135 lines
3.2 KiB
C
135 lines
3.2 KiB
C
#include "gf.h"
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#include "parameters.h"
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#include <emmintrin.h>
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#include <immintrin.h>
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#include <stdint.h>
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/**
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* @file gf.c
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* Galois field implementation with multiplication using the pclmulqdq instruction
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*/
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static uint16_t gf_reduce(uint64_t x, size_t deg_x);
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/**
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* Returns the integer i such that elt = a^i
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* where a is the primitive element of GF(2^GF_M).
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*@returns the logarithm of the given element
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*/
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uint16_t PQCLEAN_HQCRMRS128_AVX2_gf_log(uint16_t elt) {
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return log[elt];
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}
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/**
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* Reduces polynomial x modulo primitive polynomial GF_POLY.
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* @returns x mod GF_POLY
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* @param[in] x Polynomial of degree less than 64
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* @param[in] deg_x The degree of polynomial x
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*/
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static uint16_t gf_reduce(uint64_t x, size_t deg_x) {
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// Compute the distance between the primitive polynomial first two set bits
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size_t lz1 = __builtin_clz(PARAM_GF_POLY);
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size_t lz2 = __builtin_clz(PARAM_GF_POLY ^ 1 << PARAM_M);
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size_t dist = lz2 - lz1;
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// Deduce the number of steps of reduction
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size_t steps = CEIL_DIVIDE(deg_x - (PARAM_M - 1), dist);
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// Reduce
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for (size_t i = 0; i < steps; ++i) {
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uint64_t mod = x >> PARAM_M;
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x &= (1 << PARAM_M) - 1;
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x ^= mod;
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size_t tz1 = 0;
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uint16_t rmdr = PARAM_GF_POLY ^ 1;
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for (size_t j = __builtin_popcount(PARAM_GF_POLY) - 2; j; --j) {
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size_t tz2 = __builtin_ctz(rmdr);
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size_t shift = tz2 - tz1;
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mod <<= shift;
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x ^= mod;
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rmdr ^= 1 << tz2;
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tz1 = tz2;
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}
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}
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return x;
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}
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/**
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* Multiplies two elements of GF(2^GF_M).
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* @returns the product a*b
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* @param[in] a Element of GF(2^GF_M)
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* @param[in] b Element of GF(2^GF_M)
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*/
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uint16_t PQCLEAN_HQCRMRS128_AVX2_gf_mul(uint16_t a, uint16_t b) {
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__m128i va = _mm_cvtsi32_si128(a);
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__m128i vb = _mm_cvtsi32_si128(b);
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__m128i vab = _mm_clmulepi64_si128(va, vb, 0);
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uint32_t ab = _mm_cvtsi128_si32(vab);
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return gf_reduce(ab, 2 * (PARAM_M - 1));
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}
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/**
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* Squares an element of GF(2^GF_M).
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* @returns a^2
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* @param[in] a Element of GF(2^GF_M)
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*/
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uint16_t PQCLEAN_HQCRMRS128_AVX2_gf_square(uint16_t a) {
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uint32_t b = a;
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uint32_t s = b & 1;
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for (size_t i = 1; i < PARAM_M; ++i) {
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b <<= 1;
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s ^= b & (1 << 2 * i);
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}
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return gf_reduce(s, 2 * (PARAM_M - 1));
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}
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/**
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* Computes the inverse of an element of GF(2^GF_M) by fast exponentiation.
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* @returns the inverse of a
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* @param[in] a Element of GF(2^GF_M)
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*/
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uint16_t PQCLEAN_HQCRMRS128_AVX2_gf_inverse(uint16_t a) {
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size_t pow = (1 << PARAM_M) - 2;
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uint16_t inv = 1;
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do {
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if (pow & 1) {
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inv = PQCLEAN_HQCRMRS128_AVX2_gf_mul(inv, a);
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}
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a = PQCLEAN_HQCRMRS128_AVX2_gf_square(a);
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pow >>= 1;
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} while (pow);
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return inv;
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}
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/**
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* Returns i modulo 2^GF_M-1.
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* i must be less than 2*(2^GF_M-1).
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* Therefore, the return value is either i or i-2^GF_M+1.
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* @returns i mod (2^GF_M-1)
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* @param[in] i The integer whose modulo is taken
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*/
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uint16_t PQCLEAN_HQCRMRS128_AVX2_gf_mod(uint16_t i) {
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uint16_t tmp = i - PARAM_GF_MUL_ORDER;
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// mask = 0xffff if (i < GF_MUL_ORDER)
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int16_t mask = -(tmp >> 15);
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return tmp + (mask & PARAM_GF_MUL_ORDER);
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}
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