Initial commit

mnt4_753/src/curves/g2.rs

@@ -0,0 +1,177 @@
+use ark_ec::{
+    mnt4,
+    mnt4::MNT4Parameters,
+    models::{ModelParameters, SWModelParameters},
+};
+use ark_ff::{biginteger::BigInteger768, field_new};
+
+use crate::{Fq, Fq2, Fr, FQ_ZERO, G1_COEFF_A_NON_RESIDUE};
+
+pub type G2Affine = mnt4::G2Affine<crate::Parameters>;
+pub type G2Projective = mnt4::G2Projective<crate::Parameters>;
+pub type G2Prepared = mnt4::G2Prepared<crate::Parameters>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Parameters;
+
+impl ModelParameters for Parameters {
+    type BaseField = Fq2;
+    type ScalarField = Fr;
+}
+
+/// MUL_BY_A_C0 = NONRESIDUE * COEFF_A
+#[rustfmt::skip]
+pub const MUL_BY_A_C0: Fq = G1_COEFF_A_NON_RESIDUE;
+
+/// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
+#[rustfmt::skip]
+pub const MUL_BY_A_C1: Fq = G1_COEFF_A_NON_RESIDUE;
+
+impl SWModelParameters for Parameters {
+    const COEFF_A: Fq2 = crate::Parameters::TWIST_COEFF_A;
+    // B coefficient of MNT4-753 G2 =
+    // ```
+    // mnt4753_twist_coeff_b = mnt4753_Fq2(mnt4753_Fq::zero(),
+    //                                  mnt4753_G1::coeff_b * mnt4753_Fq2::non_residue);
+    // non_residue = mnt4753_Fq2::non_residue = mnt4753_Fq("13");
+    //  = (ZERO, G1_B_COEFF * NON_RESIDUE);
+    //  =
+    //  (0, 39196523001581428369576759982967177918859161321667605855515469914917622337081756705006832951954384669101573360625169461998308377011601613979275218690841934572954991361632773738259652003389826903175898479855893660378722437317212)
+    // ```
+    #[rustfmt::skip]
+    const COEFF_B: Fq2 = field_new!(Fq2,
+        FQ_ZERO,
+        field_new!(Fq, BigInteger768([
+            15129916544657421551,
+            11332543254671606602,
+            11913830318987286849,
+            13905314883394440110,
+            16479690325073358448,
+            14869098639251228898,
+            10663986895980443550,
+            10768989312009479656,
+            9469728929095040349,
+            4512954369775881939,
+            8788997129423430122,
+            459763387588954,
+        ])),
+    );
+
+    /// COFACTOR =
+    /// 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888049094905534395567574915333486969589229856772141392370549616644545554517640527237829320384324374366385444967219201
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        16436257212445032449,
+        8690275530472745198,
+        17315389657026393162,
+        1645397558963170979,
+        3544984605440726586,
+        12665092767997125024,
+        11083680675069097885,
+        575819899841080717,
+        6825179918269667443,
+        13256793349531086829,
+        1162650133526138285,
+        497830423872529,
+    ];
+
+    /// COFACTOR^(-1) mod r =
+    /// 102345604409665481004734934052318066391634848395005988700111949231215905051467807945653833683883449458834877235200
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger768([
+        1879390364380281898,
+        7926794171490610432,
+        6437239504245874253,
+        16688141022047191858,
+        17059416847145768464,
+        15065047661241262516,
+        16537575340937777321,
+        3324411942044534547,
+        3878293904770657570,
+        18116939243856833744,
+        7557533897589069385,
+        78370361203778,
+    ]));
+
+    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
+    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
+        (G2_GENERATOR_X, G2_GENERATOR_Y);
+
+    #[inline(always)]
+    fn mul_by_a(elt: &Fq2) -> Fq2 {
+        field_new!(Fq2, MUL_BY_A_C0 * &elt.c0, MUL_BY_A_C1 * &elt.c1,)
+    }
+}
+
+const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+
+// Generator of G2
+// These are two Fq elements each because X and Y (and Z) are elements of Fq^2
+// X = 29483965110843144675703364744708836524643960105538608078862508397502447349913068434941060515343254862580437318493682762113105361632548148204806052114008731372757389645383891982211245013965175213456066452587869519098351487925167,
+// 19706011319630172391076079624799753948158506771222147486237995321925443331396169656568431378974558350664383559981183980668976846806019030432389169137953988990802000581078994008283967768348275973921598166274857631001635633631000,
+// Y = 39940152670760519653940320314827327941993141403708338666925204282084477074754642625849927569427860786384998614863651207257467076192649385174108085803168743803491780568503369317093191101779534035377266300185099318717465441820654,
+// 17608637424964395737041291373756657139607306440193731804102457011726690702169238966996114255971643893157857311132388792357391583164125870757541009035041469463366528798593952884745987697403056488744603829437448927398468360797245,
+#[rustfmt::skip]
+pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger768([
+    7263636080534048301,
+    7643227961769035653,
+    15787777614640869937,
+    17661317895964274771,
+    4142647779394287783,
+    15064949873659932676,
+    4579259080596351332,
+    2207443675339702626,
+    5738725620118622838,
+    4338467638707299712,
+    6558861849926282439,
+    341078935870328
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger768([
+    13073882729051113867,
+    195909455108318710,
+    10527070038778509320,
+    16605710222187477118,
+    10442518358308209073,
+    7776589986153052354,
+    16034091384000651523,
+    17429232381273855185,
+    512853344493546034,
+    7982076214836075255,
+    3601416800138513610,
+    399028695285184
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger768([
+    4867672648970469422,
+    2453112364260322863,
+    11918672197974895143,
+    3923647310180624143,
+    12707123323825700670,
+    15781895092544451511,
+    17747112377690960911,
+    16511994611001933567,
+    15360620366665804029,
+    10252080383738480571,
+    5722654046339742760,
+    316853130349807
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger768([
+    17322957246732430708,
+    11825815087694023697,
+    7654216682602683900,
+    13544637981229618042,
+    17057060382219081849,
+    4038731408172002692,
+    6631723222530012253,
+    10585926166286435412,
+    16050667328028620117,
+    16598483946296156500,
+    11771818132648686020,
+    1230430296095
+]));