forms/short_weierstrass/jacobian_with_a4_0/ate_double_miller_loop.hpp

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//---------------------------------------------------------------------------//
// Copyright (c) 2020-2021 Mikhail Komarov <nemo@nil.foundation>
// Copyright (c) 2020-2021 Nikita Kaskov <nbering@nil.foundation>
//
// MIT License
//
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#ifndef CRYPTO3_ALGEBRA_PAIRING_SHORT_WEIERSTRASS_JACOBIAN_WITH_A4_0_ATE_DOUBLE_MILLER_LOOP_HPP
#define CRYPTO3_ALGEBRA_PAIRING_SHORT_WEIERSTRASS_JACOBIAN_WITH_A4_0_ATE_DOUBLE_MILLER_LOOP_HPP
 
#include <nil/crypto3/multiprecision/number.hpp>
#include <nil/crypto3/multiprecision/cpp_int.hpp>
 
#include <nil/crypto3/algebra/pairing/detail/forms/short_weierstrass/jacobian_with_a4_0/types.hpp>
 
namespace nil {
    namespace crypto3 {
        namespace algebra {
            namespace pairing {
 
                template<typename CurveType>
                class short_weierstrass_jacobian_with_a4_0_ate_double_miller_loop {
                    using curve_type = CurveType;
 
                    using params_type = detail::pairing_params<curve_type>;
                    typedef detail::short_weierstrass_jacobian_with_a4_0_types_policy<curve_type> policy_type;
 
                    using gt_type = typename curve_type::gt_type;
 
                public:
                    static typename gt_type::value_type
                        process(const typename policy_type::ate_g1_precomputed_type &prec_P1,
                                const typename policy_type::ate_g2_precomputed_type &prec_Q1,
                                const typename policy_type::ate_g1_precomputed_type &prec_P2,
                                const typename policy_type::ate_g2_precomputed_type &prec_Q2) {
 
                        typename gt_type::value_type f = gt_type::value_type::one();
 
                        bool found_one = false;
                        std::size_t idx = 0;
 
                        const typename policy_type::integral_type &loop_count = params_type::ate_loop_count;
 
                        for (long i = params_type::integral_type_max_bits; i >= 0; --i) {
                            const bool bit = nil::crypto3::multiprecision::bit_test(loop_count, i);
                            if (!found_one) {
                                /* this skips the MSB itself */
                                found_one |= bit;
                                continue;
                            }
 
                            /* code below gets executed for all bits (EXCEPT the MSB itself) of
                               param_p (skipping leading zeros) in MSB to LSB
                               order */
 
                            typename policy_type::ate_ell_coeffs c1 = prec_Q1.coeffs[idx];
                            typename policy_type::ate_ell_coeffs c2 = prec_Q2.coeffs[idx];
                            ++idx;
 
                            f = f.squared();
 
                            f = f.mul_by_045(c1.ell_0, prec_P1.PY * c1.ell_VW, prec_P1.PX * c1.ell_VV);
                            f = f.mul_by_045(c2.ell_0, prec_P2.PY * c2.ell_VW, prec_P2.PX * c2.ell_VV);
 
                            if (bit) {
                                typename policy_type::ate_ell_coeffs c1 = prec_Q1.coeffs[idx];
                                typename policy_type::ate_ell_coeffs c2 = prec_Q2.coeffs[idx];
                                ++idx;
 
                                f = f.mul_by_045(c1.ell_0, prec_P1.PY * c1.ell_VW, prec_P1.PX * c1.ell_VV);
                                f = f.mul_by_045(c2.ell_0, prec_P2.PY * c2.ell_VW, prec_P2.PX * c2.ell_VV);
                            }
                        }
 
                        if (params_type::ate_is_loop_count_neg) {
                            f = f.inversed();
                        }
 
                        return f;
                    }
                };
            }    // namespace pairing
        }        // namespace algebra
    }            // namespace crypto3
}    // namespace nil
#endif    // CRYPTO3_ALGEBRA_PAIRING_SHORT_WEIERSTRASS_JACOBIAN_WITH_A4_0_ATE_DOUBLE_MILLER_LOOP_HPP