/*
 *  Core bignum functions
 *
 *  Copyright The Mbed TLS Contributors
 *  SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
 */

#include "common.h"

#if defined(MBEDTLS_BIGNUM_C)

#include <string.h>

#include "mbedtls/error.h"
#include "mbedtls/platform_util.h"
#include "constant_time_internal.h"

#include "mbedtls/platform.h"

#include "bignum_core.h"
#include "bignum_core_invasive.h"
#include "bn_mul.h"
#include "constant_time_internal.h"

size_t mbedtls_mpi_core_clz(mbedtls_mpi_uint a)
{
#if defined(__has_builtin)
#if (MBEDTLS_MPI_UINT_MAX == UINT_MAX) && __has_builtin(__builtin_clz)
    #define core_clz __builtin_clz
#elif (MBEDTLS_MPI_UINT_MAX == ULONG_MAX) && __has_builtin(__builtin_clzl)
    #define core_clz __builtin_clzl
#elif (MBEDTLS_MPI_UINT_MAX == ULLONG_MAX) && __has_builtin(__builtin_clzll)
    #define core_clz __builtin_clzll
#endif
#endif
#if defined(core_clz)
    return (size_t) core_clz(a);
#else
    size_t j;
    mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);

    for (j = 0; j < biL; j++) {
        if (a & mask) {
            break;
        }

        mask >>= 1;
    }

    return j;
#endif
}

size_t mbedtls_mpi_core_bitlen(const mbedtls_mpi_uint *A, size_t A_limbs)
{
    int i;
    size_t j;

    for (i = ((int) A_limbs) - 1; i >= 0; i--) {
        if (A[i] != 0) {
            j = biL - mbedtls_mpi_core_clz(A[i]);
            return (i * biL) + j;
        }
    }

    return 0;
}

static mbedtls_mpi_uint mpi_bigendian_to_host(mbedtls_mpi_uint a)
{
    if (MBEDTLS_IS_BIG_ENDIAN) {

        return a;
    } else {
#if defined(MBEDTLS_HAVE_INT32)
        return (mbedtls_mpi_uint) MBEDTLS_BSWAP32(a);
#elif defined(MBEDTLS_HAVE_INT64)
        return (mbedtls_mpi_uint) MBEDTLS_BSWAP64(a);
#endif
    }
}

void mbedtls_mpi_core_bigendian_to_host(mbedtls_mpi_uint *A,
                                        size_t A_limbs)
{
    mbedtls_mpi_uint *cur_limb_left;
    mbedtls_mpi_uint *cur_limb_right;
    if (A_limbs == 0) {
        return;
    }

    for (cur_limb_left = A, cur_limb_right = A + (A_limbs - 1);
         cur_limb_left <= cur_limb_right;
         cur_limb_left++, cur_limb_right--) {
        mbedtls_mpi_uint tmp;

        tmp             = mpi_bigendian_to_host(*cur_limb_left);
        *cur_limb_left  = mpi_bigendian_to_host(*cur_limb_right);
        *cur_limb_right = tmp;
    }
}

mbedtls_ct_condition_t mbedtls_mpi_core_uint_le_mpi(mbedtls_mpi_uint min,
                                                    const mbedtls_mpi_uint *A,
                                                    size_t A_limbs)
{

    mbedtls_ct_condition_t min_le_lsl = mbedtls_ct_uint_ge(A[0], min);

    mbedtls_ct_condition_t msll_mask = MBEDTLS_CT_FALSE;
    for (size_t i = 1; i < A_limbs; i++) {
        msll_mask = mbedtls_ct_bool_or(msll_mask, mbedtls_ct_bool(A[i]));
    }

    return mbedtls_ct_bool_or(msll_mask, min_le_lsl);
}

mbedtls_ct_condition_t mbedtls_mpi_core_lt_ct(const mbedtls_mpi_uint *A,
                                              const mbedtls_mpi_uint *B,
                                              size_t limbs)
{
    mbedtls_ct_condition_t ret = MBEDTLS_CT_FALSE, cond = MBEDTLS_CT_FALSE, done = MBEDTLS_CT_FALSE;

    for (size_t i = limbs; i > 0; i--) {

        cond = mbedtls_ct_uint_lt(B[i - 1], A[i - 1]);
        done = mbedtls_ct_bool_or(done, cond);

        cond = mbedtls_ct_uint_lt(A[i - 1], B[i - 1]);
        ret  = mbedtls_ct_bool_or(ret, mbedtls_ct_bool_and(cond, mbedtls_ct_bool_not(done)));
        done = mbedtls_ct_bool_or(done, cond);
    }

    return ret;
}

void mbedtls_mpi_core_cond_assign(mbedtls_mpi_uint *X,
                                  const mbedtls_mpi_uint *A,
                                  size_t limbs,
                                  mbedtls_ct_condition_t assign)
{
    if (X == A) {
        return;
    }

    for (size_t i = 0; i < limbs; i++) {
        X[i] = mbedtls_ct_mpi_uint_if(assign, A[i], X[i]);
    }
}

void mbedtls_mpi_core_cond_swap(mbedtls_mpi_uint *X,
                                mbedtls_mpi_uint *Y,
                                size_t limbs,
                                mbedtls_ct_condition_t swap)
{
    if (X == Y) {
        return;
    }

    for (size_t i = 0; i < limbs; i++) {
        mbedtls_mpi_uint tmp = X[i];
        X[i] = mbedtls_ct_mpi_uint_if(swap, Y[i], X[i]);
        Y[i] = mbedtls_ct_mpi_uint_if(swap, tmp, Y[i]);
    }
}

int mbedtls_mpi_core_read_le(mbedtls_mpi_uint *X,
                             size_t X_limbs,
                             const unsigned char *input,
                             size_t input_length)
{
    const size_t limbs = CHARS_TO_LIMBS(input_length);

    if (X_limbs < limbs) {
        return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
    }

    if (X != NULL) {
        memset(X, 0, X_limbs * ciL);

        for (size_t i = 0; i < input_length; i++) {
            size_t offset = ((i % ciL) << 3);
            X[i / ciL] |= ((mbedtls_mpi_uint) input[i]) << offset;
        }
    }

    return 0;
}

int mbedtls_mpi_core_read_be(mbedtls_mpi_uint *X,
                             size_t X_limbs,
                             const unsigned char *input,
                             size_t input_length)
{
    const size_t limbs = CHARS_TO_LIMBS(input_length);

    if (X_limbs < limbs) {
        return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
    }

    if (X_limbs == 0) {
        return 0;
    }

    memset(X, 0, X_limbs * ciL);

    if (input_length != 0) {
        size_t overhead = (X_limbs * ciL) - input_length;
        unsigned char *Xp = (unsigned char *) X;
        memcpy(Xp + overhead, input, input_length);
    }

    mbedtls_mpi_core_bigendian_to_host(X, X_limbs);

    return 0;
}

int mbedtls_mpi_core_write_le(const mbedtls_mpi_uint *A,
                              size_t A_limbs,
                              unsigned char *output,
                              size_t output_length)
{
    size_t stored_bytes = A_limbs * ciL;
    size_t bytes_to_copy;

    if (stored_bytes < output_length) {
        bytes_to_copy = stored_bytes;
    } else {
        bytes_to_copy = output_length;

        for (size_t i = bytes_to_copy; i < stored_bytes; i++) {
            if (GET_BYTE(A, i) != 0) {
                return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
            }
        }
    }

    for (size_t i = 0; i < bytes_to_copy; i++) {
        output[i] = GET_BYTE(A, i);
    }

    if (stored_bytes < output_length) {

        memset(output + stored_bytes, 0, output_length - stored_bytes);
    }

    return 0;
}

int mbedtls_mpi_core_write_be(const mbedtls_mpi_uint *X,
                              size_t X_limbs,
                              unsigned char *output,
                              size_t output_length)
{
    size_t stored_bytes;
    size_t bytes_to_copy;
    unsigned char *p;

    stored_bytes = X_limbs * ciL;

    if (stored_bytes < output_length) {

        bytes_to_copy = stored_bytes;
        p = output + output_length - stored_bytes;
        memset(output, 0, output_length - stored_bytes);
    } else {

        bytes_to_copy = output_length;
        p = output;
        for (size_t i = bytes_to_copy; i < stored_bytes; i++) {
            if (GET_BYTE(X, i) != 0) {
                return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL;
            }
        }
    }

    for (size_t i = 0; i < bytes_to_copy; i++) {
        p[bytes_to_copy - i - 1] = GET_BYTE(X, i);
    }

    return 0;
}

void mbedtls_mpi_core_shift_r(mbedtls_mpi_uint *X, size_t limbs,
                              size_t count)
{
    size_t i, v0, v1;
    mbedtls_mpi_uint r0 = 0, r1;

    v0 = count /  biL;
    v1 = count & (biL - 1);

    if (v0 > limbs || (v0 == limbs && v1 > 0)) {
        memset(X, 0, limbs * ciL);
        return;
    }

    if (v0 > 0) {
        for (i = 0; i < limbs - v0; i++) {
            X[i] = X[i + v0];
        }

        for (; i < limbs; i++) {
            X[i] = 0;
        }
    }

    if (v1 > 0) {
        for (i = limbs; i > 0; i--) {
            r1 = X[i - 1] << (biL - v1);
            X[i - 1] >>= v1;
            X[i - 1] |= r0;
            r0 = r1;
        }
    }
}

void mbedtls_mpi_core_shift_l(mbedtls_mpi_uint *X, size_t limbs,
                              size_t count)
{
    size_t i, v0, v1;
    mbedtls_mpi_uint r0 = 0, r1;

    v0 = count / (biL);
    v1 = count & (biL - 1);

    if (v0 > 0) {
        for (i = limbs; i > v0; i--) {
            X[i - 1] = X[i - v0 - 1];
        }

        for (; i > 0; i--) {
            X[i - 1] = 0;
        }
    }

    if (v1 > 0) {
        for (i = v0; i < limbs; i++) {
            r1 = X[i] >> (biL - v1);
            X[i] <<= v1;
            X[i] |= r0;
            r0 = r1;
        }
    }
}

mbedtls_mpi_uint mbedtls_mpi_core_add(mbedtls_mpi_uint *X,
                                      const mbedtls_mpi_uint *A,
                                      const mbedtls_mpi_uint *B,
                                      size_t limbs)
{
    mbedtls_mpi_uint c = 0;

    for (size_t i = 0; i < limbs; i++) {
        mbedtls_mpi_uint t = c + A[i];
        c = (t < A[i]);
        t += B[i];
        c += (t < B[i]);
        X[i] = t;
    }

    return c;
}

mbedtls_mpi_uint mbedtls_mpi_core_add_if(mbedtls_mpi_uint *X,
                                         const mbedtls_mpi_uint *A,
                                         size_t limbs,
                                         unsigned cond)
{
    mbedtls_mpi_uint c = 0;

    mbedtls_ct_condition_t do_add = mbedtls_ct_bool(cond);

    for (size_t i = 0; i < limbs; i++) {
        mbedtls_mpi_uint add = mbedtls_ct_mpi_uint_if_else_0(do_add, A[i]);
        mbedtls_mpi_uint t = c + X[i];
        c = (t < X[i]);
        t += add;
        c += (t < add);
        X[i] = t;
    }

    return c;
}

mbedtls_mpi_uint mbedtls_mpi_core_sub(mbedtls_mpi_uint *X,
                                      const mbedtls_mpi_uint *A,
                                      const mbedtls_mpi_uint *B,
                                      size_t limbs)
{
    mbedtls_mpi_uint c = 0;

    for (size_t i = 0; i < limbs; i++) {
        mbedtls_mpi_uint z = (A[i] < c);
        mbedtls_mpi_uint t = A[i] - c;
        c = (t < B[i]) + z;
        X[i] = t - B[i];
    }

    return c;
}

mbedtls_mpi_uint mbedtls_mpi_core_mla(mbedtls_mpi_uint *d, size_t d_len,
                                      const mbedtls_mpi_uint *s, size_t s_len,
                                      mbedtls_mpi_uint b)
{
    mbedtls_mpi_uint c = 0;

    if (d_len < s_len) {
        s_len = d_len;
    }
    size_t excess_len = d_len - s_len;
    size_t steps_x8 = s_len / 8;
    size_t steps_x1 = s_len & 7;

    while (steps_x8--) {
        MULADDC_X8_INIT
        MULADDC_X8_CORE
            MULADDC_X8_STOP
    }

    while (steps_x1--) {
        MULADDC_X1_INIT
        MULADDC_X1_CORE
            MULADDC_X1_STOP
    }

    while (excess_len--) {
        *d += c;
        c = (*d < c);
        d++;
    }

    return c;
}

void mbedtls_mpi_core_mul(mbedtls_mpi_uint *X,
                          const mbedtls_mpi_uint *A, size_t A_limbs,
                          const mbedtls_mpi_uint *B, size_t B_limbs)
{
    memset(X, 0, (A_limbs + B_limbs) * ciL);

    for (size_t i = 0; i < B_limbs; i++) {
        (void) mbedtls_mpi_core_mla(X + i, A_limbs + 1, A, A_limbs, B[i]);
    }
}

mbedtls_mpi_uint mbedtls_mpi_core_montmul_init(const mbedtls_mpi_uint *N)
{
    mbedtls_mpi_uint x = N[0];

    x += ((N[0] + 2) & 4) << 1;

    for (unsigned int i = biL; i >= 8; i /= 2) {
        x *= (2 - (N[0] * x));
    }

    return ~x + 1;
}

void mbedtls_mpi_core_montmul(mbedtls_mpi_uint *X,
                              const mbedtls_mpi_uint *A,
                              const mbedtls_mpi_uint *B,
                              size_t B_limbs,
                              const mbedtls_mpi_uint *N,
                              size_t AN_limbs,
                              mbedtls_mpi_uint mm,
                              mbedtls_mpi_uint *T)
{
    memset(T, 0, (2 * AN_limbs + 1) * ciL);

    for (size_t i = 0; i < AN_limbs; i++) {

        mbedtls_mpi_uint u0 = A[i];
        mbedtls_mpi_uint u1 = (T[0] + u0 * B[0]) * mm;

        (void) mbedtls_mpi_core_mla(T, AN_limbs + 2, B, B_limbs, u0);
        (void) mbedtls_mpi_core_mla(T, AN_limbs + 2, N, AN_limbs, u1);

        T++;
    }

    mbedtls_mpi_uint carry  = T[AN_limbs];
    mbedtls_mpi_uint borrow = mbedtls_mpi_core_sub(X, T, N, AN_limbs);

    mbedtls_ct_memcpy_if(mbedtls_ct_bool(carry ^ borrow),
                         (unsigned char *) X,
                         (unsigned char *) T,
                         NULL,
                         AN_limbs * sizeof(mbedtls_mpi_uint));
}

int mbedtls_mpi_core_get_mont_r2_unsafe(mbedtls_mpi *X,
                                        const mbedtls_mpi *N)
{
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;

    MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 1));
    MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(X, N->n * 2 * biL));
    MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(X, X, N));
    MBEDTLS_MPI_CHK(mbedtls_mpi_shrink(X, N->n));

cleanup:
    return ret;
}

MBEDTLS_STATIC_TESTABLE
void mbedtls_mpi_core_ct_uint_table_lookup(mbedtls_mpi_uint *dest,
                                           const mbedtls_mpi_uint *table,
                                           size_t limbs,
                                           size_t count,
                                           size_t index)
{
    for (size_t i = 0; i < count; i++, table += limbs) {
        mbedtls_ct_condition_t assign = mbedtls_ct_uint_eq(i, index);
        mbedtls_mpi_core_cond_assign(dest, table, limbs, assign);
    }
}

int mbedtls_mpi_core_fill_random(
    mbedtls_mpi_uint *X, size_t X_limbs,
    size_t n_bytes,
    int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
    const size_t limbs = CHARS_TO_LIMBS(n_bytes);
    const size_t overhead = (limbs * ciL) - n_bytes;

    if (X_limbs < limbs) {
        return MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
    }

    memset(X, 0, overhead);
    memset((unsigned char *) X + limbs * ciL, 0, (X_limbs - limbs) * ciL);
    MBEDTLS_MPI_CHK(f_rng(p_rng, (unsigned char *) X + overhead, n_bytes));
    mbedtls_mpi_core_bigendian_to_host(X, limbs);

cleanup:
    return ret;
}

int mbedtls_mpi_core_random(mbedtls_mpi_uint *X,
                            mbedtls_mpi_uint min,
                            const mbedtls_mpi_uint *N,
                            size_t limbs,
                            int (*f_rng)(void *, unsigned char *, size_t),
                            void *p_rng)
{
    mbedtls_ct_condition_t ge_lower = MBEDTLS_CT_TRUE, lt_upper = MBEDTLS_CT_FALSE;
    size_t n_bits = mbedtls_mpi_core_bitlen(N, limbs);
    size_t n_bytes = (n_bits + 7) / 8;
    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;

    int count = (n_bytes > 4 ? 30 : 250);

    do {
        MBEDTLS_MPI_CHK(mbedtls_mpi_core_fill_random(X, limbs,
                                                     n_bytes,
                                                     f_rng, p_rng));
        mbedtls_mpi_core_shift_r(X, limbs, 8 * n_bytes - n_bits);

        if (--count == 0) {
            ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
            goto cleanup;
        }

        ge_lower = mbedtls_mpi_core_uint_le_mpi(min, X, limbs);
        lt_upper = mbedtls_mpi_core_lt_ct(X, N, limbs);
    } while (mbedtls_ct_bool_and(ge_lower, lt_upper) == MBEDTLS_CT_FALSE);

cleanup:
    return ret;
}

static size_t exp_mod_get_window_size(size_t Ebits)
{
#if MBEDTLS_MPI_WINDOW_SIZE >= 6
    return (Ebits > 671) ? 6 : (Ebits > 239) ? 5 : (Ebits >  79) ? 4 : 1;
#elif MBEDTLS_MPI_WINDOW_SIZE == 5
    return (Ebits > 239) ? 5 : (Ebits >  79) ? 4 : 1;
#elif MBEDTLS_MPI_WINDOW_SIZE > 1
    return (Ebits >  79) ? MBEDTLS_MPI_WINDOW_SIZE : 1;
#else
    (void) Ebits;
    return 1;
#endif
}

size_t mbedtls_mpi_core_exp_mod_working_limbs(size_t AN_limbs, size_t E_limbs)
{
    const size_t wsize = exp_mod_get_window_size(E_limbs * biL);
    const size_t welem = ((size_t) 1) << wsize;

    const size_t table_limbs   = welem * AN_limbs;
    const size_t select_limbs  = AN_limbs;
    const size_t temp_limbs    = 2 * AN_limbs + 1;

    return table_limbs + select_limbs + temp_limbs;
}

static void exp_mod_precompute_window(const mbedtls_mpi_uint *A,
                                      const mbedtls_mpi_uint *N,
                                      size_t AN_limbs,
                                      mbedtls_mpi_uint mm,
                                      const mbedtls_mpi_uint *RR,
                                      size_t welem,
                                      mbedtls_mpi_uint *Wtable,
                                      mbedtls_mpi_uint *temp)
{

    memset(Wtable, 0, AN_limbs * ciL);
    Wtable[0] = 1;
    mbedtls_mpi_core_montmul(Wtable, Wtable, RR, AN_limbs, N, AN_limbs, mm, temp);

    mbedtls_mpi_uint *W1 = Wtable + AN_limbs;
    memcpy(W1, A, AN_limbs * ciL);

    mbedtls_mpi_uint *Wprev = W1;
    for (size_t i = 2; i < welem; i++) {
        mbedtls_mpi_uint *Wcur = Wprev + AN_limbs;
        mbedtls_mpi_core_montmul(Wcur, Wprev, W1, AN_limbs, N, AN_limbs, mm, temp);
        Wprev = Wcur;
    }
}

#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
void (*mbedtls_safe_codepath_hook)(void) = NULL;
void (*mbedtls_unsafe_codepath_hook)(void) = NULL;
#endif

static inline void exp_mod_calc_first_bit_optionally_safe(const mbedtls_mpi_uint *E,
                                                          size_t E_limbs,
                                                          int E_public,
                                                          size_t *E_limb_index,
                                                          size_t *E_bit_index)
{
    if (E_public == MBEDTLS_MPI_IS_PUBLIC) {

        size_t E_bits = mbedtls_mpi_core_bitlen(E, E_limbs);
        if (E_bits == 0) {

            E_bits = 1;
        }

        *E_limb_index = E_bits / biL;
        *E_bit_index = E_bits % biL;

#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
        if (mbedtls_unsafe_codepath_hook != NULL) {
            mbedtls_unsafe_codepath_hook();
        }
#endif
    } else {

        *E_limb_index = E_limbs;
        *E_bit_index = 0;
#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
        if (mbedtls_safe_codepath_hook != NULL) {
            mbedtls_safe_codepath_hook();
        }
#endif
    }
}

static inline void exp_mod_table_lookup_optionally_safe(mbedtls_mpi_uint *Wselect,
                                                        mbedtls_mpi_uint *Wtable,
                                                        size_t AN_limbs, size_t welem,
                                                        mbedtls_mpi_uint window,
                                                        int window_public)
{
    if (window_public == MBEDTLS_MPI_IS_PUBLIC) {
        memcpy(Wselect, Wtable + window * AN_limbs, AN_limbs * ciL);
#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
        if (mbedtls_unsafe_codepath_hook != NULL) {
            mbedtls_unsafe_codepath_hook();
        }
#endif
    } else {

        mbedtls_mpi_core_ct_uint_table_lookup(Wselect, Wtable,
                                              AN_limbs, welem, window);
#if defined(MBEDTLS_TEST_HOOKS) && !defined(MBEDTLS_THREADING_C)
        if (mbedtls_safe_codepath_hook != NULL) {
            mbedtls_safe_codepath_hook();
        }
#endif
    }
}

static void mbedtls_mpi_core_exp_mod_optionally_safe(mbedtls_mpi_uint *X,
                                                     const mbedtls_mpi_uint *A,
                                                     const mbedtls_mpi_uint *N,
                                                     size_t AN_limbs,
                                                     const mbedtls_mpi_uint *E,
                                                     size_t E_limbs,
                                                     int E_public,
                                                     const mbedtls_mpi_uint *RR,
                                                     mbedtls_mpi_uint *T)
{

    size_t E_limb_index = E_limbs;
    size_t E_bit_index = 0;
    exp_mod_calc_first_bit_optionally_safe(E, E_limbs, E_public,
                                           &E_limb_index, &E_bit_index);

    const size_t wsize = exp_mod_get_window_size(E_limb_index * biL);
    const size_t welem = ((size_t) 1) << wsize;

    const size_t table_limbs  = welem * AN_limbs;
    const size_t select_limbs = AN_limbs;

    mbedtls_mpi_uint *const Wtable  = T;
    mbedtls_mpi_uint *const Wselect = Wtable  +  table_limbs;
    mbedtls_mpi_uint *const temp    = Wselect + select_limbs;

    const mbedtls_mpi_uint mm = mbedtls_mpi_core_montmul_init(N);

    exp_mod_precompute_window(A, N, AN_limbs,
                              mm, RR,
                              welem, Wtable, temp);

    memcpy(X, Wtable, AN_limbs * ciL);

    size_t window_bits = 0;
    mbedtls_mpi_uint window = 0;

    do {

        mbedtls_mpi_core_montmul(X, X, X, AN_limbs, N, AN_limbs, mm, temp);

        if (E_bit_index == 0) {
            --E_limb_index;
            E_bit_index = biL - 1;
        } else {
            --E_bit_index;
        }

        ++window_bits;
        window <<= 1;
        window |= (E[E_limb_index] >> E_bit_index) & 1;

        if (window_bits == wsize ||
            (E_bit_index == 0 && E_limb_index == 0)) {

            exp_mod_table_lookup_optionally_safe(Wselect, Wtable, AN_limbs, welem,
                                                 window, E_public);

            mbedtls_mpi_core_montmul(X, X, Wselect, AN_limbs, N, AN_limbs, mm,
                                     temp);
            window = 0;
            window_bits = 0;
        }
    } while (!(E_bit_index == 0 && E_limb_index == 0));
}

void mbedtls_mpi_core_exp_mod(mbedtls_mpi_uint *X,
                              const mbedtls_mpi_uint *A,
                              const mbedtls_mpi_uint *N, size_t AN_limbs,
                              const mbedtls_mpi_uint *E, size_t E_limbs,
                              const mbedtls_mpi_uint *RR,
                              mbedtls_mpi_uint *T)
{
    mbedtls_mpi_core_exp_mod_optionally_safe(X,
                                             A,
                                             N,
                                             AN_limbs,
                                             E,
                                             E_limbs,
                                             MBEDTLS_MPI_IS_SECRET,
                                             RR,
                                             T);
}

void mbedtls_mpi_core_exp_mod_unsafe(mbedtls_mpi_uint *X,
                                     const mbedtls_mpi_uint *A,
                                     const mbedtls_mpi_uint *N, size_t AN_limbs,
                                     const mbedtls_mpi_uint *E, size_t E_limbs,
                                     const mbedtls_mpi_uint *RR,
                                     mbedtls_mpi_uint *T)
{
    mbedtls_mpi_core_exp_mod_optionally_safe(X,
                                             A,
                                             N,
                                             AN_limbs,
                                             E,
                                             E_limbs,
                                             MBEDTLS_MPI_IS_PUBLIC,
                                             RR,
                                             T);
}

mbedtls_mpi_uint mbedtls_mpi_core_sub_int(mbedtls_mpi_uint *X,
                                          const mbedtls_mpi_uint *A,
                                          mbedtls_mpi_uint c,
                                          size_t limbs)
{
    for (size_t i = 0; i < limbs; i++) {
        mbedtls_mpi_uint s = A[i];
        mbedtls_mpi_uint t = s - c;
        c = (t > s);
        X[i] = t;
    }

    return c;
}

mbedtls_ct_condition_t mbedtls_mpi_core_check_zero_ct(const mbedtls_mpi_uint *A,
                                                      size_t limbs)
{
    volatile const mbedtls_mpi_uint *force_read_A = A;
    mbedtls_mpi_uint bits = 0;

    for (size_t i = 0; i < limbs; i++) {
        bits |= force_read_A[i];
    }

    return mbedtls_ct_bool(bits);
}

void mbedtls_mpi_core_to_mont_rep(mbedtls_mpi_uint *X,
                                  const mbedtls_mpi_uint *A,
                                  const mbedtls_mpi_uint *N,
                                  size_t AN_limbs,
                                  mbedtls_mpi_uint mm,
                                  const mbedtls_mpi_uint *rr,
                                  mbedtls_mpi_uint *T)
{
    mbedtls_mpi_core_montmul(X, A, rr, AN_limbs, N, AN_limbs, mm, T);
}

void mbedtls_mpi_core_from_mont_rep(mbedtls_mpi_uint *X,
                                    const mbedtls_mpi_uint *A,
                                    const mbedtls_mpi_uint *N,
                                    size_t AN_limbs,
                                    mbedtls_mpi_uint mm,
                                    mbedtls_mpi_uint *T)
{
    const mbedtls_mpi_uint Rinv = 1;

    mbedtls_mpi_core_montmul(X, A, &Rinv, 1, N, AN_limbs, mm, T);
}

static void mpi_core_sub_mod(mbedtls_mpi_uint *X,
                             const mbedtls_mpi_uint *A,
                             const mbedtls_mpi_uint *B,
                             const mbedtls_mpi_uint *N,
                             size_t limbs)
{
    mbedtls_mpi_uint c = mbedtls_mpi_core_sub(X, A, B, limbs);
    (void) mbedtls_mpi_core_add_if(X, N, limbs, (unsigned) c);
}

MBEDTLS_STATIC_TESTABLE
void mbedtls_mpi_core_div2_mod_odd(mbedtls_mpi_uint *X,
                                   const mbedtls_mpi_uint *N,
                                   size_t limbs)
{

    unsigned odd = (unsigned) X[0] & 1;
    mbedtls_mpi_uint c = mbedtls_mpi_core_add_if(X, N, limbs, odd);
    mbedtls_mpi_core_shift_r(X, limbs, 1);
    X[limbs - 1] |= c << (biL - 1);
}

void mbedtls_mpi_core_gcd_modinv_odd(mbedtls_mpi_uint *G,
                                     mbedtls_mpi_uint *I,
                                     const mbedtls_mpi_uint *A,
                                     size_t A_limbs,
                                     const mbedtls_mpi_uint *N,
                                     size_t N_limbs,
                                     mbedtls_mpi_uint *T)
{

    mbedtls_mpi_uint *u = T + 0 * N_limbs;
    mbedtls_mpi_uint *v = G;

    mbedtls_mpi_uint *d = T + 1 * N_limbs;

    mbedtls_mpi_uint *t1 = T + 2 * N_limbs;
    mbedtls_mpi_uint *t2 = T + 3 * N_limbs;

    mbedtls_mpi_uint *q = I;
    mbedtls_mpi_uint *r = I != NULL ? T + 4 * N_limbs : NULL;

    if (A_limbs > N_limbs) {

        A_limbs = N_limbs;
    }
    memcpy(u, A, A_limbs * ciL);
    memset((char *) u + A_limbs * ciL, 0, (N_limbs - A_limbs) * ciL);

    if (v != N) {
        memcpy(v, N, N_limbs * ciL);
    }

    if (I != NULL) {
        memset(q, 0, N_limbs * ciL);

        memset(r, 0, N_limbs * ciL);
        r[0] = 1;
    }

    for (size_t i = 0; i < (A_limbs + N_limbs) * biL; i++) {

        mbedtls_ct_condition_t u_odd = mbedtls_ct_bool(u[0] & 1);
        mbedtls_ct_condition_t v_odd = mbedtls_ct_bool(v[0] & 1);

        mbedtls_ct_condition_t u_odd_v_odd = mbedtls_ct_bool_and(u_odd, v_odd);
        mbedtls_ct_condition_t v_even = mbedtls_ct_bool_not(v_odd);
        mbedtls_ct_condition_t u_odd_v_even = mbedtls_ct_bool_and(u_odd, v_even);

        (void) mbedtls_mpi_core_sub(d, v, u, N_limbs);

        memcpy(t1, d, N_limbs * ciL);
        mbedtls_mpi_core_cond_assign(t1, u, N_limbs, u_odd_v_odd);

        memcpy(t2, u, N_limbs * ciL);
        mbedtls_mpi_core_cond_assign(t2, v, N_limbs, u_odd_v_even);
        mbedtls_mpi_core_cond_assign(t2, d, N_limbs, u_odd_v_odd);

        mbedtls_mpi_core_shift_r(t2, N_limbs, 1);

        memcpy(u, t1, N_limbs * ciL);
        memcpy(v, t2, N_limbs * ciL);
        mbedtls_ct_condition_t swap = mbedtls_mpi_core_lt_ct(v, u, N_limbs);
        mbedtls_mpi_core_cond_swap(u, v, N_limbs, swap);

        if (I != NULL) {

            mpi_core_sub_mod(d, q, r, N, N_limbs);

            memcpy(t1, d, N_limbs * ciL);
            mbedtls_mpi_core_cond_assign(t1, r, N_limbs, u_odd_v_odd);

            memcpy(t2, r, N_limbs * ciL);
            mbedtls_mpi_core_cond_assign(t2, q, N_limbs, u_odd_v_even);
            mbedtls_mpi_core_cond_assign(t2, d, N_limbs, u_odd_v_odd);

            mbedtls_mpi_core_div2_mod_odd(t2, N, N_limbs);

            memcpy(r, t1, N_limbs * ciL);
            memcpy(q, t2, N_limbs * ciL);
            mbedtls_mpi_core_cond_swap(r, q, N_limbs, swap);
        }
    }

}

#endif
