Initial commit

bw6_761/src/fields/fq.rs

@@ -0,0 +1,175 @@
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    field_new,
+    fields::{FftParameters, Fp768, Fp768Parameters, FpParameters},
+};
+
+pub type Fq = Fp768<FqParameters>;
+
+pub struct FqParameters;
+
+pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
+pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
+
+impl Fp768Parameters for FqParameters {}
+impl FftParameters for FqParameters {
+    type BigInt = BigInteger;
+
+    // The internal representation of this type is six 64-bit unsigned
+    // integers in little-endian order. Values are always in
+    // Montgomery form; i.e., Scalar(a) = aR mod p, with R=2^768.
+
+    // (MODULUS - 1) % 2^TWO_ADICITY == 0
+    const TWO_ADICITY: u32 = 1;
+
+    // least_quadratic_nonresidue(MODULUS) in Sage.
+    #[rustfmt::skip]
+    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
+        17481284903592032950u64,
+        10104133845767975835u64,
+        8607375506753517913u64,
+        13706168424391191299u64,
+        9580010308493592354u64,
+        14241333420363995524u64,
+        6665632285037357566u64,
+        5559902898979457045u64,
+        15504799981718861253u64,
+        8332096944629367896u64,
+        18005297320867222879u64,
+        58811391084848524u64,
+    ]);
+}
+impl FpParameters for FqParameters {
+    /// MODULUS = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
+    #[rustfmt::skip]
+    const MODULUS: BigInteger = BigInteger([
+       0xf49d00000000008b,
+       0xe6913e6870000082,
+       0x160cf8aeeaf0a437,
+       0x98a116c25667a8f8,
+       0x71dcd3dc73ebff2e,
+       0x8689c8ed12f9fd90,
+       0x03cebaff25b42304,
+       0x707ba638e584e919,
+       0x528275ef8087be41,
+       0xb926186a81d14688,
+       0xd187c94004faff3e,
+       0x122e824fb83ce0a
+    ]);
+
+    const MODULUS_BITS: u32 = 761;
+
+    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
+
+    // gap to 64-bit machine word
+    const REPR_SHAVE_BITS: u32 = 7;
+
+    // 2^768 % MODULUS
+    #[rustfmt::skip]
+    const R: BigInteger = BigInteger([
+        144959613005956565u64,
+        6509995272855063783u64,
+        11428286765660613342u64,
+        15738672438262922740u64,
+        17071399330169272331u64,
+        13899911246788437003u64,
+        12055474021000362245u64,
+        2545351818702954755u64,
+        8887388221587179644u64,
+        5009280847225881135u64,
+        15539704305423854047u64,
+        23071597697427581u64,
+    ]);
+
+    // R^2
+    #[rustfmt::skip]
+    const R2: BigInteger = BigInteger([
+        14305184132582319705u64,
+        8868935336694416555u64,
+        9196887162930508889u64,
+        15486798265448570248u64,
+        5402985275949444416u64,
+        10893197322525159598u64,
+        3204916688966998390u64,
+        12417238192559061753u64,
+        12426306557607898622u64,
+        1305582522441154384u64,
+        10311846026977660324u64,
+        48736111365249031u64,
+    ]);
+
+    // (-1/MODULUS) % 2^64
+    const INV: u64 = 744663313386281181u64;
+
+    /// GENERATOR = 2
+    // primitive_root(MODULUS)
+    #[rustfmt::skip]
+    const GENERATOR: BigInteger = BigInteger([
+        289919226011913130u64,
+        13019990545710127566u64,
+        4409829457611675068u64,
+        13030600802816293865u64,
+        15696054586628993047u64,
+        9353078419867322391u64,
+        5664203968291172875u64,
+        5090703637405909511u64,
+        17774776443174359288u64,
+        10018561694451762270u64,
+        12632664537138156478u64,
+        46143195394855163u64,
+    ]);
+
+    // (MODULUS - 1) / 2
+    #[rustfmt::skip]
+    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0x7a4e800000000045,
+        0xf3489f3438000041,
+        0x0b067c577578521b,
+        0x4c508b612b33d47c,
+        0x38ee69ee39f5ff97,
+        0x4344e476897cfec8,
+        0x81e75d7f92da1182,
+        0xb83dd31c72c2748c,
+        0x29413af7c043df20,
+        0x5c930c3540e8a344,
+        0x68c3e4a0027d7f9f,
+        0x9174127dc1e705,
+    ]);
+
+    // T =
+    // 3445725192157866269698394841137828771239834456268075054756895080104811711121745868043841591644705843820432283876893306725580879560277123879674755849562650799475802549689254425186271815711798397975949850214984556421382456559534149
+    // (MODULUS - 1) / 2 ^ TWO_ADICITY
+    #[rustfmt::skip]
+    const T: BigInteger = BigInteger([
+        0x7a4e800000000045,
+        0xf3489f3438000041,
+        0x0b067c577578521b,
+        0x4c508b612b33d47c,
+        0x38ee69ee39f5ff97,
+        0x4344e476897cfec8,
+        0x81e75d7f92da1182,
+        0xb83dd31c72c2748c,
+        0x29413af7c043df20,
+        0x5c930c3540e8a344,
+        0x68c3e4a0027d7f9f,
+        0x9174127dc1e705,
+    ]);
+
+    // (T - 1)/2 =
+    // 1722862596078933134849197420568914385619917228134037527378447540052405855560872934021920795822352921910216141938446653362790439780138561939837377924781325399737901274844627212593135907855899198987974925107492278210691228279767074
+    #[rustfmt::skip]
+    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0xbd27400000000022,
+        0xf9a44f9a1c000020,
+        0x05833e2bbabc290d,
+        0xa62845b09599ea3e,
+        0x1c7734f71cfaffcb,
+        0x21a2723b44be7f64,
+        0x40f3aebfc96d08c1,
+        0x5c1ee98e39613a46,
+        0x14a09d7be021ef90,
+        0xae49861aa07451a2,
+        0xb461f250013ebfcf,
+        0x48ba093ee0f382,
+    ]);
+}