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120 lines
4.4 KiB
120 lines
4.4 KiB
/** @file
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*****************************************************************************
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Implementation of arithmetic in the finite field F[p^2].
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*****************************************************************************
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* @author This file is part of libsnark, developed by SCIPR Lab
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* and contributors (see AUTHORS).
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* @copyright MIT license (see LICENSE file)
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*****************************************************************************/
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#ifndef FP2_HPP_
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#define FP2_HPP_
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#include "algebra/fields/fp.hpp"
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#include <vector>
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namespace libsnark {
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template<mp_size_t n, const bigint<n>& modulus>
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class Fp2_model;
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template<mp_size_t n, const bigint<n>& modulus>
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std::ostream& operator<<(std::ostream &, const Fp2_model<n, modulus> &);
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template<mp_size_t n, const bigint<n>& modulus>
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std::istream& operator>>(std::istream &, Fp2_model<n, modulus> &);
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/**
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* Arithmetic in the field F[p^3].
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*
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* Let p := modulus. This interface provides arithmetic for the extension field
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* Fp2 = Fp[U]/(U^2-non_residue), where non_residue is in Fp.
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*
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* ASSUMPTION: p = 1 (mod 6)
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*/
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template<mp_size_t n, const bigint<n>& modulus>
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class Fp2_model {
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public:
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typedef Fp_model<n, modulus> my_Fp;
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static bigint<2*n> euler; // (modulus^2-1)/2
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static size_t s; // modulus^2 = 2^s * t + 1
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static bigint<2*n> t; // with t odd
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static bigint<2*n> t_minus_1_over_2; // (t-1)/2
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static my_Fp non_residue; // X^4-non_residue irreducible over Fp; used for constructing Fp2 = Fp[X] / (X^2 - non_residue)
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static Fp2_model<n, modulus> nqr; // a quadratic nonresidue in Fp2
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static Fp2_model<n, modulus> nqr_to_t; // nqr^t
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static my_Fp Frobenius_coeffs_c1[2]; // non_residue^((modulus^i-1)/2) for i=0,1
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my_Fp c0, c1;
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Fp2_model() {};
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Fp2_model(const my_Fp& c0, const my_Fp& c1) : c0(c0), c1(c1) {};
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void clear() { c0.clear(); c1.clear(); }
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void print() const { printf("c0/c1:\n"); c0.print(); c1.print(); }
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static Fp2_model<n, modulus> zero();
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static Fp2_model<n, modulus> one();
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static Fp2_model<n, modulus> random_element();
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bool is_zero() const { return c0.is_zero() && c1.is_zero(); }
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bool operator==(const Fp2_model &other) const;
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bool operator!=(const Fp2_model &other) const;
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Fp2_model operator+(const Fp2_model &other) const;
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Fp2_model operator-(const Fp2_model &other) const;
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Fp2_model operator*(const Fp2_model &other) const;
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Fp2_model operator-() const;
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Fp2_model squared() const; // default is squared_complex
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Fp2_model inverse() const;
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Fp2_model Frobenius_map(unsigned long power) const;
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Fp2_model sqrt() const; // HAS TO BE A SQUARE (else does not terminate)
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Fp2_model squared_karatsuba() const;
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Fp2_model squared_complex() const;
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template<mp_size_t m>
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Fp2_model operator^(const bigint<m> &other) const;
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static size_t size_in_bits() { return 2*my_Fp::size_in_bits(); }
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static bigint<n> base_field_char() { return modulus; }
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friend std::ostream& operator<< <n, modulus>(std::ostream &out, const Fp2_model<n, modulus> &el);
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friend std::istream& operator>> <n, modulus>(std::istream &in, Fp2_model<n, modulus> &el);
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};
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template<mp_size_t n, const bigint<n>& modulus>
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std::ostream& operator<<(std::ostream& out, const std::vector<Fp2_model<n, modulus> > &v);
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template<mp_size_t n, const bigint<n>& modulus>
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std::istream& operator>>(std::istream& in, std::vector<Fp2_model<n, modulus> > &v);
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template<mp_size_t n, const bigint<n>& modulus>
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Fp2_model<n, modulus> operator*(const Fp_model<n, modulus> &lhs, const Fp2_model<n, modulus> &rhs);
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template<mp_size_t n, const bigint<n>& modulus>
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bigint<2*n> Fp2_model<n, modulus>::euler;
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template<mp_size_t n, const bigint<n>& modulus>
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size_t Fp2_model<n, modulus>::s;
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template<mp_size_t n, const bigint<n>& modulus>
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bigint<2*n> Fp2_model<n, modulus>::t;
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template<mp_size_t n, const bigint<n>& modulus>
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bigint<2*n> Fp2_model<n, modulus>::t_minus_1_over_2;
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template<mp_size_t n, const bigint<n>& modulus>
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Fp_model<n, modulus> Fp2_model<n, modulus>::non_residue;
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template<mp_size_t n, const bigint<n>& modulus>
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Fp2_model<n, modulus> Fp2_model<n, modulus>::nqr;
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template<mp_size_t n, const bigint<n>& modulus>
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Fp2_model<n, modulus> Fp2_model<n, modulus>::nqr_to_t;
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template<mp_size_t n, const bigint<n>& modulus>
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Fp_model<n, modulus> Fp2_model<n, modulus>::Frobenius_coeffs_c1[2];
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} // libsnark
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#include "algebra/fields/fp2.tcc"
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#endif // FP2_HPP_
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