pqcrypto/crypto_kem/hqc-256-3-cca2/leaktime/fft.c

/**
 * @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
 */

#include "fft.h"
#include "gf.h"
#include "parameters.h"
#include <stdint.h>
#include <string.h>

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 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 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) {
    for (size_t 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) {
    subset_sums[0] = 0;

    for (size_t i = 0; i < set_size; ++i) {
        for (size_t j = 0; j < (((size_t)1) << i); ++j) {
            subset_sums[(((size_t)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];
        return;

    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];
        return;

    case 2:
        f[0] = f0[0];
        f[1] = f1[0];
        f[2] = f0[1] ^ f1[0];
        f[3] = f[2] ^ f1[1];
        return;

    case 1:
        f[0] = f0[0];
        f[1] = f1[0];
        return;

    default:
        ;

        size_t n = ((size_t)1) << (m_f - 2);

        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};

        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 (size_t 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) {
    size_t k = ((size_t)1) << (m - 1);
    uint16_t gammas[PARAM_M - 2] = {0};
    uint16_t deltas[PARAM_M - 2] = {0};
    uint16_t gammas_sums[1 << (PARAM_M - 1)];
    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};

    // Step 1
    if (m_f == 1) {
        for (size_t i = 0; i < (((size_t)1) << m); ++i) {
            f[0] ^= w[i];
        }

        for (size_t j = 0; j < m; ++j) {
            for (size_t ki = 0; ki < (((size_t)1) << j); ++ki) {
                size_t index = (((size_t)1) << j) + ki;
                betas_sums[index] = betas_sums[ki] ^ betas[j];
                f[1] ^= PQCLEAN_HQC2563CCA2_LEAKTIME_gf_mul(betas_sums[index], w[index]);
            }
        }

        return;
    }

    // Compute gammas and deltas
    for (uint8_t i = 0; i < m - 1; ++i) {
        gammas[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_gf_mul(betas[i], PQCLEAN_HQC2563CCA2_LEAKTIME_gf_inverse(betas[m - 1]));
        deltas[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_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] */
    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 (size_t i = 1; i < k; ++i) {
            u[i] = w[i] ^ w[k + i];
            f1[0] ^= PQCLEAN_HQC2563CCA2_LEAKTIME_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 {
        uint16_t v[1 << (PARAM_M - 2)] = {0};

        u[0] = w[0] ^ w[k];
        v[0] = w[k];

        for (size_t i = 1; i < k; ++i) {
            u[i] = w[i] ^ w[k + i];
            v[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_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) {
        uint16_t beta_m_pow = 1;
        for (size_t i = 1; i < (((size_t)1) << m_f); ++i) {
            beta_m_pow = PQCLEAN_HQC2563CCA2_LEAKTIME_gf_mul(beta_m_pow, betas[m - 1]);
            f[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_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_HQC2563CCA2_LEAKTIME_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];
    uint16_t betas_sums[1 << (PARAM_M - 1)];
    size_t k = 1 << (PARAM_M - 1);
    uint16_t u[1 << (PARAM_M - 1)] = {0};
    uint16_t v[1 << (PARAM_M - 1)] = {0};
    uint16_t deltas[PARAM_M - 1];
    uint16_t f0[1 << (PARAM_FFT_T - 1)];
    uint16_t f1[1 << (PARAM_FFT_T - 1)];

    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] */
    u[0] = w[0] ^ w[k];
    v[0] = w[k];
    for (size_t i = 1; i < k; ++i) {
        u[i] = w[i] ^ w[k + i];
        v[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_gf_mul(betas_sums[i], u[i]) ^ w[k + i];
    }

    // Compute deltas
    for (size_t i = 0; i < PARAM_M - 1; ++i) {
        deltas[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_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];
        return;

    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];
        return;

    case 2:
        f0[0] = f[0];
        f0[1] = f[2] ^ f[3];
        f1[0] = f[1] ^ f0[1];
        f1[1] = f[3];
        return;

    case 1:
        f0[0] = f[0];
        f1[0] = f[1];
        return;

    default:
        ;
        size_t n = ((size_t)1) << (m_f - 2);

        uint16_t Q[2 * (1 << (PARAM_FFT - 2))];
        uint16_t R[2 * (1 << (PARAM_FFT - 2))];

        uint16_t Q0[1 << (PARAM_FFT - 2)];
        uint16_t Q1[1 << (PARAM_FFT - 2)];
        uint16_t R0[1 << (PARAM_FFT - 2)];
        uint16_t R1[1 << (PARAM_FFT - 2)];

        memcpy(Q, f + 3 * n, 2 * n);
        memcpy(Q + n, f + 3 * n, 2 * n);
        memcpy(R, f, 4 * n);

        for (size_t 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};
    size_t k = ((size_t)1) << (m - 1);
    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};

    // Step 1
    if (m_f == 1) {
        uint16_t tmp[PARAM_M - (PARAM_FFT - 1)];
        for (size_t i = 0; i < m; ++i) {
            tmp[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_gf_mul(betas[i], f[1]);
        }

        w[0] = f[0];
        for (size_t j = 0; j < m; ++j) {
            for (size_t ki = 0; ki < (((size_t)1) << j); ++ki) {
                w[(((size_t)1) << j) + ki] = w[ki] ^ tmp[j];
            }
        }

        return;
    }

    // Step 2: compute g
    if (betas[m - 1] != 1) {
        uint16_t beta_m_pow = 1;
        for (size_t i = 1; i < (((size_t)1) << m_f); ++i) {
            beta_m_pow = PQCLEAN_HQC2563CCA2_LEAKTIME_gf_mul(beta_m_pow, betas[m - 1]);
            f[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_gf_mul(beta_m_pow, f[i]);
        }
    }

    // Step 3
    radix(f0, f1, f, m_f);

    // Step 4: compute gammas and deltas
    for (uint8_t i = 0; i < m - 1; ++i) {
        gammas[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_gf_mul(betas[i], PQCLEAN_HQC2563CCA2_LEAKTIME_gf_inverse(betas[m - 1]));
        deltas[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_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);

    if (f_coeffs <= 3) { // 3-coefficient polynomial f case: f1 is constant
        w[0] = u[0];
        w[k] = u[0] ^ f1[0];
        for (size_t i = 1; i < k; ++i) {
            w[i] = u[i] ^ PQCLEAN_HQC2563CCA2_LEAKTIME_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 (size_t i = 1; i < k; ++i) {
            w[i] = u[i] ^ PQCLEAN_HQC2563CCA2_LEAKTIME_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>
 * Constants betas, gammas and deltas involved in the algorithm are either hardcoded or precomputed
 * by the subroutine compute_fft_lut(...). <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_HQC2563CCA2_LEAKTIME_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];
    size_t k = 1 << (PARAM_M - 1);
    uint16_t u[1 << (PARAM_M - 1)] = {0};
    uint16_t v[1 << (PARAM_M - 1)] = {0};

    // 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 (size_t i = 0; i < PARAM_M - 1; ++i) {
        deltas[i] = PQCLEAN_HQC2563CCA2_LEAKTIME_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);

    // 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 (size_t i = 1; i < k; ++i) {
        w[i] = u[i] ^ PQCLEAN_HQC2563CCA2_LEAKTIME_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_HQC2563CCA2_LEAKTIME_fft_t_preprocess_bch_codeword(uint16_t *w, const uint8_t *vector) {
    uint16_t r[1 << PARAM_M];
    uint16_t gammas[PARAM_M - 1];
    uint16_t gammas_sums[1 << (PARAM_M - 1)];
    size_t k = 1 << (PARAM_M - 1);

    // Unpack the received word vector into array r
    size_t i;
    for (i = 0; i < VEC_N1_SIZE_BYTES - (PARAM_N1 % 8 != 0); ++i) {
        for (size_t j = 0; j < 8; ++j) {
            r[8 * i + j] = (vector[i] >> j) & 1;
        }
    }

    // Last byte
    for (size_t j = 0; j < PARAM_N1 % 8; ++j) {
        r[8 * i + j] = (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
    w[0] = 0;
    w[k] = -r[0] & 1;
    for (i = 1; i < k; ++i) {
        w[i] = -r[PQCLEAN_HQC2563CCA2_LEAKTIME_gf_log(gammas_sums[i])] & gammas_sums[i];
        w[k + i] = -r[PQCLEAN_HQC2563CCA2_LEAKTIME_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_HQC2563CCA2_LEAKTIME_fft_retrieve_bch_error_poly(uint8_t *error, const uint16_t *w) {
    uint16_t gammas[PARAM_M - 1];
    uint16_t gammas_sums[1 << (PARAM_M - 1)];
    size_t k = 1 << (PARAM_M - 1);
    size_t index = PARAM_GF_MUL_ORDER;

    compute_fft_betas(gammas);
    compute_subset_sums(gammas_sums, gammas, PARAM_M - 1);

    error[0] ^= 1 ^ ((uint16_t) - w[0] >> 15);
    uint8_t bit = 1 ^ ((uint16_t) - w[k] >> 15);
    error[index / 8] ^= bit << (index % 8);

    for (size_t i = 1; i < k; ++i) {
        index = PARAM_GF_MUL_ORDER - PQCLEAN_HQC2563CCA2_LEAKTIME_gf_log(gammas_sums[i]);
        bit = 1 ^ ((uint16_t) - w[i] >> 15);
        error[index / 8] ^= bit << (index % 8);

        index = PARAM_GF_MUL_ORDER - PQCLEAN_HQC2563CCA2_LEAKTIME_gf_log(gammas_sums[i] ^ 1);
        bit = 1 ^ ((uint16_t) - w[k + i] >> 15);
        error[index / 8] ^= bit << (index % 8);
    }
}