edwards_init.cpp

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#include <libff/algebra/curves/edwards/edwards_g1.hpp>
#include <libff/algebra/curves/edwards/edwards_g2.hpp>
#include <libff/algebra/curves/edwards/edwards_init.hpp>
 
namespace libff
{
 
bigint<edwards_r_limbs> edwards_modulus_r;
bigint<edwards_q_limbs> edwards_modulus_q;
 
edwards_Fq edwards_coeff_a;
edwards_Fq edwards_coeff_d;
edwards_Fq3 edwards_twist;
edwards_Fq3 edwards_twist_coeff_a;
edwards_Fq3 edwards_twist_coeff_d;
edwards_Fq edwards_twist_mul_by_a_c0;
edwards_Fq edwards_twist_mul_by_a_c1;
edwards_Fq edwards_twist_mul_by_a_c2;
edwards_Fq edwards_twist_mul_by_d_c0;
edwards_Fq edwards_twist_mul_by_d_c1;
edwards_Fq edwards_twist_mul_by_d_c2;
edwards_Fq edwards_twist_mul_by_q_Y;
edwards_Fq edwards_twist_mul_by_q_Z;
 
bigint<edwards_q_limbs> edwards_ate_loop_count;
bigint<6 * edwards_q_limbs> edwards_final_exponent;
bigint<edwards_q_limbs> edwards_final_exponent_last_chunk_abs_of_w0;
bool edwards_final_exponent_last_chunk_is_w0_neg;
bigint<edwards_q_limbs> edwards_final_exponent_last_chunk_w1;
 
void init_edwards_params()
{
    typedef bigint<edwards_r_limbs> bigint_r;
    typedef bigint<edwards_q_limbs> bigint_q;
 
    assert(
        sizeof(mp_limb_t) == 8 ||
        sizeof(mp_limb_t) == 4); // Montgomery assumes this
 
    /* parameters for scalar field Fr */
 
    edwards_modulus_r =
        bigint_r("1552511030102430251236801561344621993261920897571225601");
    assert(edwards_Fr::modulus_is_valid());
    if (sizeof(mp_limb_t) == 8) {
        edwards_Fr::Rsquared =
            bigint_r("621738487827897760168419760282818735947979812540885779");
        edwards_Fr::Rcubed =
            bigint_r("899968968216802386013510389846941393831065658679774050");
        edwards_Fr::inv = 0xdde553277fffffff;
    }
    if (sizeof(mp_limb_t) == 4) {
        edwards_Fr::Rsquared =
            bigint_r("621738487827897760168419760282818735947979812540885779");
        edwards_Fr::Rcubed =
            bigint_r("899968968216802386013510389846941393831065658679774050");
        edwards_Fr::inv = 0x7fffffff;
    }
    edwards_Fr::num_bits = 181;
    edwards_Fr::euler =
        bigint_r("776255515051215125618400780672310996630960448785612800");
    edwards_Fr::s = 31;
    edwards_Fr::t = bigint_r("722944284836962004768104088187507350585386575");
    edwards_Fr::t_minus_1_over_2 =
        bigint_r("361472142418481002384052044093753675292693287");
    edwards_Fr::multiplicative_generator = edwards_Fr("19");
    edwards_Fr::root_of_unity =
        edwards_Fr("695314865466598274460565335217615316274564719601897184");
    edwards_Fr::nqr = edwards_Fr("11");
    edwards_Fr::nqr_to_t =
        edwards_Fr("1326707053668679463752768729767248251415639579872144553");
    edwards_Fr::static_init();
 
    /* parameters for base field Fq */
 
    edwards_modulus_q =
        bigint_q("6210044120409721004947206240885978274523751269793792001");
    assert(edwards_Fq::modulus_is_valid());
    if (sizeof(mp_limb_t) == 8) {
        edwards_Fq::Rsquared =
            bigint_q("5943559676554581037560514598978484097352477055348195432");
        edwards_Fq::Rcubed =
            bigint_q("1081560488703514202058739223469726982199727506489234349");
        edwards_Fq::inv = 0x76eb690b7fffffff;
    }
    if (sizeof(mp_limb_t) == 4) {
        edwards_Fq::Rsquared =
            bigint_q("5943559676554581037560514598978484097352477055348195432");
        edwards_Fq::Rcubed =
            bigint_q("1081560488703514202058739223469726982199727506489234349");
        edwards_Fq::inv = 0x7fffffff;
    }
    edwards_Fq::num_bits = 183;
    edwards_Fq::euler =
        bigint_q("3105022060204860502473603120442989137261875634896896000");
    edwards_Fq::s = 31;
    edwards_Fq::t = bigint_q("2891777139347848019072416350658041552884388375");
    edwards_Fq::t_minus_1_over_2 =
        bigint_q("1445888569673924009536208175329020776442194187");
    edwards_Fq::multiplicative_generator = edwards_Fq("61");
    edwards_Fq::root_of_unity =
        edwards_Fq("4692813029219384139894873043933463717810008194158530536");
    edwards_Fq::nqr = edwards_Fq("23");
    edwards_Fq::nqr_to_t =
        edwards_Fq("2626736066325740702418554487368721595489070118548299138");
    edwards_Fq::static_init();
 
    /* parameters for twist field Fq3 */
 
    edwards_Fq3::euler = bigint<3 * edwards_q_limbs>(
        "1197440827139715029629926131910678366982050433739789489038399345641529"
        "9485805128465854550297120332503183164742441311116131831414476564652505"
        "7914792711854057586688000");
    edwards_Fq3::s = 31;
    edwards_Fq3::t = bigint<3 * edwards_q_limbs>(
        "1115203674081447561858153093523046343570622088145268605126439915636116"
        "5908915110366283497118503164968623933142462103735778323760700006645643"
        "8894190557165125");
    edwards_Fq3::t_minus_1_over_2 = bigint<3 * edwards_q_limbs>(
        "5576018370407237809290765467615231717853110440726343025632199578180582"
        "9544575551831417485592515824843119665712310518678891618803500033228219"
        "447095278582562");
    edwards_Fq3::non_residue = edwards_Fq("61");
    edwards_Fq3::nqr =
        edwards_Fq3(edwards_Fq("23"), edwards_Fq("0"), edwards_Fq("0"));
    edwards_Fq3::nqr_to_t = edwards_Fq3(
        edwards_Fq("104810943629412208121981114244673004633270996333237516"),
        edwards_Fq("0"),
        edwards_Fq("0"));
    edwards_Fq3::Frobenius_coeffs_c1[0] = edwards_Fq("1");
    edwards_Fq3::Frobenius_coeffs_c1[1] =
        edwards_Fq("1073752683758513276629212192812154536507607213288832061");
    edwards_Fq3::Frobenius_coeffs_c1[2] =
        edwards_Fq("5136291436651207728317994048073823738016144056504959939");
    edwards_Fq3::Frobenius_coeffs_c2[0] = edwards_Fq("1");
    edwards_Fq3::Frobenius_coeffs_c2[1] =
        edwards_Fq("5136291436651207728317994048073823738016144056504959939");
    edwards_Fq3::Frobenius_coeffs_c2[2] =
        edwards_Fq("1073752683758513276629212192812154536507607213288832061");
 
    /* parameters for Fq6 */
 
    edwards_Fq6::non_residue = edwards_Fq("61");
    edwards_Fq6::Frobenius_coeffs_c1[0] = edwards_Fq("1");
    edwards_Fq6::Frobenius_coeffs_c1[1] =
        edwards_Fq("1073752683758513276629212192812154536507607213288832062");
    edwards_Fq6::Frobenius_coeffs_c1[2] =
        edwards_Fq("1073752683758513276629212192812154536507607213288832061");
    edwards_Fq6::Frobenius_coeffs_c1[3] =
        edwards_Fq("6210044120409721004947206240885978274523751269793792000");
    edwards_Fq6::Frobenius_coeffs_c1[4] =
        edwards_Fq("5136291436651207728317994048073823738016144056504959939");
    edwards_Fq6::Frobenius_coeffs_c1[5] =
        edwards_Fq("5136291436651207728317994048073823738016144056504959940");
    edwards_Fq6::my_Fp2::non_residue = edwards_Fq3::non_residue;
 
    /* choice of Edwards curve and its twist */
 
    edwards_coeff_a = edwards_Fq::one();
    edwards_coeff_d =
        edwards_Fq("600581931845324488256649384912508268813600056237543024");
    edwards_twist =
        edwards_Fq3(edwards_Fq::zero(), edwards_Fq::one(), edwards_Fq::zero());
    edwards_twist_coeff_a = edwards_coeff_a * edwards_twist;
    edwards_twist_coeff_d = edwards_coeff_d * edwards_twist;
    edwards_twist_mul_by_a_c0 = edwards_coeff_a * edwards_Fq3::non_residue;
    edwards_twist_mul_by_a_c1 = edwards_coeff_a;
    edwards_twist_mul_by_a_c2 = edwards_coeff_a;
    edwards_twist_mul_by_d_c0 = edwards_coeff_d * edwards_Fq3::non_residue;
    edwards_twist_mul_by_d_c1 = edwards_coeff_d;
    edwards_twist_mul_by_d_c2 = edwards_coeff_d;
    edwards_twist_mul_by_q_Y =
        edwards_Fq("1073752683758513276629212192812154536507607213288832062");
    edwards_twist_mul_by_q_Z =
        edwards_Fq("1073752683758513276629212192812154536507607213288832062");
 
    /* choice of group G1 */
 
    edwards_G1::G1_zero = edwards_G1(edwards_Fq::zero(), edwards_Fq::one());
    edwards_G1::G1_one = edwards_G1(
        edwards_Fq("3713709671941291996998665608188072510389821008693530490"),
        edwards_Fq("4869953702976555123067178261685365085639705297852816679"));
 
    edwards_G1::wnaf_window_table.resize(0);
    edwards_G1::wnaf_window_table.push_back(9);
    edwards_G1::wnaf_window_table.push_back(14);
    edwards_G1::wnaf_window_table.push_back(24);
    edwards_G1::wnaf_window_table.push_back(117);
 
    edwards_G1::fixed_base_exp_window_table.resize(0);
    // window 1 is unbeaten in [-inf, 4.10]
    edwards_G1::fixed_base_exp_window_table.push_back(1);
    // window 2 is unbeaten in [4.10, 9.69]
    edwards_G1::fixed_base_exp_window_table.push_back(4);
    // window 3 is unbeaten in [9.69, 25.21]
    edwards_G1::fixed_base_exp_window_table.push_back(10);
    // window 4 is unbeaten in [25.21, 60.00]
    edwards_G1::fixed_base_exp_window_table.push_back(25);
    // window 5 is unbeaten in [60.00, 149.33]
    edwards_G1::fixed_base_exp_window_table.push_back(60);
    // window 6 is unbeaten in [149.33, 369.61]
    edwards_G1::fixed_base_exp_window_table.push_back(149);
    // window 7 is unbeaten in [369.61, 849.07]
    edwards_G1::fixed_base_exp_window_table.push_back(370);
    // window 8 is unbeaten in [849.07, 1764.94]
    edwards_G1::fixed_base_exp_window_table.push_back(849);
    // window 9 is unbeaten in [1764.94, 4429.59]
    edwards_G1::fixed_base_exp_window_table.push_back(1765);
    // window 10 is unbeaten in [4429.59, 13388.78]
    edwards_G1::fixed_base_exp_window_table.push_back(4430);
    // window 11 is unbeaten in [13388.78, 15368.00]
    edwards_G1::fixed_base_exp_window_table.push_back(13389);
    // window 12 is unbeaten in [15368.00, 74912.07]
    edwards_G1::fixed_base_exp_window_table.push_back(15368);
    // window 13 is unbeaten in [74912.07, 438107.20]
    edwards_G1::fixed_base_exp_window_table.push_back(74912);
    // window 14 is never the best
    edwards_G1::fixed_base_exp_window_table.push_back(0);
    // window 15 is unbeaten in [438107.20, 1045626.18]
    edwards_G1::fixed_base_exp_window_table.push_back(438107);
    // window 16 is never the best
    edwards_G1::fixed_base_exp_window_table.push_back(0);
    // window 17 is unbeaten in [1045626.18, 1577434.48]
    edwards_G1::fixed_base_exp_window_table.push_back(1045626);
    // window 18 is unbeaten in [1577434.48, 17350594.23]
    edwards_G1::fixed_base_exp_window_table.push_back(1577434);
    // window 19 is never the best
    edwards_G1::fixed_base_exp_window_table.push_back(0);
    // window 20 is never the best
    edwards_G1::fixed_base_exp_window_table.push_back(0);
    // window 21 is unbeaten in [17350594.23, inf]
    edwards_G1::fixed_base_exp_window_table.push_back(17350594);
    // window 22 is never the best
    edwards_G1::fixed_base_exp_window_table.push_back(0);
 
    /* choice of group G2 */
 
    edwards_G2::G2_zero = edwards_G2(edwards_Fq3::zero(), edwards_Fq3::one());
    edwards_G2::G2_one = edwards_G2(
        edwards_Fq3(
            edwards_Fq(
                "4531683359223370252210990718516622098304721701253228128"),
            edwards_Fq(
                "5339624155305731263217400504407647531329993548123477368"),
            edwards_Fq(
                "3964037981777308726208525982198654699800283729988686552")),
        edwards_Fq3(
            edwards_Fq(
                "364634864866983740775341816274081071386963546650700569"),
            edwards_Fq(
                "3264380230116139014996291397901297105159834497864380415"),
            edwards_Fq(
                "3504781284999684163274269077749440837914479176282903747")));
 
    edwards_G2::wnaf_window_table.resize(0);
    edwards_G2::wnaf_window_table.push_back(6);
    edwards_G2::wnaf_window_table.push_back(12);
    edwards_G2::wnaf_window_table.push_back(42);
    edwards_G2::wnaf_window_table.push_back(97);
 
    edwards_G2::fixed_base_exp_window_table.resize(0);
    // window 1 is unbeaten in [-inf, 4.74]
    edwards_G2::fixed_base_exp_window_table.push_back(1);
    // window 2 is unbeaten in [4.74, 10.67]
    edwards_G2::fixed_base_exp_window_table.push_back(5);
    // window 3 is unbeaten in [10.67, 25.53]
    edwards_G2::fixed_base_exp_window_table.push_back(11);
    // window 4 is unbeaten in [25.53, 60.67]
    edwards_G2::fixed_base_exp_window_table.push_back(26);
    // window 5 is unbeaten in [60.67, 145.77]
    edwards_G2::fixed_base_exp_window_table.push_back(61);
    // window 6 is unbeaten in [145.77, 356.76]
    edwards_G2::fixed_base_exp_window_table.push_back(146);
    // window 7 is unbeaten in [356.76, 823.08]
    edwards_G2::fixed_base_exp_window_table.push_back(357);
    // window 8 is unbeaten in [823.08, 1589.45]
    edwards_G2::fixed_base_exp_window_table.push_back(823);
    // window 9 is unbeaten in [1589.45, 4135.70]
    edwards_G2::fixed_base_exp_window_table.push_back(1589);
    // window 10 is unbeaten in [4135.70, 14297.74]
    edwards_G2::fixed_base_exp_window_table.push_back(4136);
    // window 11 is unbeaten in [14297.74, 16744.85]
    edwards_G2::fixed_base_exp_window_table.push_back(14298);
    // window 12 is unbeaten in [16744.85, 51768.98]
    edwards_G2::fixed_base_exp_window_table.push_back(16745);
    // window 13 is unbeaten in [51768.98, 99811.01]
    edwards_G2::fixed_base_exp_window_table.push_back(51769);
    // window 14 is unbeaten in [99811.01, 193306.72]
    edwards_G2::fixed_base_exp_window_table.push_back(99811);
    // window 15 is unbeaten in [193306.72, 907184.68]
    edwards_G2::fixed_base_exp_window_table.push_back(193307);
    // window 16 is never the best
    edwards_G2::fixed_base_exp_window_table.push_back(0);
    // window 17 is unbeaten in [907184.68, 1389682.59]
    edwards_G2::fixed_base_exp_window_table.push_back(907185);
    // window 18 is unbeaten in [1389682.59, 6752695.74]
    edwards_G2::fixed_base_exp_window_table.push_back(1389683);
    // window 19 is never the best
    edwards_G2::fixed_base_exp_window_table.push_back(0);
    // window 20 is unbeaten in [6752695.74, 193642894.51]
    edwards_G2::fixed_base_exp_window_table.push_back(6752696);
    // window 21 is unbeaten in [193642894.51, 226760202.29]
    edwards_G2::fixed_base_exp_window_table.push_back(193642895);
    // window 22 is unbeaten in [226760202.29, inf]
    edwards_G2::fixed_base_exp_window_table.push_back(226760202);
 
    /* pairing parameters */
 
    edwards_ate_loop_count = bigint_q("4492509698523932320491110403");
    edwards_final_exponent = bigint<6 * edwards_q_limbs>(
        "3694310717796169464961879734644687013874865157861174841512820742949159"
        "3976636391130175425245705674550269561361208979548749447898941828686017"
        "7657304194168755396159416512697939289624688998560831692274575039424707"
        "21108165443528513330156264699608120624990672333642644221591552000");
    edwards_final_exponent_last_chunk_abs_of_w0 =
        bigint_q("17970038794095729281964441603");
    edwards_final_exponent_last_chunk_is_w0_neg = true;
    edwards_final_exponent_last_chunk_w1 = bigint_q("4");
}
} // namespace libff