp384r1/src/fields/mod.rs

@@ -0,0 +1,8 @@
+pub mod fq;
+pub use self::fq::*;
+
+pub mod fr;
+pub use self::fr::*;
+
+#[cfg(test)]
+mod tests;

secp384r1/src/fields/tests.rs

@@ -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);

secp384r1/src/lib.rs

@@ -0,0 +1,29 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the secp384r1 curve.
+//! Source: <https://neuromancer.sk/std/nist/P-384>
+//!
+//! Curve information:
+//! * Base field: q =
+//!   0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
+//! * Scalar field: r =
+//!   0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973
+//! * a = -3
+//! * b = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef
+//! * Curve equation: y^2 = x^3 + ax + b
+
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;

secq256k1/src/curves/mod.rs

@@ -43,10 +43,12 @@ impl SWCurveConfig for Config {
     }
 }
 
-/// G_GENERATOR_X = 53718550993811904772965658690407829053653678808745171666022356150019200052646
+/// G_GENERATOR_X =
+/// 53718550993811904772965658690407829053653678808745171666022356150019200052646
 pub const G_GENERATOR_X: Fq =
     MontFp!("53718550993811904772965658690407829053653678808745171666022356150019200052646");
 
-/// G_GENERATOR_Y = 28941648020349172432234515805717979317553499307621291159490218670604692907903
+/// G_GENERATOR_Y =
+/// 28941648020349172432234515805717979317553499307621291159490218670604692907903
 pub const G_GENERATOR_Y: Fq =
     MontFp!("28941648020349172432234515805717979317553499307621291159490218670604692907903");

secq256k1/src/fields/fq.rs

@@ -1,2 +1 @@
-pub use ark_secp256k1::Fr as Fq;
-pub use ark_secp256k1::FrConfig as FqConfig;
+pub use ark_secp256k1::{Fr as Fq, FrConfig as FqConfig};

secq256k1/src/fields/fr.rs

@@ -1,2 +1 @@
-pub use ark_secp256k1::Fq as Fr;
-pub use ark_secp256k1::FqConfig as FrConfig;
+pub use ark_secp256k1::{Fq as Fr, FqConfig as FrConfig};