146 lines
3.5 KiB
C
146 lines
3.5 KiB
C
#include "gf.h"
|
|
#include "parameters.h"
|
|
#include <emmintrin.h>
|
|
#include <immintrin.h>
|
|
#include <stdint.h>
|
|
/**
|
|
* @file gf.c
|
|
* Galois field implementation with multiplication using the pclmulqdq instruction
|
|
*/
|
|
|
|
|
|
static uint16_t gf_reduce(uint64_t x, size_t deg_x);
|
|
static uint16_t gf_quad(uint64_t a);
|
|
|
|
|
|
|
|
/**
|
|
* Reduces polynomial x modulo primitive polynomial GF_POLY.
|
|
* @returns x mod GF_POLY
|
|
* @param[in] x Polynomial of degree less than 64
|
|
* @param[in] deg_x The degree of polynomial x
|
|
*/
|
|
static uint16_t gf_reduce(uint64_t x, size_t deg_x) {
|
|
uint16_t z1, z2, rmdr, dist;
|
|
uint64_t mod;
|
|
size_t steps, i, j;
|
|
|
|
// Deduce the number of steps of reduction
|
|
steps = CEIL_DIVIDE(deg_x - (PARAM_M - 1), PARAM_GF_POLY_M2);
|
|
|
|
// Reduce
|
|
for (i = 0; i < steps; ++i) {
|
|
mod = x >> PARAM_M;
|
|
x &= (1 << PARAM_M) - 1;
|
|
x ^= mod;
|
|
|
|
z1 = 0;
|
|
rmdr = PARAM_GF_POLY ^ 1;
|
|
for (j = PARAM_GF_POLY_WT - 2; j; --j) {
|
|
z2 = __tzcnt_u16(rmdr);
|
|
dist = (uint16_t) (z2 - z1);
|
|
mod <<= dist;
|
|
x ^= mod;
|
|
rmdr ^= 1 << z2;
|
|
z1 = z2;
|
|
}
|
|
}
|
|
|
|
return x;
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
* Multiplies two elements of GF(2^GF_M).
|
|
* @returns the product a*b
|
|
* @param[in] a Element of GF(2^GF_M)
|
|
* @param[in] b Element of GF(2^GF_M)
|
|
*/
|
|
uint16_t PQCLEAN_HQC192_AVX2_gf_mul(uint16_t a, uint16_t b) {
|
|
__m128i va = _mm_cvtsi32_si128(a);
|
|
__m128i vb = _mm_cvtsi32_si128(b);
|
|
__m128i vab = _mm_clmulepi64_si128(va, vb, 0);
|
|
uint32_t ab = _mm_cvtsi128_si32(vab);
|
|
|
|
return gf_reduce(ab, 2 * (PARAM_M - 1));
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
* Squares an element of GF(2^GF_M).
|
|
* @returns a^2
|
|
* @param[in] a Element of GF(2^GF_M)
|
|
*/
|
|
uint16_t PQCLEAN_HQC192_AVX2_gf_square(uint16_t a) {
|
|
uint32_t b = a;
|
|
uint32_t s = b & 1;
|
|
for (size_t i = 1; i < PARAM_M; ++i) {
|
|
b <<= 1;
|
|
s ^= b & (1 << 2 * i);
|
|
}
|
|
|
|
return gf_reduce(s, 2 * (PARAM_M - 1));
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
* Computes the 4th power of an element of GF(2^GF_M).
|
|
* @returns a^4
|
|
* @param[in] a Element of GF(2^GF_M)
|
|
*/
|
|
static uint16_t gf_quad(uint64_t a) {
|
|
uint64_t q = a & 1;
|
|
for (size_t i = 1; i < PARAM_M; ++i) {
|
|
a <<= 3;
|
|
q ^= a & (1ull << 4 * i);
|
|
}
|
|
|
|
return gf_reduce(q, 4 * (PARAM_M - 1));
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
* Computes the inverse of an element of GF(2^10),
|
|
* using a shorter chain of squares and multiplications than fast exponentiation.
|
|
* @returns the inverse of a
|
|
* @param[in] a Element of GF(2^10)
|
|
*/
|
|
uint16_t PQCLEAN_HQC192_AVX2_gf_inverse(uint16_t a) {
|
|
uint16_t p;
|
|
uint16_t a2;
|
|
|
|
a2 = PQCLEAN_HQC192_AVX2_gf_square(a); // a^2
|
|
a = PQCLEAN_HQC192_AVX2_gf_mul(a2, a); // a^2.a
|
|
p = gf_quad(a); // a^8.a^4
|
|
a = PQCLEAN_HQC192_AVX2_gf_mul(p, a); // a^8.a^4.a^2.a
|
|
p = gf_quad(a); // a^32.a^16.a^8.a^4
|
|
p = gf_quad(p); // a^128.a^64.a^32.a^16
|
|
a = PQCLEAN_HQC192_AVX2_gf_mul(p, a); // a^128.a^64.a^32.a^16.a^8.a^4.a^2.a
|
|
p = gf_quad(a); // a^512.a^256.a^128.a^64.a^32.a^16.a^8.a^4
|
|
p = PQCLEAN_HQC192_AVX2_gf_mul(p, a2); // a^-1
|
|
|
|
return p;
|
|
}
|
|
|
|
|
|
|
|
/**
|
|
* Returns i modulo 2^GF_M-1.
|
|
* i must be less than 2*(2^GF_M-1).
|
|
* Therefore, the return value is either i or i-2^GF_M+1.
|
|
* @returns i mod (2^GF_M-1)
|
|
* @param[in] i The integer whose modulo is taken
|
|
*/
|
|
uint16_t PQCLEAN_HQC192_AVX2_gf_mod(uint16_t i) {
|
|
uint16_t tmp = (uint16_t) (i - PARAM_GF_MUL_ORDER);
|
|
|
|
// mask = 0xffff if (i < GF_MUL_ORDER)
|
|
uint16_t mask = -(tmp >> 15);
|
|
|
|
return tmp + (mask & PARAM_GF_MUL_ORDER);
|
|
}
|