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pqcrypto/crypto_kem/hqc-256/clean/fft.c

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#include "fft.h"
#include "gf.h"
#include "parameters.h"
#include <stdint.h>
#include <stdio.h>
#include <string.h>
/**
* @file fft.c
* Implementation of the additive FFT and its transpose.
* This implementation is based on the paper from Gao and Mateer: <br>
* Shuhong Gao and Todd Mateer, Additive Fast Fourier Transforms over Finite Fields,
* IEEE Transactions on Information Theory 56 (2010), 6265--6272.
* http://www.math.clemson.edu/~sgao/papers/GM10.pdf <br>
* and includes improvements proposed by Bernstein, Chou and Schwabe here:
* https://binary.cr.yp.to/mcbits-20130616.pdf
*/
static void compute_fft_betas(uint16_t *betas);
static void compute_subset_sums(uint16_t *subset_sums, const uint16_t *set, size_t set_size);
static void radix_t(uint16_t *f, const uint16_t *f0, const uint16_t *f1, uint32_t m_f);
static void radix_t_big(uint16_t *f, const uint16_t *f0, const uint16_t *f1, uint32_t m_f);
static void fft_t_rec(uint16_t *f, const uint16_t *w, size_t f_coeffs, uint8_t m, uint32_t m_f, const uint16_t *betas);
static void radix(uint16_t *f0, uint16_t *f1, const uint16_t *f, uint32_t m_f);
static void radix_big(uint16_t *f0, uint16_t *f1, const uint16_t *f, uint32_t m_f);
static void fft_rec(uint16_t *w, uint16_t *f, size_t f_coeffs, uint8_t m, uint32_t m_f, const uint16_t *betas);
/**
* @brief Computes the basis of betas (omitting 1) used in the additive FFT and its transpose
*
* @param[out] betas Array of size PARAM_M-1
*/
static void compute_fft_betas(uint16_t *betas) {
size_t i;
for (i = 0 ; i < PARAM_M - 1 ; ++i) {
betas[i] = 1 << (PARAM_M - 1 - i);
}
}
/**
* @brief Computes the subset sums of the given set
*
* The array subset_sums is such that its ith element is
* the subset sum of the set elements given by the binary form of i.
*
* @param[out] subset_sums Array of size 2^set_size receiving the subset sums
* @param[in] set Array of set_size elements
* @param[in] set_size Size of the array set
*/
static void compute_subset_sums(uint16_t *subset_sums, const uint16_t *set, size_t set_size) {
size_t i, j;
subset_sums[0] = 0;
for (i = 0 ; i < set_size ; ++i) {
for (j = 0 ; j < (1U << i) ; ++j) {
subset_sums[(1 << i) + j] = set[i] ^ subset_sums[j];
}
}
}
/**
* @brief Transpose of the linear radix conversion
*
* This is a direct transposition of the radix function
* implemented following the process of transposing a linear function as exposed by Bernstein, Chou and Schwabe here:
* https://binary.cr.yp.to/mcbits-20130616.pdf
*
* @param[out] f Array of size a power of 2
* @param[in] f0 Array half the size of f
* @param[in] f1 Array half the size of f
* @param[in] m_f 2^{m_f} is the smallest power of 2 greater or equal to the number of coefficients of f
*/
static void radix_t(uint16_t *f, const uint16_t *f0, const uint16_t *f1, uint32_t m_f) {
switch (m_f) {
case 4:
f[0] = f0[0];
f[1] = f1[0];
f[2] = f0[1] ^ f1[0];
f[3] = f[2] ^ f1[1];
f[4] = f[2] ^ f0[2];
f[5] = f[3] ^ f1[2];
f[6] = f[4] ^ f0[3] ^ f1[2];
f[7] = f[3] ^ f0[3] ^ f1[3];
f[8] = f[4] ^ f0[4];
f[9] = f[5] ^ f1[4];
f[10] = f[6] ^ f0[5] ^ f1[4];
f[11] = f[7] ^ f0[5] ^ f1[4] ^ f1[5];
f[12] = f[8] ^ f0[5] ^ f0[6] ^ f1[4];
f[13] = f[7] ^ f[9] ^ f[11] ^ f1[6];
f[14] = f[6] ^ f0[6] ^ f0[7] ^ f1[6];
f[15] = f[7] ^ f0[7] ^ f1[7];
break;
case 3:
f[0] = f0[0];
f[1] = f1[0];
f[2] = f0[1] ^ f1[0];
f[3] = f[2] ^ f1[1];
f[4] = f[2] ^ f0[2];
f[5] = f[3] ^ f1[2];
f[6] = f[4] ^ f0[3] ^ f1[2];
f[7] = f[3] ^ f0[3] ^ f1[3];
break;
case 2:
f[0] = f0[0];
f[1] = f1[0];
f[2] = f0[1] ^ f1[0];
f[3] = f[2] ^ f1[1];
break;
case 1:
f[0] = f0[0];
f[1] = f1[0];
break;
default:
radix_t_big(f, f0, f1, m_f);
break;
}
}
static void radix_t_big(uint16_t *f, const uint16_t *f0, const uint16_t *f1, uint32_t m_f) {
uint16_t Q0[1 << (PARAM_FFT_T - 2)] = {0};
uint16_t Q1[1 << (PARAM_FFT_T - 2)] = {0};
uint16_t R0[1 << (PARAM_FFT_T - 2)] = {0};
uint16_t R1[1 << (PARAM_FFT_T - 2)] = {0};
uint16_t Q[1 << 2 * (PARAM_FFT_T - 2)] = {0};
uint16_t R[1 << 2 * (PARAM_FFT_T - 2)] = {0};
size_t i, n;
n = 1 << (m_f - 2);
memcpy(Q0, f0 + n, 2 * n);
memcpy(Q1, f1 + n, 2 * n);
memcpy(R0, f0, 2 * n);
memcpy(R1, f1, 2 * n);
radix_t (Q, Q0, Q1, m_f - 1);
radix_t (R, R0, R1, m_f - 1);
memcpy(f, R, 4 * n);
memcpy(f + 2 * n, R + n, 2 * n);
memcpy(f + 3 * n, Q + n, 2 * n);
for (i = 0 ; i < n ; ++i) {
f[2 * n + i] ^= Q[i];
f[3 * n + i] ^= f[2 * n + i];
}
}
/**
* @brief Recursively computes syndromes of family w
*
* This function is a subroutine of the function fft_t
*
* @param[out] f Array receiving the syndromes
* @param[in] w Array storing the family
* @param[in] f_coeffs Length of syndromes vector
* @param[in] m 2^m is the smallest power of 2 greater or equal to the length of family w
* @param[in] m_f 2^{m_f} is the smallest power of 2 greater or equal to the length of f
* @param[in] betas FFT constants
*/
static void fft_t_rec(uint16_t *f, const uint16_t *w, size_t f_coeffs, uint8_t m, uint32_t m_f, const uint16_t *betas) {
uint16_t gammas[PARAM_M - 2] = {0};
uint16_t deltas[PARAM_M - 2] = {0};
uint16_t gammas_sums[1 << (PARAM_M - 1)] = {0};
uint16_t u[1 << (PARAM_M - 2)] = {0};
uint16_t f0[1 << (PARAM_FFT_T - 2)] = {0};
uint16_t f1[1 << (PARAM_FFT_T - 2)] = {0};
uint16_t betas_sums[1 << (PARAM_M - 1)] = {0};
uint16_t v[1 << (PARAM_M - 2)] = {0};
uint16_t beta_m_pow;
size_t i, j, k;
// Step 1
if (m_f == 1) {
f[0] = 0;
for (i = 0 ; i < (1U << m) ; ++i) {
f[0] ^= w[i];
}
f[1] = 0;
betas_sums[0] = 0;
for (j = 0 ; j < m ; ++j) {
for (k = 0 ; k < (1U << j) ; ++k) {
betas_sums[(1 << j) + k] = betas_sums[k] ^ betas[j];
f[1] ^= PQCLEAN_HQC256_CLEAN_gf_mul(betas_sums[(1 << j) + k], w[(1 << j) + k]);
}
}
return;
}
// Compute gammas and deltas
for (i = 0 ; i + 1 < m ; ++i) {
gammas[i] = PQCLEAN_HQC256_CLEAN_gf_mul(betas[i], PQCLEAN_HQC256_CLEAN_gf_inverse(betas[m - 1]));
deltas[i] = PQCLEAN_HQC256_CLEAN_gf_square(gammas[i]) ^ gammas[i];
}
// Compute gammas subset sums
compute_subset_sums(gammas_sums, gammas, m - 1);
/* Step 6: Compute u and v from w (aka w)
* w[i] = u[i] + G[i].v[i]
* w[k+i] = w[i] + v[i] = u[i] + (G[i]+1).v[i]
* Transpose:
* u[i] = w[i] + w[k+i]
* v[i] = G[i].w[i] + (G[i]+1).w[k+i] = G[i].u[i] + w[k+i] */
k = 1 << ((m - 1) & 0xf); // &0xf is to let the compiler know that m-1 is small.
if (f_coeffs <= 3) { // 3-coefficient polynomial f case
// Step 5: Compute f0 from u and f1 from v
f1[1] = 0;
u[0] = w[0] ^ w[k];
f1[0] = w[k];
for (i = 1 ; i < k ; ++i) {
u[i] = w[i] ^ w[k + i];
f1[0] ^= PQCLEAN_HQC256_CLEAN_gf_mul(gammas_sums[i], u[i]) ^ w[k + i];
}
fft_t_rec(f0, u, (f_coeffs + 1) / 2, m - 1, m_f - 1, deltas);
} else {
u[0] = w[0] ^ w[k];
v[0] = w[k];
for (i = 1 ; i < k ; ++i) {
u[i] = w[i] ^ w[k + i];
v[i] = PQCLEAN_HQC256_CLEAN_gf_mul(gammas_sums[i], u[i]) ^ w[k + i];
}
// Step 5: Compute f0 from u and f1 from v
fft_t_rec(f0, u, (f_coeffs + 1) / 2, m - 1, m_f - 1, deltas);
fft_t_rec(f1, v, f_coeffs / 2, m - 1, m_f - 1, deltas);
}
// Step 3: Compute g from g0 and g1
radix_t(f, f0, f1, m_f);
// Step 2: compute f from g
if (betas[m - 1] != 1) {
beta_m_pow = 1;
for (i = 1 ; i < (1U << m_f) ; ++i) {
beta_m_pow = PQCLEAN_HQC256_CLEAN_gf_mul(beta_m_pow, betas[m - 1]);
f[i] = PQCLEAN_HQC256_CLEAN_gf_mul(beta_m_pow, f[i]);
}
}
}
/**
* @brief Computes the syndromes f of the family w
*
* Since the syndromes linear map is the transpose of multipoint evaluation,
* it uses exactly the same constants, either hardcoded or precomputed by compute_fft_lut(...). <br>
* This follows directives from Bernstein, Chou and Schwabe given here:
* https://binary.cr.yp.to/mcbits-20130616.pdf
*
* @param[out] f Array of size 2*(PARAM_FFT_T) elements receiving the syndromes
* @param[in] w Array of PARAM_GF_MUL_ORDER+1 elements
* @param[in] f_coeffs Length of syndromes vector f
*/
void PQCLEAN_HQC256_CLEAN_fft_t(uint16_t *f, const uint16_t *w, size_t f_coeffs) {
// Transposed from Gao and Mateer algorithm
uint16_t betas[PARAM_M - 1] = {0};
uint16_t betas_sums[1 << (PARAM_M - 1)] = {0};
uint16_t u[1 << (PARAM_M - 1)] = {0};
uint16_t v[1 << (PARAM_M - 1)] = {0};
uint16_t deltas[PARAM_M - 1] = {0};
uint16_t f0[1 << (PARAM_FFT_T - 1)] = {0};
uint16_t f1[1 << (PARAM_FFT_T - 1)] = {0};
size_t i, k;
compute_fft_betas(betas);
compute_subset_sums(betas_sums, betas, PARAM_M - 1);
/* Step 6: Compute u and v from w (aka w)
*
* We had:
* w[i] = u[i] + G[i].v[i]
* w[k+i] = w[i] + v[i] = u[i] + (G[i]+1).v[i]
* Transpose:
* u[i] = w[i] + w[k+i]
* v[i] = G[i].w[i] + (G[i]+1).w[k+i] = G[i].u[i] + w[k+i] */
k = 1 << (PARAM_M - 1);
u[0] = w[0] ^ w[k];
v[0] = w[k];
for (i = 1 ; i < k ; ++i) {
u[i] = w[i] ^ w[k + i];
v[i] = PQCLEAN_HQC256_CLEAN_gf_mul(betas_sums[i], u[i]) ^ w[k + i];
}
// Compute deltas
for (i = 0 ; i < PARAM_M - 1 ; ++i) {
deltas[i] = PQCLEAN_HQC256_CLEAN_gf_square(betas[i]) ^ betas[i];
}
// Step 5: Compute f0 from u and f1 from v
fft_t_rec(f0, u, (f_coeffs + 1) / 2, PARAM_M - 1, PARAM_FFT_T - 1, deltas);
fft_t_rec(f1, v, f_coeffs / 2, PARAM_M - 1, PARAM_FFT_T - 1, deltas);
// Step 3: Compute g from g0 and g1
radix_t(f, f0, f1, PARAM_FFT_T);
// Step 2: beta_m = 1 so f = g
}
/**
* @brief Computes the radix conversion of a polynomial f in GF(2^m)[x]
*
* Computes f0 and f1 such that f(x) = f0(x^2-x) + x.f1(x^2-x)
* as proposed by Bernstein, Chou and Schwabe:
* https://binary.cr.yp.to/mcbits-20130616.pdf
*
* @param[out] f0 Array half the size of f
* @param[out] f1 Array half the size of f
* @param[in] f Array of size a power of 2
* @param[in] m_f 2^{m_f} is the smallest power of 2 greater or equal to the number of coefficients of f
*/
static void radix(uint16_t *f0, uint16_t *f1, const uint16_t *f, uint32_t m_f) {
switch (m_f) {
case 4:
f0[4] = f[8] ^ f[12];
f0[6] = f[12] ^ f[14];
f0[7] = f[14] ^ f[15];
f1[5] = f[11] ^ f[13];
f1[6] = f[13] ^ f[14];
f1[7] = f[15];
f0[5] = f[10] ^ f[12] ^ f1[5];
f1[4] = f[9] ^ f[13] ^ f0[5];
f0[0] = f[0];
f1[3] = f[7] ^ f[11] ^ f[15];
f0[3] = f[6] ^ f[10] ^ f[14] ^ f1[3];
f0[2] = f[4] ^ f0[4] ^ f0[3] ^ f1[3];
f1[1] = f[3] ^ f[5] ^ f[9] ^ f[13] ^ f1[3];
f1[2] = f[3] ^ f1[1] ^ f0[3];
f0[1] = f[2] ^ f0[2] ^ f1[1];
f1[0] = f[1] ^ f0[1];
break;
case 3:
f0[0] = f[0];
f0[2] = f[4] ^ f[6];
f0[3] = f[6] ^ f[7];
f1[1] = f[3] ^ f[5] ^ f[7];
f1[2] = f[5] ^ f[6];
f1[3] = f[7];
f0[1] = f[2] ^ f0[2] ^ f1[1];
f1[0] = f[1] ^ f0[1];
break;
case 2:
f0[0] = f[0];
f0[1] = f[2] ^ f[3];
f1[0] = f[1] ^ f0[1];
f1[1] = f[3];
break;
case 1:
f0[0] = f[0];
f1[0] = f[1];
break;
default:
radix_big(f0, f1, f, m_f);
break;
}
}
static void radix_big(uint16_t *f0, uint16_t *f1, const uint16_t *f, uint32_t m_f) {
uint16_t Q[2 * (1 << (PARAM_FFT - 2))] = {0};
uint16_t R[2 * (1 << (PARAM_FFT - 2))] = {0};
uint16_t Q0[1 << (PARAM_FFT - 2)] = {0};
uint16_t Q1[1 << (PARAM_FFT - 2)] = {0};
uint16_t R0[1 << (PARAM_FFT - 2)] = {0};
uint16_t R1[1 << (PARAM_FFT - 2)] = {0};
size_t i, n;
n = 1 << (m_f - 2);
memcpy(Q, f + 3 * n, 2 * n);
memcpy(Q + n, f + 3 * n, 2 * n);
memcpy(R, f, 4 * n);
for (i = 0 ; i < n ; ++i) {
Q[i] ^= f[2 * n + i];
R[n + i] ^= Q[i];
}
radix(Q0, Q1, Q, m_f - 1);
radix(R0, R1, R, m_f - 1);
memcpy(f0, R0, 2 * n);
memcpy(f0 + n, Q0, 2 * n);
memcpy(f1, R1, 2 * n);
memcpy(f1 + n, Q1, 2 * n);
}
/**
* @brief Evaluates f at all subset sums of a given set
*
* This function is a subroutine of the function fft.
*
* @param[out] w Array
* @param[in] f Array
* @param[in] f_coeffs Number of coefficients of f
* @param[in] m Number of betas
* @param[in] m_f Number of coefficients of f (one more than its degree)
* @param[in] betas FFT constants
*/
static void fft_rec(uint16_t *w, uint16_t *f, size_t f_coeffs, uint8_t m, uint32_t m_f, const uint16_t *betas) {
uint16_t f0[1 << (PARAM_FFT - 2)] = {0};
uint16_t f1[1 << (PARAM_FFT - 2)] = {0};
uint16_t gammas[PARAM_M - 2] = {0};
uint16_t deltas[PARAM_M - 2] = {0};
uint16_t gammas_sums[1 << (PARAM_M - 2)] = {0};
uint16_t u[1 << (PARAM_M - 2)] = {0};
uint16_t v[1 << (PARAM_M - 2)] = {0};
uint16_t tmp[PARAM_M - (PARAM_FFT - 1)] = {0};
uint16_t beta_m_pow;
size_t i, j, k;
// Step 1
if (m_f == 1) {
for (i = 0 ; i < m ; ++i) {
tmp[i] = PQCLEAN_HQC256_CLEAN_gf_mul(betas[i], f[1]);
}
w[0] = f[0];
for (j = 0 ; j < m ; ++j) {
for (k = 0 ; k < (1U << j) ; ++k) {
w[(1 << j) + k] = w[k] ^ tmp[j];
}
}
return;
}
// Step 2: compute g
if (betas[m - 1] != 1) {
beta_m_pow = 1;
for (i = 1 ; i < (1U << m_f) ; ++i) {
beta_m_pow = PQCLEAN_HQC256_CLEAN_gf_mul(beta_m_pow, betas[m - 1]);
f[i] = PQCLEAN_HQC256_CLEAN_gf_mul(beta_m_pow, f[i]);
}
}
// Step 3
radix(f0, f1, f, m_f);
// Step 4: compute gammas and deltas
for (i = 0 ; i + 1 < m ; ++i) {
gammas[i] = PQCLEAN_HQC256_CLEAN_gf_mul(betas[i], PQCLEAN_HQC256_CLEAN_gf_inverse(betas[m - 1]));
deltas[i] = PQCLEAN_HQC256_CLEAN_gf_square(gammas[i]) ^ gammas[i];
}
// Compute gammas sums
compute_subset_sums(gammas_sums, gammas, m - 1);
// Step 5
fft_rec(u, f0, (f_coeffs + 1) / 2, m - 1, m_f - 1, deltas);
k = 1 << ((m - 1) & 0xf); // &0xf is to let the compiler know that m-1 is small.
if (f_coeffs <= 3) { // 3-coefficient polynomial f case: f1 is constant
w[0] = u[0];
w[k] = u[0] ^ f1[0];
for (i = 1 ; i < k ; ++i) {
w[i] = u[i] ^ PQCLEAN_HQC256_CLEAN_gf_mul(gammas_sums[i], f1[0]);
w[k + i] = w[i] ^ f1[0];
}
} else {
fft_rec(v, f1, f_coeffs / 2, m - 1, m_f - 1, deltas);
// Step 6
memcpy(w + k, v, 2 * k);
w[0] = u[0];
w[k] ^= u[0];
for (i = 1 ; i < k ; ++i) {
w[i] = u[i] ^ PQCLEAN_HQC256_CLEAN_gf_mul(gammas_sums[i], v[i]);
w[k + i] ^= w[i];
}
}
}
/**
* @brief Evaluates f on all fields elements using an additive FFT algorithm
*
* f_coeffs is the number of coefficients of f (one less than its degree). <br>
* The FFT proceeds recursively to evaluate f at all subset sums of a basis B. <br>
* This implementation is based on the paper from Gao and Mateer: <br>
* Shuhong Gao and Todd Mateer, Additive Fast Fourier Transforms over Finite Fields,
* IEEE Transactions on Information Theory 56 (2010), 6265--6272.
* http://www.math.clemson.edu/~sgao/papers/GM10.pdf <br>
* and includes improvements proposed by Bernstein, Chou and Schwabe here:
* https://binary.cr.yp.to/mcbits-20130616.pdf <br>
* Note that on this first call (as opposed to the recursive calls to fft_rec), gammas are equal to betas,
* meaning the first gammas subset sums are actually the subset sums of betas (except 1). <br>
* Also note that f is altered during computation (twisted at each level).
*
* @param[out] w Array
* @param[in] f Array of 2^PARAM_FFT elements
* @param[in] f_coeffs Number coefficients of f (i.e. deg(f)+1)
*/
void PQCLEAN_HQC256_CLEAN_fft(uint16_t *w, const uint16_t *f, size_t f_coeffs) {
uint16_t betas[PARAM_M - 1] = {0};
uint16_t betas_sums[1 << (PARAM_M - 1)] = {0};
uint16_t f0[1 << (PARAM_FFT - 1)] = {0};
uint16_t f1[1 << (PARAM_FFT - 1)] = {0};
uint16_t deltas[PARAM_M - 1] = {0};
uint16_t u[1 << (PARAM_M - 1)] = {0};
uint16_t v[1 << (PARAM_M - 1)] = {0};
size_t i, k;
// Follows Gao and Mateer algorithm
compute_fft_betas(betas);
// Step 1: PARAM_FFT > 1, nothing to do
// Compute gammas sums
compute_subset_sums(betas_sums, betas, PARAM_M - 1);
// Step 2: beta_m = 1, nothing to do
// Step 3
radix(f0, f1, f, PARAM_FFT);
// Step 4: Compute deltas
for (i = 0 ; i < PARAM_M - 1 ; ++i) {
deltas[i] = PQCLEAN_HQC256_CLEAN_gf_square(betas[i]) ^ betas[i];
}
// Step 5
fft_rec(u, f0, (f_coeffs + 1) / 2, PARAM_M - 1, PARAM_FFT - 1, deltas);
fft_rec(v, f1, f_coeffs / 2, PARAM_M - 1, PARAM_FFT - 1, deltas);
k = 1 << (PARAM_M - 1);
// Step 6, 7 and error polynomial computation
memcpy(w + k, v, 2 * k);
// Check if 0 is root
w[0] = u[0];
// Check if 1 is root
w[k] ^= u[0];
// Find other roots
for (i = 1 ; i < k ; ++i) {
w[i] = u[i] ^ PQCLEAN_HQC256_CLEAN_gf_mul(betas_sums[i], v[i]);
w[k + i] ^= w[i];
}
}
/**
* @brief Arranges the received word vector in a form w such that applying the additive FFT transpose to w yields the BCH syndromes of the received word vector.
*
* Since the received word vector gives coefficients of the primitive element alpha, we twist accordingly. <br>
* Furthermore, the additive FFT transpose needs elements indexed by their decomposition on the chosen basis,
* so we apply the adequate permutation.
*
* @param[out] w Array of size 2^PARAM_M
* @param[in] vector Array of size VEC_N1_SIZE_BYTES
*/
void PQCLEAN_HQC256_CLEAN_fft_t_preprocess_bch_codeword(uint16_t *w, const uint64_t *vector) {
uint16_t r[1 << PARAM_M] = {0};
uint16_t gammas[PARAM_M - 1] = {0};
uint16_t gammas_sums[1 << (PARAM_M - 1)] = {0};
size_t i, j, k;
// Unpack the received word vector into array r
for (i = 0 ; i < VEC_N1_SIZE_64 - (PARAM_N1 % 64 != 0) ; ++i) {
for (j = 0 ; j < 64 ; ++j) {
r[64 * i + j] = (uint8_t) ((vector[i] >> j) & 1);
}
}
// Last byte
for (j = 0 ; j < PARAM_N1 % 64 ; ++j) {
r[64 * i + j] = (uint8_t) ((vector[i] >> j) & 1);
}
// Complete r with zeros
memset(r + PARAM_N1, 0, 2 * ((1 << PARAM_M) - PARAM_N1));
compute_fft_betas(gammas);
compute_subset_sums(gammas_sums, gammas, PARAM_M - 1);
// Twist and permute r adequately to obtain w
k = 1 << (PARAM_M - 1);
w[0] = 0;
w[k] = -r[0] & 1;
for (i = 1 ; i < k ; ++i) {
w[i] = -r[PQCLEAN_HQC256_CLEAN_gf_log(gammas_sums[i])] & gammas_sums[i];
w[k + i] = -r[PQCLEAN_HQC256_CLEAN_gf_log(gammas_sums[i] ^ 1)] & (gammas_sums[i] ^ 1);
}
}
/**
* @brief Retrieves the error polynomial error from the evaluations w of the ELP (Error Locator Polynomial) on all field elements.
*
* @param[out] error Array of size VEC_N1_SIZE_BYTES
* @param[in] w Array of size 2^PARAM_M
*/
void PQCLEAN_HQC256_CLEAN_fft_retrieve_bch_error_poly(uint64_t *error, const uint16_t *w) {
uint16_t gammas[PARAM_M - 1] = {0};
uint16_t gammas_sums[1 << (PARAM_M - 1)] = {0};
uint64_t bit;
size_t i, k, index;
compute_fft_betas(gammas);
compute_subset_sums(gammas_sums, gammas, PARAM_M - 1);
error[0] ^= 1 ^ ((uint16_t) - w[0] >> 15);
k = 1 << (PARAM_M - 1);
index = PARAM_GF_MUL_ORDER;
bit = 1 ^ ((uint16_t) - w[k] >> 15);
error[index / 8] ^= bit << (index % 64);
for (i = 1 ; i < k ; ++i) {
index = PARAM_GF_MUL_ORDER - PQCLEAN_HQC256_CLEAN_gf_log(gammas_sums[i]);
bit = 1 ^ ((uint16_t) - w[i] >> 15);
error[index / 64] ^= bit << (index % 64);
index = PARAM_GF_MUL_ORDER - PQCLEAN_HQC256_CLEAN_gf_log(gammas_sums[i] ^ 1);
bit = 1 ^ ((uint16_t) - w[k + i] >> 15);
error[index / 64] ^= bit << (index % 64);
}
}
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