bsnes/nall/elliptic-curve/modulo25519-reference.hpp

85 lines
2.4 KiB
C++

#pragma once
//warning: this implementation leaks side-channel information
//use modulo25519-optimized.hpp in production
#include <nall/arithmetic/barrett.hpp>
namespace nall::EllipticCurve {
static const uint256_t P = (1_u256 << 255) - 19;
struct Modulo25519 {
inline Modulo25519() = default;
inline Modulo25519(const Modulo25519& source) : value(source.value) {}
template<typename T> inline Modulo25519(const T& value) : value(value) {}
inline explicit operator bool() const { return (bool)value; }
inline auto operator()() const -> uint256_t { return value; }
private:
uint256_t value;
};
inline auto operator-(const Modulo25519& lhs) -> Modulo25519 {
return P - lhs();
}
inline auto operator+(const Modulo25519& lhs, const Modulo25519& rhs) -> Modulo25519 {
uint512_t value = (uint512_t)lhs() + rhs();
if(value >= P) value -= P;
return value;
}
inline auto operator-(const Modulo25519& lhs, const Modulo25519& rhs) -> Modulo25519 {
uint512_t value = (uint512_t)lhs();
if(value < rhs()) value += P;
return uint256_t(value - rhs());
}
inline auto operator*(const Modulo25519& lhs, const Modulo25519& rhs) -> Modulo25519 {
static const BarrettReduction<256> P{EllipticCurve::P};
uint256_t hi, lo;
mul(lhs(), rhs(), hi, lo);
return uint512_t{hi, lo} % P;
}
inline auto operator&(const Modulo25519& lhs, uint256_t rhs) -> uint256_t {
return lhs() & rhs;
}
inline auto square(const Modulo25519& lhs) -> Modulo25519 {
static const BarrettReduction<256> P{EllipticCurve::P};
uint256_t hi, lo;
square(lhs(), hi, lo);
return uint512_t{hi, lo} % P;
}
inline auto exponentiate(const Modulo25519& lhs, uint256_t exponent) -> Modulo25519 {
if(exponent == 0) return 1;
Modulo25519 value = square(exponentiate(lhs, exponent >> 1));
if(exponent & 1) value = value * lhs;
return value;
}
inline auto reciprocal(const Modulo25519& lhs) -> Modulo25519 {
return exponentiate(lhs, P - 2);
}
inline auto squareRoot(const Modulo25519& lhs) -> Modulo25519 {
static const Modulo25519 I = exponentiate(Modulo25519(2), P - 1 >> 2); //I = sqrt(-1)
Modulo25519 value = exponentiate(lhs, P + 3 >> 3);
if(square(value) - lhs) value = value * I;
if(value & 1) value = -value;
return value;
}
inline auto cmove(bool condition, Modulo25519& lhs, const Modulo25519& rhs) -> void {
if(condition) lhs = rhs;
}
inline auto cswap(bool condition, Modulo25519& lhs, Modulo25519& rhs) -> void {
if(condition) swap(lhs, rhs);
}
}