test_bilinearity.cpp

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#include <libff/algebra/curves/edwards/edwards_pp.hpp>
#include <libff/common/profiling.hpp>
#ifdef CURVE_BN128
#include <libff/algebra/curves/bn128/bn128_pp.hpp>
#endif
#include <libff/algebra/curves/alt_bn128/alt_bn128_pp.hpp>
#include <libff/algebra/curves/mnt/mnt4/mnt4_pp.hpp>
#include <libff/algebra/curves/mnt/mnt6/mnt6_pp.hpp>
 
using namespace libff;
 
#ifndef NDEBUG
template<typename ppT>
void pairing_test()
{
    GT<ppT> GT_one = GT<ppT>::one();
 
    printf("Running bilinearity tests:\n");
    G1<ppT> P = (Fr<ppT>::random_element()) * G1<ppT>::one();
    //G1<ppT> P = Fr<ppT>("2") * G1<ppT>::one();
    G2<ppT> Q = (Fr<ppT>::random_element()) * G2<ppT>::one();
    //G2<ppT> Q = Fr<ppT>("3") * G2<ppT>::one();
 
    printf("P:\n");
    P.print();
    P.print_coordinates();
    printf("Q:\n");
    Q.print();
    Q.print_coordinates();
    printf("\n\n");
 
    Fr<ppT> s = Fr<ppT>::random_element();
    //Fr<ppT> s = Fr<ppT>("2");
    G1<ppT> sP = s * P;
    G2<ppT> sQ = s * Q;
 
    printf("Pairing bilinearity tests (three must match):\n");
    GT<ppT> ans1 = ppT::reduced_pairing(sP, Q);
    GT<ppT> ans2 = ppT::reduced_pairing(P, sQ);
    GT<ppT> ans3 = ppT::reduced_pairing(P, Q)^s;
    ans1.print();
    ans2.print();
    ans3.print();
    assert(ans1 == ans2);
    assert(ans2 == ans3);
 
    assert(ans1 != GT_one);
    assert((ans1^Fr<ppT>::field_char()) == GT_one);
    printf("\n\n");
}
 
template<typename ppT>
void double_miller_loop_test()
{
    const G1<ppT> P1 = (Fr<ppT>::random_element()) * G1<ppT>::one();
    const G1<ppT> P2 = (Fr<ppT>::random_element()) * G1<ppT>::one();
    const G2<ppT> Q1 = (Fr<ppT>::random_element()) * G2<ppT>::one();
    const G2<ppT> Q2 = (Fr<ppT>::random_element()) * G2<ppT>::one();
 
    const G1_precomp<ppT> prec_P1 = ppT::precompute_G1(P1);
    const G1_precomp<ppT> prec_P2 = ppT::precompute_G1(P2);
    const G2_precomp<ppT> prec_Q1 = ppT::precompute_G2(Q1);
    const G2_precomp<ppT> prec_Q2 = ppT::precompute_G2(Q2);
 
    const Fqk<ppT> ans_1 = ppT::miller_loop(prec_P1, prec_Q1);
    const Fqk<ppT> ans_2 = ppT::miller_loop(prec_P2, prec_Q2);
    const Fqk<ppT> ans_12 = ppT::double_miller_loop(prec_P1, prec_Q1, prec_P2, prec_Q2);
    assert(ans_1 * ans_2 == ans_12);
}
 
template<typename ppT>
void affine_pairing_test()
{
    GT<ppT> GT_one = GT<ppT>::one();
 
    printf("Running bilinearity tests:\n");
    G1<ppT> P = (Fr<ppT>::random_element()) * G1<ppT>::one();
    G2<ppT> Q = (Fr<ppT>::random_element()) * G2<ppT>::one();
 
    printf("P:\n");
    P.print();
    printf("Q:\n");
    Q.print();
    printf("\n\n");
 
    Fr<ppT> s = Fr<ppT>::random_element();
    G1<ppT> sP = s * P;
    G2<ppT> sQ = s * Q;
 
    printf("Pairing bilinearity tests (three must match):\n");
    GT<ppT> ans1 = ppT::affine_reduced_pairing(sP, Q);
    GT<ppT> ans2 = ppT::affine_reduced_pairing(P, sQ);
    GT<ppT> ans3 = ppT::affine_reduced_pairing(P, Q)^s;
    ans1.print();
    ans2.print();
    ans3.print();
    assert(ans1 == ans2);
    assert(ans2 == ans3);
 
    assert(ans1 != GT_one);
    assert((ans1^Fr<ppT>::field_char()) == GT_one);
    printf("\n\n");
}
 
int main(void)
{
    start_profiling();
    edwards_pp::init_public_params();
    pairing_test<edwards_pp>();
    double_miller_loop_test<edwards_pp>();
 
    mnt6_pp::init_public_params();
    pairing_test<mnt6_pp>();
    double_miller_loop_test<mnt6_pp>();
    affine_pairing_test<mnt6_pp>();
 
    mnt4_pp::init_public_params();
    pairing_test<mnt4_pp>();
    double_miller_loop_test<mnt4_pp>();
    affine_pairing_test<mnt4_pp>();
 
    alt_bn128_pp::init_public_params();
    pairing_test<alt_bn128_pp>();
    double_miller_loop_test<alt_bn128_pp>();
 
#ifdef CURVE_BN128       // BN128 has fancy dependencies so it may be disabled
    bn128_pp::init_public_params();
    pairing_test<bn128_pp>();
    double_miller_loop_test<bn128_pp>();
#endif
}
 
#else // NDEBUG
 
int main()
{
    printf("All tests here depend on assert() which is disabled by -DNDEBUG. Please recompile and run again.\n");
}
#endif // NDEBUG