Upgrade to work with latest ark-ff (#95)

Co-authored-by: Sun <huachuang20@gmail.com>
2026-01-09 07:21:30 +01:00 · 2022-03-07 13:12:03 -08:00
parent d0dc200f22
commit 1551d6d76c
231 changed files with 2830 additions and 4343 deletions
--- a/bn254/scripts/base_field.sage
+++ b/bn254/scripts/base_field.sage
@@ -0,0 +1,28 @@
+modulus = 21888242871839275222246405745257275088696311157297823662689037894645226208583
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
--- a/bn254/scripts/scalar_field.sage
+++ b/bn254/scripts/scalar_field.sage
@@ -0,0 +1,28 @@
+modulus = 21888242871839275222246405745257275088548364400416034343698204186575808495617
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
--- a/bn254/src/curves/g1.rs
+++ b/bn254/src/curves/g1.rs
@@ -1,5 +1,5 @@
 use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{field_new, Zero};
+use ark_ff::{MontFp, Zero};

 use crate::{Fq, Fr};

@@ -14,15 +14,15 @@ impl ModelParameters for Parameters {
    const COFACTOR: &'static [u64] = &[0x1];

    /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
-    const COFACTOR_INV: Fr = field_new!(Fr, "1");
+    const COFACTOR_INV: Fr = MontFp!(Fr, "1");
 }

 impl SWModelParameters for Parameters {
    /// COEFF_A = 0
-    const COEFF_A: Fq = field_new!(Fq, "0");
+    const COEFF_A: Fq = MontFp!(Fq, "0");

    /// COEFF_B = 3
-    const COEFF_B: Fq = field_new!(Fq, "3");
+    const COEFF_B: Fq = MontFp!(Fq, "3");

    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@@ -35,7 +35,7 @@ impl SWModelParameters for Parameters {
 }

 /// G1_GENERATOR_X = 1
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, "1");
+pub const G1_GENERATOR_X: Fq = MontFp!(Fq, "1");

 /// G1_GENERATOR_Y = 2
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "2");
+pub const G1_GENERATOR_Y: Fq = MontFp!(Fq, "2");
--- a/bn254/src/curves/g2.rs
+++ b/bn254/src/curves/g2.rs
@@ -1,5 +1,5 @@
 use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{field_new, Zero};
+use ark_ff::{MontFp, QuadExt, Zero};

 use crate::{Fq, Fq2, Fr};

@@ -11,7 +11,7 @@ impl ModelParameters for Parameters {
    type ScalarField = Fr;

    /// COFACTOR = (36 * X^4) + (36 * X^3) + (30 * X^2) + 6*X + 1
-    ///          = 21888242871839275222246405745257275088844257914179612981679871602714643921549
+    /// 21888242871839275222246405745257275088844257914179612981679871602714643921549
    #[rustfmt::skip]
    const COFACTOR: &'static [u64] = &[
        0x345f2299c0f9fa8d,
@@ -21,21 +21,27 @@ impl ModelParameters for Parameters {
    ];

    /// COFACTOR_INV = COFACTOR^{-1} mod r
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "10944121435919637613327163357776759465618812564592884533313067514031822496649");
+    const COFACTOR_INV: Fr = MontFp!(
+        Fr,
+        "10944121435919637613327163357776759465618812564592884533313067514031822496649"
+    );
 }

 impl SWModelParameters for Parameters {
    /// COEFF_A = [0, 0]
-    #[rustfmt::skip]
-    const COEFF_A: Fq2 = field_new!(Fq2, field_new!(Fq, "0"), field_new!(Fq, "0"));
+    const COEFF_A: Fq2 = QuadExt!(MontFp!(Fq, "0"), MontFp!(Fq, "0"));

    /// COEFF_B = 3/(u+9)
-    ///         = (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
-    #[rustfmt::skip]
-    const COEFF_B: Fq2 = field_new!(Fq2,
-        field_new!(Fq, "19485874751759354771024239261021720505790618469301721065564631296452457478373"),
-        field_new!(Fq, "266929791119991161246907387137283842545076965332900288569378510910307636690"),
+    /// (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
+    const COEFF_B: Fq2 = QuadExt!(
+        MontFp!(
+            Fq,
+            "19485874751759354771024239261021720505790618469301721065564631296452457478373"
+        ),
+        MontFp!(
+            Fq,
+            "266929791119991161246907387137283842545076965332900288569378510910307636690"
+        ),
    );

    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
@@ -48,27 +54,33 @@ impl SWModelParameters for Parameters {
    }
 }

-#[rustfmt::skip]
-pub const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+pub const G2_GENERATOR_X: Fq2 = QuadExt!(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+pub const G2_GENERATOR_Y: Fq2 = QuadExt!(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);

 /// G2_GENERATOR_X_C0 =
 /// 10857046999023057135944570762232829481370756359578518086990519993285655852781
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "10857046999023057135944570762232829481370756359578518086990519993285655852781");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!(
+    Fq,
+    "10857046999023057135944570762232829481370756359578518086990519993285655852781"
+);

 /// G2_GENERATOR_X_C1 =
 /// 11559732032986387107991004021392285783925812861821192530917403151452391805634
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "11559732032986387107991004021392285783925812861821192530917403151452391805634");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!(
+    Fq,
+    "11559732032986387107991004021392285783925812861821192530917403151452391805634"
+);

 /// G2_GENERATOR_Y_C0 =
 /// 8495653923123431417604973247489272438418190587263600148770280649306958101930
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "8495653923123431417604973247489272438418190587263600148770280649306958101930");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!(
+    Fq,
+    "8495653923123431417604973247489272438418190587263600148770280649306958101930"
+);

 /// G2_GENERATOR_Y_C1 =
 /// 4082367875863433681332203403145435568316851327593401208105741076214120093531
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "4082367875863433681332203403145435568316851327593401208105741076214120093531");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!(
+    Fq,
+    "4082367875863433681332203403145435568316851327593401208105741076214120093531"
+);
--- a/bn254/src/curves/mod.rs
+++ b/bn254/src/curves/mod.rs
@@ -1,9 +1,11 @@
-use crate::*;
 use ark_ec::{
    bn,
    bn::{Bn, BnParameters, TwistType},
 };
-use ark_ff::field_new;
+use ark_ff::{MontFp, QuadExt};
+
+use crate::*;
+
 pub mod g1;
 pub mod g2;

@@ -22,33 +24,31 @@ impl BnParameters for Parameters {
        -1, 0, 0, 1, 0, 1, 1,
    ];

-    const TWIST_MUL_BY_Q_X: Fq2 = field_new!(
-        Fq2,
-        field_new!(
+    const TWIST_MUL_BY_Q_X: Fq2 = QuadExt!(
+        MontFp!(
            Fq,
            "21575463638280843010398324269430826099269044274347216827212613867836435027261"
        ),
-        field_new!(
+        MontFp!(
            Fq,
            "10307601595873709700152284273816112264069230130616436755625194854815875713954"
        ),
    );
-    const TWIST_MUL_BY_Q_Y: Fq2 = field_new!(
-        Fq2,
-        field_new!(
+    const TWIST_MUL_BY_Q_Y: Fq2 = QuadExt!(
+        MontFp!(
            Fq,
            "2821565182194536844548159561693502659359617185244120367078079554186484126554"
        ),
-        field_new!(
+        MontFp!(
            Fq,
            "3505843767911556378687030309984248845540243509899259641013678093033130930403"
        ),
    );
    const TWIST_TYPE: TwistType = TwistType::D;
    type Fp = Fq;
-    type Fp2Params = Fq2Parameters;
-    type Fp6Params = Fq6Parameters;
-    type Fp12Params = Fq12Parameters;
+    type Fp2Config = Fq2Config;
+    type Fp6Config = Fq6Config;
+    type Fp12Config = Fq12Config;
    type G1Parameters = g1::Parameters;
    type G2Parameters = g2::Parameters;
 }
--- a/bn254/src/curves/tests.rs
+++ b/bn254/src/curves/tests.rs
@@ -1,18 +1,15 @@
-#![allow(unused_imports)]
-use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    fields::{Field, FpParameters, PrimeField, SquareRootField},
-    One, Zero,
-};
-use ark_serialize::CanonicalSerialize;
-use ark_std::{rand::Rng, test_rng};
-use core::ops::{AddAssign, MulAssign};
-
-use crate::{g1, g2, Bn254, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
-
 use ark_algebra_test_templates::{
    curves::*, generate_bilinearity_test, generate_g1_test, generate_g2_test, groups::*, msm::*,
 };
+use ark_ec::{AffineCurve, PairingEngine};
+use ark_ff::{
+    fields::{Field, PrimeField},
+    One,
+};
+use ark_std::{rand::Rng, test_rng};
+use core::ops::MulAssign;
+
+use crate::{g1, g2, Bn254, Fq12, Fr, G1Affine, G1Projective, G2Affine, G2Projective};

 generate_g1_test!(bn254; curve_tests; sw_tests;);
 generate_g2_test!(bn254; curve_tests; sw_tests;);
--- a/bn254/src/fields/fq.rs
+++ b/bn254/src/fields/fq.rs
@@ -1,100 +1,10 @@
-use ark_ff::{
-    biginteger::{BigInt, BigInteger256 as BigInteger},
-    field_new,
-    fields::*,
-};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig, MontFp};

-pub type Fq = Fp256<FqParameters>;
+#[derive(MontConfig)]
+#[modulus = "21888242871839275222246405745257275088696311157297823662689037894645226208583"]
+#[generator = "3"]
+pub struct FqConfig;
+pub type Fq = Fp256<MontBackend<FqConfig, 4>>;

-pub struct FqParameters;
-
-impl Fp256Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 1;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInt::new([
-        0x68c3488912edefaa,
-        0x8d087f6872aabf4f,
-        0x51e1a24709081231,
-        0x2259d6b14729c0fa,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 21888242871839275222246405745257275088696311157297823662689037894645226208583
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInt::new([
-        0x3c208c16d87cfd47,
-        0x97816a916871ca8d,
-        0xb85045b68181585d,
-        0x30644e72e131a029,
-    ]);
-
-    const MODULUS_BITS: u32 = 254;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 2;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInt::new([
-        0xd35d438dc58f0d9d,
-        0x0a78eb28f5c70b3d,
-        0x666ea36f7879462c,
-        0xe0a77c19a07df2f,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInt::new([
-        0xf32cfc5b538afa89,
-        0xb5e71911d44501fb,
-        0x47ab1eff0a417ff6,
-        0x6d89f71cab8351f,
-    ]);
-
-    const INV: u64 = 9786893198990664585u64;
-
-    // GENERATOR = 3
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInt::new([
-        0x7a17caa950ad28d7,
-        0x1f6ac17ae15521b9,
-        0x334bea4e696bd284,
-        0x2a1f6744ce179d8e,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
-        0x9e10460b6c3e7ea3,
-        0xcbc0b548b438e546,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-
-    // T = (MODULUS - 1) // 2^S =
-    // 10944121435919637611123202872628637544348155578648911831344518947322613104291
-    #[rustfmt::skip]
-    const T: BigInteger = BigInt::new([
-        0x9e10460b6c3e7ea3,
-        0xcbc0b548b438e546,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // (T - 1) // 2 =
-    // 5472060717959818805561601436314318772174077789324455915672259473661306552145
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
-        0x4f082305b61f3f51,
-        0x65e05aa45a1c72a3,
-        0x6e14116da0605617,
-        0xc19139cb84c680a,
-    ]);
-}
-
-pub const FQ_ONE: Fq = field_new!(Fq, "1");
-pub const FQ_ZERO: Fq = field_new!(Fq, "0");
+pub const FQ_ONE: Fq = MontFp!(Fq, "1");
+pub const FQ_ZERO: Fq = MontFp!(Fq, "0");
--- a/bn254/src/fields/fq12.rs
+++ b/bn254/src/fields/fq12.rs
@@ -1,77 +1,119 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, CubicExt, MontFp, QuadExt};

-pub type Fq12 = Fp12<Fq12Parameters>;
+use crate::*;
+
+pub type Fq12 = Fp12<Fq12Config>;

 #[derive(Clone, Copy)]
-pub struct Fq12Parameters;
+pub struct Fq12Config;

-impl Fp12Parameters for Fq12Parameters {
-    type Fp6Params = Fq6Parameters;
+impl Fp12Config for Fq12Config {
+    type Fp6Config = Fq6Config;

-    const NONRESIDUE: Fq6 = field_new!(Fq6, FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = CubicExt!(FQ2_ZERO, FQ2_ONE, FQ2_ZERO);

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
-        ),
+        QuadExt!(MontFp!(Fq, "1"), MontFp!(Fq, "0"),),
        // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "8376118865763821496583973867626364092589906065868298776909617916018768340080"),
-            field_new!(Fq, "16469823323077808223889137241176536799009286646108169935659301613961712198316"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "8376118865763821496583973867626364092589906065868298776909617916018768340080"
+            ),
+            MontFp!(
+                Fq,
+                "16469823323077808223889137241176536799009286646108169935659301613961712198316"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556617"),
-            field_new!(Fq, "0"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "21888242871839275220042445260109153167277707414472061641714758635765020556617"
+            ),
+            MontFp!(Fq, "0"),
        ),
        // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "11697423496358154304825782922584725312912383441159505038794027105778954184319"),
-            field_new!(Fq, "303847389135065887422783454877609941456349188919719272345083954437860409601"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "11697423496358154304825782922584725312912383441159505038794027105778954184319"
+            ),
+            MontFp!(
+                Fq,
+                "303847389135065887422783454877609941456349188919719272345083954437860409601"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
-            field_new!(Fq, "0"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            MontFp!(Fq, "0"),
        ),
        // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "3321304630594332808241809054958361220322477375291206261884409189760185844239"),
-            field_new!(Fq, "5722266937896532885780051958958348231143373700109372999374820235121374419868"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "3321304630594332808241809054958361220322477375291206261884409189760185844239"
+            ),
+            MontFp!(
+                Fq,
+                "5722266937896532885780051958958348231143373700109372999374820235121374419868"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "-1"),
-            field_new!(Fq, "0"),
-        ),
+        QuadExt!(MontFp!(Fq, "-1"), MontFp!(Fq, "0"),),
        // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "13512124006075453725662431877630910996106405091429524885779419978626457868503"),
-            field_new!(Fq, "5418419548761466998357268504080738289687024511189653727029736280683514010267"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "13512124006075453725662431877630910996106405091429524885779419978626457868503"
+            ),
+            MontFp!(
+                Fq,
+                "5418419548761466998357268504080738289687024511189653727029736280683514010267"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
-            field_new!(Fq, "0"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "2203960485148121921418603742825762020974279258880205651966"
+            ),
+            MontFp!(Fq, "0"),
        ),
        // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "10190819375481120917420622822672549775783927716138318623895010788866272024264"),
-            field_new!(Fq, "21584395482704209334823622290379665147239961968378104390343953940207365798982"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "10190819375481120917420622822672549775783927716138318623895010788866272024264"
+            ),
+            MontFp!(
+                Fq,
+                "21584395482704209334823622290379665147239961968378104390343953940207365798982"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "2203960485148121921418603742825762020974279258880205651967"),
-            field_new!(Fq, "0"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "2203960485148121921418603742825762020974279258880205651967"
+            ),
+            MontFp!(Fq, "0"),
        ),
        // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "18566938241244942414004596690298913868373833782006617400804628704885040364344"),
-            field_new!(Fq, "16165975933942742336466353786298926857552937457188450663314217659523851788715"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "18566938241244942414004596690298913868373833782006617400804628704885040364344"
+            ),
+            MontFp!(
+                Fq,
+                "16165975933942742336466353786298926857552937457188450663314217659523851788715"
+            ),
        ),
    ];
 }
--- a/bn254/src/fields/fq2.rs
+++ b/bn254/src/fields/fq2.rs
@@ -1,31 +1,26 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp, QuadExt};

-pub type Fq2 = Fp2<Fq2Parameters>;
+use crate::*;

-pub struct Fq2Parameters;
+pub type Fq2 = Fp2<Fq2Config>;

-impl Fp2Parameters for Fq2Parameters {
+pub struct Fq2Config;
+
+impl Fp2Config for Fq2Config {
    type Fp = Fq;

    /// NONRESIDUE = -1
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, "-1");
+    const NONRESIDUE: Fq = MontFp!(Fq, "-1");

    /// QUADRATIC_NONRESIDUE = U+2
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE: (Fq, Fq) = (
-        field_new!(Fq, "2"),
-        field_new!(Fq, "1"),
-    );
+    const QUADRATIC_NONRESIDUE: Fq2 = QuadExt!(MontFp!(Fq, "2"), MontFp!(Fq, "1"));

    /// Coefficients for the Frobenius automorphism.
-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
        // NONRESIDUE**(((q^0) - 1) / 2)
-        field_new!(Fq, "1"),
+        MontFp!(Fq, "1"),
        // NONRESIDUE**(((q^1) - 1) / 2)
-        field_new!(Fq, "-1"),
+        MontFp!(Fq, "-1"),
    ];

    #[inline(always)]
@@ -34,5 +29,5 @@ impl Fp2Parameters for Fq2Parameters {
    }
 }

-pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = field_new!(Fq2, FQ_ONE, FQ_ZERO);
+pub const FQ2_ZERO: Fq2 = QuadExt!(FQ_ZERO, FQ_ZERO);
+pub const FQ2_ONE: Fq2 = QuadExt!(FQ_ONE, FQ_ZERO);
--- a/bn254/src/fields/fq6.rs
+++ b/bn254/src/fields/fq6.rs
@@ -1,82 +1,123 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp, QuadExt};

-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::*;
+
+pub type Fq6 = Fp6<Fq6Config>;

 #[derive(Clone, Copy)]
-pub struct Fq6Parameters;
+pub struct Fq6Config;

-impl Fp6Parameters for Fq6Parameters {
-    type Fp2Params = Fq2Parameters;
+impl Fp6Config for Fq6Config {
+    type Fp2Config = Fq2Config;

    /// NONRESIDUE = U+9
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq2 = field_new!(Fq2, field_new!(Fq, "9"), field_new!(Fq, "1"));
+    const NONRESIDUE: Fq2 = QuadExt!(MontFp!(Fq, "9"), MontFp!(Fq, "1"));

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
-        ),
+        QuadExt!(MontFp!(Fq, "1"), MontFp!(Fq, "0"),),
        // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "21575463638280843010398324269430826099269044274347216827212613867836435027261"),
-            field_new!(Fq, "10307601595873709700152284273816112264069230130616436755625194854815875713954"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "21575463638280843010398324269430826099269044274347216827212613867836435027261"
+            ),
+            MontFp!(
+                Fq,
+                "10307601595873709700152284273816112264069230130616436755625194854815875713954"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
-            field_new!(Fq, "0"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            MontFp!(Fq, "0"),
        ),
        // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "3772000881919853776433695186713858239009073593817195771773381919316419345261"),
-            field_new!(Fq, "2236595495967245188281701248203181795121068902605861227855261137820944008926"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "3772000881919853776433695186713858239009073593817195771773381919316419345261"
+            ),
+            MontFp!(
+                Fq,
+                "2236595495967245188281701248203181795121068902605861227855261137820944008926"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
-            field_new!(Fq, "0"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "2203960485148121921418603742825762020974279258880205651966"
+            ),
+            MontFp!(Fq, "0"),
        ),
        // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "18429021223477853657660792034369865839114504446431234726392080002137598044644"),
-            field_new!(Fq, "9344045779998320333812420223237981029506012124075525679208581902008406485703"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "18429021223477853657660792034369865839114504446431234726392080002137598044644"
+            ),
+            MontFp!(
+                Fq,
+                "9344045779998320333812420223237981029506012124075525679208581902008406485703"
+            ),
        ),
    ];
-    #[rustfmt::skip]
+
    const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
-        ),
+        QuadExt!(MontFp!(Fq, "1"), MontFp!(Fq, "0"),),
        // Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "2581911344467009335267311115468803099551665605076196740867805258568234346338"),
-            field_new!(Fq, "19937756971775647987995932169929341994314640652964949448313374472400716661030"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "2581911344467009335267311115468803099551665605076196740867805258568234346338"
+            ),
+            MontFp!(
+                Fq,
+                "19937756971775647987995932169929341994314640652964949448313374472400716661030"
+            ),
        ),
        // Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
-            field_new!(Fq, "0"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "2203960485148121921418603742825762020974279258880205651966"
+            ),
+            MontFp!(Fq, "0"),
        ),
        // Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "5324479202449903542726783395506214481928257762400643279780343368557297135718"),
-            field_new!(Fq, "16208900380737693084919495127334387981393726419856888799917914180988844123039"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "5324479202449903542726783395506214481928257762400643279780343368557297135718"
+            ),
+            MontFp!(
+                Fq,
+                "16208900380737693084919495127334387981393726419856888799917914180988844123039"
+            ),
        ),
        // Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
-            field_new!(Fq, "0"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            MontFp!(Fq, "0"),
        ),
        // Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "13981852324922362344252311234282257507216387789820983642040889267519694726527"),
-            field_new!(Fq, "7629828391165209371577384193250820201684255241773809077146787135900891633097"),
+        QuadExt!(
+            MontFp!(
+                Fq,
+                "13981852324922362344252311234282257507216387789820983642040889267519694726527"
+            ),
+            MontFp!(
+                Fq,
+                "7629828391165209371577384193250820201684255241773809077146787135900891633097"
+            ),
        ),
    ];

@@ -85,8 +126,8 @@ impl Fp6Parameters for Fq6Parameters {
        // (c0+u*c1)*(9+u) = (9*c0-c1)+u*(9*c1+c0)
        let mut f = *fe;
        f.double_in_place().double_in_place().double_in_place();
-        let c0 = f.c0 + fe.c0 + Fq2Parameters::mul_fp_by_nonresidue(&fe.c1);
+        let c0 = f.c0 + fe.c0 + Fq2Config::mul_fp_by_nonresidue(&fe.c1);
        let c1 = f.c1 + fe.c1 + fe.c0;
-        field_new!(Fq2, c0, c1)
+        QuadExt!(c0, c1)
    }
 }
--- a/bn254/src/fields/fr.rs
+++ b/bn254/src/fields/fr.rs
@@ -1,103 +1,7 @@
-use ark_ff::{
-    biginteger::{BigInt, BigInteger256 as BigInteger},
-    fields::*,
-};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};

-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 28;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInt::new([
-        7164790868263648668u64,
-        11685701338293206998u64,
-        6216421865291908056u64,
-        1756667274303109607u64,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// MODULUS = 21888242871839275222246405745257275088548364400416034343698204186575808495617
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInt::new([
-        4891460686036598785u64,
-        2896914383306846353u64,
-        13281191951274694749u64,
-        3486998266802970665u64,
-    ]);
-
-    const MODULUS_BITS: u32 = 254;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 2;
-
-    /// R = pow(2, 256) % MODULUS
-    ///   = 6350874878119819312338956282401532410528162663560392320966563075034087161851
-    #[rustfmt::skip]
-    const R: BigInteger = BigInt::new([
-        12436184717236109307u64,
-        3962172157175319849u64,
-        7381016538464732718u64,
-        1011752739694698287u64,
-    ]);
-
-    /// R2 = R * R % MODULUS
-    ///    = 944936681149208446651664254269745548490766851729442924617792859073125903783
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInt::new([
-        1997599621687373223u64,
-        6052339484930628067u64,
-        10108755138030829701u64,
-        150537098327114917u64,
-    ]);
-
-    /// INV = (-MODULUS) ^ {-1} % pow(2, 64) = 14042775128853446655
-    const INV: u64 = 14042775128853446655u64;
-
-    /// GENERATOR = 5
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInt::new([
-        1949230679015292902u64,
-        16913946402569752895u64,
-        5177146667339417225u64,
-        1571765431670520771u64,
-    ]);
-
-    /// (MODULUS - 1)/2 =
-    /// 10944121435919637611123202872628637544274182200208017171849102093287904247808
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
-        0xa1f0fac9f8000000,
-        0x9419f4243cdcb848,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where r - 1 = 2^s * t
-
-    /// T = (MODULUS - 1) / 2^s =
-    /// 81540058820840996586704275553141814055101440848469862132140264610111
-    #[rustfmt::skip]
-    const T: BigInteger = BigInt::new([
-        0x9b9709143e1f593f,
-        0x181585d2833e8487,
-        0x131a029b85045b68,
-        0x30644e72e,
-    ]);
-
-    /// (T - 1) / 2 =
-    /// 40770029410420498293352137776570907027550720424234931066070132305055
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInt::new([
-        0xcdcb848a1f0fac9f,
-        0x0c0ac2e9419f4243,
-        0x098d014dc2822db4,
-        0x183227397,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "21888242871839275222246405745257275088548364400416034343698204186575808495617"]
+#[generator = "5"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;
--- a/bn254/src/fields/tests.rs
+++ b/bn254/src/fields/tests.rs
@@ -1,9 +1,9 @@
+use ark_algebra_test_templates::{
+    fields::*, generate_field_serialization_test, generate_field_test,
+};
 use ark_ff::{
    biginteger::{BigInt, BigInteger, BigInteger256},
-    fields::{
-        fp6_3over2::Fp6Parameters, FftField, FftParameters, Field, FpParameters, PrimeField,
-        SquareRootField,
-    },
+    fields::{FftField, Field, Fp6Config, PrimeField, SquareRootField},
    One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
@@ -13,12 +13,9 @@ use core::{
    ops::{AddAssign, MulAssign, SubAssign},
 };

-use crate::{Fq, Fq12, Fq2, Fq6, Fq6Parameters, FqParameters, Fr};
-use ark_algebra_test_templates::{
-    fields::*, generate_field_serialization_test, generate_field_test,
-};
+use crate::{Fq, Fq12, Fq2, Fq6, Fq6Config, FqConfig, Fr, FrConfig};

-generate_field_test!(bn254; fq2; fq6; fq12;);
+generate_field_test!(bn254; fq2; fq6; fq12; mont(4, 4); );
 generate_field_serialization_test!(bn254; fq2; fq6; fq12;);

 #[test]
@@ -28,14 +25,14 @@ fn test_fq_repr_from() {

 #[test]
 fn test_fq_repr_is_odd() {
-    assert!(!BigInteger256::from(0).is_odd());
-    assert!(BigInteger256::from(0).is_even());
-    assert!(BigInteger256::from(1).is_odd());
-    assert!(!BigInteger256::from(1).is_even());
-    assert!(!BigInteger256::from(324834872).is_odd());
-    assert!(BigInteger256::from(324834872).is_even());
-    assert!(BigInteger256::from(324834873).is_odd());
-    assert!(!BigInteger256::from(324834873).is_even());
+    assert!(!BigInteger256::from(0u64).is_odd());
+    assert!(BigInteger256::from(0u64).is_even());
+    assert!(BigInteger256::from(1u64).is_odd());
+    assert!(!BigInteger256::from(1u64).is_even());
+    assert!(!BigInteger256::from(324834872u64).is_odd());
+    assert!(BigInteger256::from(324834872u64).is_even());
+    assert!(BigInteger256::from(324834873u64).is_odd());
+    assert!(!BigInteger256::from(324834873u64).is_even());
 }

 #[test]
@@ -47,9 +44,9 @@ fn test_fq_repr_is_zero() {

 #[test]
 fn test_fq_repr_num_bits() {
-    let mut a = BigInteger256::from(0);
+    let mut a = BigInteger256::from(0u64);
    assert_eq!(0, a.num_bits());
-    a = BigInteger256::from(1);
+    a = BigInteger256::from(1u64);
    for i in 1..257 {
        assert_eq!(i, a.num_bits());
        a.mul2();
@@ -59,34 +56,33 @@ fn test_fq_repr_num_bits() {

 #[test]
 fn test_fq_num_bits() {
-    assert_eq!(FqParameters::MODULUS_BITS, 254);
-    assert_eq!(FqParameters::CAPACITY, 253);
+    assert_eq!(Fq::MODULUS_BIT_SIZE, 254);
 }

 #[test]
 fn test_fq_root_of_unity() {
-    assert_eq!(FqParameters::TWO_ADICITY, 1);
+    assert_eq!(Fq::TWO_ADICITY, 1);
    assert_eq!(
-        Fq::multiplicative_generator().pow([
+        Fq::GENERATOR.pow([
            0x9e10460b6c3e7ea3,
            0xcbc0b548b438e546,
            0xdc2822db40c0ac2e,
            0x183227397098d014,
        ]),
-        Fq::two_adic_root_of_unity()
+        Fq::TWO_ADIC_ROOT_OF_UNITY
    );
    assert_eq!(
-        Fq::two_adic_root_of_unity().pow([1 << FqParameters::TWO_ADICITY]),
+        Fq::TWO_ADIC_ROOT_OF_UNITY.pow([1 << Fq::TWO_ADICITY]),
        Fq::one()
    );
-    assert!(Fq::multiplicative_generator().sqrt().is_none());
+    assert!(Fq::GENERATOR.sqrt().is_none());
 }

 #[test]
 fn test_fq_ordering() {
    // BigInteger256's ordering is well-tested, but we still need to make sure the
    // Fq elements aren't being compared in Montgomery form.
-    for i in 0..100 {
+    for i in 0..100u64 {
        assert!(Fq::from(BigInteger256::from(i + 1)) > Fq::from(BigInteger256::from(i)));
    }
 }
@@ -99,11 +95,11 @@ fn test_fq_legendre() {
    assert_eq!(Zero, Fq::zero().legendre());
    assert_eq!(
        QuadraticResidue,
-        Fq::from(BigInteger256::from(4)).legendre()
+        Fq::from(BigInteger256::from(4u64)).legendre()
    );
    assert_eq!(
        QuadraticNonResidue,
-        Fq::from(BigInteger256::from(5)).legendre()
+        Fq::from(BigInteger256::from(5u64)).legendre()
    );
 }

@@ -144,7 +140,7 @@ fn test_fq2_legendre() {
    // i^2 = -1
    let mut m1 = -Fq2::one();
    assert_eq!(QuadraticResidue, m1.legendre());
-    m1 = Fq6Parameters::mul_fp2_by_nonresidue(&m1);
+    m1 = Fq6Config::mul_fp2_by_nonresidue(&m1);
    assert_eq!(QuadraticNonResidue, m1.legendre());
 }

--- a/bn254/src/lib.rs
+++ b/bn254/src/lib.rs
@@ -20,14 +20,17 @@
 //!
 //!
 //! Curve information:
-//! * Base field: q = 21888242871839275222246405745257275088696311157297823662689037894645226208583
-//! * Scalar field: r = 21888242871839275222246405745257275088548364400416034343698204186575808495617
+//! * Base field: q =
+//!   21888242871839275222246405745257275088696311157297823662689037894645226208583
+//! * Scalar field: r =
+//!   21888242871839275222246405745257275088548364400416034343698204186575808495617
 //! * valuation(q - 1, 2) = 1
 //! * valuation(r - 1, 2) = 28
 //! * G1 curve equation: y^2 = x^3 + 3
 //! * G2 curve equation: y^2 = x^3 + B, where
-//!    * B = 3/(u+9) where Fq2 is represented as Fq\[u\]/(u^2+1)
-//!        = Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
+//!    * B = 3/(u+9) where Fq2 is represented as Fq\[u\]/(u^2+1) =
+//!      Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373,
+//!      266929791119991161246907387137283842545076965332900288569378510910307636690)

 #[cfg(feature = "curve")]
 mod curves;