path: root/security/nss/lib/freebl/mpi/mpmontg.c

/* This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

/* This file implements moduluar exponentiation using Montgomery's
 * method for modular reduction.  This file implements the method
 * described as "Improvement 2" in the paper "A Cryptogrpahic Library for
 * the Motorola DSP56000" by Stephen R. Dusse' and Burton S. Kaliski Jr.
 * published in "Advances in Cryptology: Proceedings of EUROCRYPT '90"
 * "Lecture Notes in Computer Science" volume 473, 1991, pg 230-244,
 * published by Springer Verlag.
 */

#define MP_USING_CACHE_SAFE_MOD_EXP 1
#include <string.h>
#include "mpi-priv.h"
#include "mplogic.h"
#include "mpprime.h"
#ifdef MP_USING_MONT_MULF
#include "montmulf.h"
#endif
#include <stddef.h> /* ptrdiff_t */
#include <assert.h>

#define STATIC

#define MAX_ODD_INTS 32 /* 2 ** (WINDOW_BITS - 1) */

/*! computes T = REDC(T), 2^b == R
    \param T < RN
*/
mp_err
s_mp_redc(mp_int *T, mp_mont_modulus *mmm)
{
    mp_err res;
    mp_size i;

    i = (MP_USED(&mmm->N) << 1) + 1;
    MP_CHECKOK(s_mp_pad(T, i));
    for (i = 0; i < MP_USED(&mmm->N); ++i) {
        mp_digit m_i = MP_DIGIT(T, i) * mmm->n0prime;
        /* T += N * m_i * (MP_RADIX ** i); */
        s_mp_mul_d_add_offset(&mmm->N, m_i, T, i);
    }
    s_mp_clamp(T);

    /* T /= R */
    s_mp_rshd(T, MP_USED(&mmm->N));

    if ((res = s_mp_cmp(T, &mmm->N)) >= 0) {
        /* T = T - N */
        MP_CHECKOK(s_mp_sub(T, &mmm->N));
#ifdef DEBUG
        if ((res = mp_cmp(T, &mmm->N)) >= 0) {
            res = MP_UNDEF;
            goto CLEANUP;
        }
#endif
    }
    res = MP_OKAY;
CLEANUP:
    return res;
}

#if !defined(MP_MONT_USE_MP_MUL)

/*! c <- REDC( a * b ) mod N
    \param a < N  i.e. "reduced"
    \param b < N  i.e. "reduced"
    \param mmm modulus N and n0' of N
*/
mp_err
s_mp_mul_mont(const mp_int *a, const mp_int *b, mp_int *c,
              mp_mont_modulus *mmm)
{
    mp_digit *pb;
    mp_digit m_i;
    mp_err res;
    mp_size ib; /* "index b": index of current digit of B */
    mp_size useda, usedb;

    ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);

    if (MP_USED(a) < MP_USED(b)) {
        const mp_int *xch = b; /* switch a and b, to do fewer outer loops */
        b = a;
        a = xch;
    }

    MP_USED(c) = 1;
    MP_DIGIT(c, 0) = 0;
    ib = (MP_USED(&mmm->N) << 1) + 1;
    if ((res = s_mp_pad(c, ib)) != MP_OKAY)
        goto CLEANUP;

    useda = MP_USED(a);
    pb = MP_DIGITS(b);
    s_mpv_mul_d(MP_DIGITS(a), useda, *pb++, MP_DIGITS(c));
    s_mp_setz(MP_DIGITS(c) + useda + 1, ib - (useda + 1));
    m_i = MP_DIGIT(c, 0) * mmm->n0prime;
    s_mp_mul_d_add_offset(&mmm->N, m_i, c, 0);

    /* Outer loop:  Digits of b */
    usedb = MP_USED(b);
    for (ib = 1; ib < usedb; ib++) {
        mp_digit b_i = *pb++;

        /* Inner product:  Digits of a */
        if (b_i)
            s_mpv_mul_d_add_prop(MP_DIGITS(a), useda, b_i, MP_DIGITS(c) + ib);
        m_i = MP_DIGIT(c, ib) * mmm->n0prime;
        s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
    }
    if (usedb < MP_USED(&mmm->N)) {
        for (usedb = MP_USED(&mmm->N); ib < usedb; ++ib) {
            m_i = MP_DIGIT(c, ib) * mmm->n0prime;
            s_mp_mul_d_add_offset(&mmm->N, m_i, c, ib);
        }
    }
    s_mp_clamp(c);
    s_mp_rshd(c, MP_USED(&mmm->N)); /* c /= R */
    if (s_mp_cmp(c, &mmm->N) >= 0) {
        MP_CHECKOK(s_mp_sub(c, &mmm->N));
    }
    res = MP_OKAY;

CLEANUP:
    return res;
}
#endif

mp_err
mp_to_mont(const mp_int *x, const mp_int *N, mp_int *xMont)
{
    mp_err res;

    /* xMont = x * R mod N   where  N is modulus */
    if (x != xMont) {
        MP_CHECKOK(mp_copy(x, xMont));
    }
    MP_CHECKOK(s_mp_lshd(xMont, MP_USED(N))); /* xMont = x << b */
    MP_CHECKOK(mp_div(xMont, N, 0, xMont));   /*         mod N */
CLEANUP:
    return res;
}

mp_digit
mp_calculate_mont_n0i(const mp_int *N)
{
    return 0 - s_mp_invmod_radix(MP_DIGIT(N, 0));
}

#ifdef MP_USING_MONT_MULF

/* the floating point multiply is already cache safe,
 * don't turn on cache safe unless we specifically
 * force it */
#ifndef MP_FORCE_CACHE_SAFE
#undef MP_USING_CACHE_SAFE_MOD_EXP
#endif

unsigned int mp_using_mont_mulf = 1;

/* computes montgomery square of the integer in mResult */
#define SQR                                              \
    conv_i32_to_d32_and_d16(dm1, d16Tmp, mResult, nLen); \
    mont_mulf_noconv(mResult, dm1, d16Tmp,               \
                     dTmp, dn, MP_DIGITS(modulus), nLen, dn0)

/* computes montgomery product of x and the integer in mResult */
#define MUL(x)                                   \
    conv_i32_to_d32(dm1, mResult, nLen);         \
    mont_mulf_noconv(mResult, dm1, oddPowers[x], \
                     dTmp, dn, MP_DIGITS(modulus), nLen, dn0)

/* Do modular exponentiation using floating point multiply code. */
mp_err
mp_exptmod_f(const mp_int *montBase,
             const mp_int *exponent,
             const mp_int *modulus,
             mp_int *result,
             mp_mont_modulus *mmm,
             int nLen,
             mp_size bits_in_exponent,
             mp_size window_bits,
             mp_size odd_ints)
{
    mp_digit *mResult;
    double *dBuf = 0, *dm1, *dn, *dSqr, *d16Tmp, *dTmp;
    double dn0;
    mp_size i;
    mp_err res;
    int expOff;
    int dSize = 0, oddPowSize, dTmpSize;
    mp_int accum1;
    double *oddPowers[MAX_ODD_INTS];

    /* function for computing n0prime only works if n0 is odd */

    MP_DIGITS(&accum1) = 0;

    for (i = 0; i < MAX_ODD_INTS; ++i)
        oddPowers[i] = 0;

    MP_CHECKOK(mp_init_size(&accum1, 3 * nLen + 2));

    mp_set(&accum1, 1);
    MP_CHECKOK(mp_to_mont(&accum1, &(mmm->N), &accum1));
    MP_CHECKOK(s_mp_pad(&accum1, nLen));

    oddPowSize = 2 * nLen + 1;
    dTmpSize = 2 * oddPowSize;
    dSize = sizeof(double) * (nLen * 4 + 1 +
                              ((odd_ints + 1) * oddPowSize) + dTmpSize);
    dBuf = malloc(dSize);
    if (!dBuf) {
        res = MP_MEM;
        goto CLEANUP;
    }
    dm1 = dBuf;           /* array of d32 */
    dn = dBuf + nLen;     /* array of d32 */
    dSqr = dn + nLen;     /* array of d32 */
    d16Tmp = dSqr + nLen; /* array of d16 */
    dTmp = d16Tmp + oddPowSize;

    for (i = 0; i < odd_ints; ++i) {
        oddPowers[i] = dTmp;
        dTmp += oddPowSize;
    }
    mResult = (mp_digit *)(dTmp + dTmpSize); /* size is nLen + 1 */

    /* Make dn and dn0 */
    conv_i32_to_d32(dn, MP_DIGITS(modulus), nLen);
    dn0 = (double)(mmm->n0prime & 0xffff);

    /* Make dSqr */
    conv_i32_to_d32_and_d16(dm1, oddPowers[0], MP_DIGITS(montBase), nLen);
    mont_mulf_noconv(mResult, dm1, oddPowers[0],
                     dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
    conv_i32_to_d32(dSqr, mResult, nLen);

    for (i = 1; i < odd_ints; ++i) {
        mont_mulf_noconv(mResult, dSqr, oddPowers[i - 1],
                         dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
        conv_i32_to_d16(oddPowers[i], mResult, nLen);
    }

    s_mp_copy(MP_DIGITS(&accum1), mResult, nLen); /* from, to, len */

    for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
        mp_size smallExp;
        MP_CHECKOK(mpl_get_bits(exponent, expOff, window_bits));
        smallExp = (mp_size)res;

        if (window_bits == 1) {
            if (!smallExp) {
                SQR;
            } else if (smallExp & 1) {
                SQR;
                MUL(0);
            } else {
                abort();
            }
        } else if (window_bits == 4) {
            if (!smallExp) {
                SQR;
                SQR;
                SQR;
                SQR;
            } else if (smallExp & 1) {
                SQR;
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 2);
            } else if (smallExp & 2) {
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 4);
                SQR;
            } else if (smallExp & 4) {
                SQR;
                SQR;
                MUL(smallExp / 8);
                SQR;
                SQR;
            } else if (smallExp & 8) {
                SQR;
                MUL(smallExp / 16);
                SQR;
                SQR;
                SQR;
            } else {
                abort();
            }
        } else if (window_bits == 5) {
            if (!smallExp) {
                SQR;
                SQR;
                SQR;
                SQR;
                SQR;
            } else if (smallExp & 1) {
                SQR;
                SQR;
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 2);
            } else if (smallExp & 2) {
                SQR;
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 4);
                SQR;
            } else if (smallExp & 4) {
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 8);
                SQR;
                SQR;
            } else if (smallExp & 8) {
                SQR;
                SQR;
                MUL(smallExp / 16);
                SQR;
                SQR;
                SQR;
            } else if (smallExp & 0x10) {
                SQR;
                MUL(smallExp / 32);
                SQR;
                SQR;
                SQR;
                SQR;
            } else {
                abort();
            }
        } else if (window_bits == 6) {
            if (!smallExp) {
                SQR;
                SQR;
                SQR;
                SQR;
                SQR;
                SQR;
            } else if (smallExp & 1) {
                SQR;
                SQR;
                SQR;
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 2);
            } else if (smallExp & 2) {
                SQR;
                SQR;
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 4);
                SQR;
            } else if (smallExp & 4) {
                SQR;
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 8);
                SQR;
                SQR;
            } else if (smallExp & 8) {
                SQR;
                SQR;
                SQR;
                MUL(smallExp / 16);
                SQR;
                SQR;
                SQR;
            } else if (smallExp & 0x10) {
                SQR;
                SQR;
                MUL(smallExp / 32);
                SQR;
                SQR;
                SQR;
                SQR;
            } else if (smallExp & 0x20) {
                SQR;
                MUL(smallExp / 64);
                SQR;
                SQR;
                SQR;
                SQR;
                SQR;
            } else {
                abort();
            }
        } else {
            abort();
        }
    }

    s_mp_copy(mResult, MP_DIGITS(&accum1), nLen); /* from, to, len */

    res = s_mp_redc(&accum1, mmm);
    mp_exch(&accum1, result);

CLEANUP:
    mp_clear(&accum1);
    if (dBuf) {
        if (dSize)
            memset(dBuf, 0, dSize);
        free(dBuf);
    }

    return res;
}
#undef SQR
#undef MUL
#endif

#define SQR(a, b)             \
    MP_CHECKOK(mp_sqr(a, b)); \
    MP_CHECKOK(s_mp_redc(b, mmm))

#if defined(MP_MONT_USE_MP_MUL)
#define MUL(x, a, b)                           \
    MP_CHECKOK(mp_mul(a, oddPowers + (x), b)); \
    MP_CHECKOK(s_mp_redc(b, mmm))
#else
#define MUL(x, a, b) \
    MP_CHECKOK(s_mp_mul_mont(a, oddPowers + (x), b, mmm))
#endif

#define SWAPPA  \
    ptmp = pa1; \
    pa1 = pa2;  \
    pa2 = ptmp

/* Do modular exponentiation using integer multiply code. */
mp_err
mp_exptmod_i(const mp_int *montBase,
             const mp_int *exponent,
             const mp_int *modulus,
             mp_int *result,
             mp_mont_modulus *mmm,
             int nLen,
             mp_size bits_in_exponent,
             mp_size window_bits,
             mp_size odd_ints)
{
    mp_int *pa1, *pa2, *ptmp;
    mp_size i;
    mp_err res;
    int expOff;
    mp_int accum1, accum2, power2, oddPowers[MAX_ODD_INTS];

    /* power2 = base ** 2; oddPowers[i] = base ** (2*i + 1); */
    /* oddPowers[i] = base ** (2*i + 1); */

    MP_DIGITS(&accum1) = 0;
    MP_DIGITS(&accum2) = 0;
    MP_DIGITS(&power2) = 0;
    for (i = 0; i < MAX_ODD_INTS; ++i) {
        MP_DIGITS(oddPowers + i) = 0;
    }

    MP_CHECKOK(mp_init_size(&accum1, 3 * nLen + 2));
    MP_CHECKOK(mp_init_size(&accum2, 3 * nLen + 2));

    MP_CHECKOK(mp_init_copy(&oddPowers[0], montBase));

    MP_CHECKOK(mp_init_size(&power2, nLen + 2 * MP_USED(montBase) + 2));
    MP_CHECKOK(mp_sqr(montBase, &power2)); /* power2 = montBase ** 2 */
    MP_CHECKOK(s_mp_redc(&power2, mmm));

    for (i = 1; i < odd_ints; ++i) {
        MP_CHECKOK(mp_init_size(oddPowers + i, nLen + 2 * MP_USED(&power2) + 2));
        MP_CHECKOK(mp_mul(oddPowers + (i - 1), &power2, oddPowers + i));
        MP_CHECKOK(s_mp_redc(oddPowers + i, mmm));
    }

    /* set accumulator to montgomery residue of 1 */
    mp_set(&accum1, 1);
    MP_CHECKOK(mp_to_mont(&accum1, &(mmm->N), &accum1));
    pa1 = &accum1;
    pa2 = &accum2;

    for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
        mp_size smallExp;
        MP_CHECKOK(mpl_get_bits(exponent, expOff, window_bits));
        smallExp = (mp_size)res;

        if (window_bits == 1) {
            if (!smallExp) {
                SQR(pa1, pa2);
                SWAPPA;
            } else if (smallExp & 1) {
                SQR(pa1, pa2);
                MUL(0, pa2, pa1);
            } else {
                abort();
            }
        } else if (window_bits == 4) {
            if (!smallExp) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
            } else if (smallExp & 1) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                MUL(smallExp / 2, pa1, pa2);
                SWAPPA;
            } else if (smallExp & 2) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                MUL(smallExp / 4, pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else if (smallExp & 4) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                MUL(smallExp / 8, pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else if (smallExp & 8) {
                SQR(pa1, pa2);
                MUL(smallExp / 16, pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else {
                abort();
            }
        } else if (window_bits == 5) {
            if (!smallExp) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else if (smallExp & 1) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                MUL(smallExp / 2, pa2, pa1);
            } else if (smallExp & 2) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                MUL(smallExp / 4, pa1, pa2);
                SQR(pa2, pa1);
            } else if (smallExp & 4) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                MUL(smallExp / 8, pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
            } else if (smallExp & 8) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                MUL(smallExp / 16, pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
            } else if (smallExp & 0x10) {
                SQR(pa1, pa2);
                MUL(smallExp / 32, pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
            } else {
                abort();
            }
        } else if (window_bits == 6) {
            if (!smallExp) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
            } else if (smallExp & 1) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                MUL(smallExp / 2, pa1, pa2);
                SWAPPA;
            } else if (smallExp & 2) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                MUL(smallExp / 4, pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else if (smallExp & 4) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                MUL(smallExp / 8, pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else if (smallExp & 8) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                MUL(smallExp / 16, pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else if (smallExp & 0x10) {
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                MUL(smallExp / 32, pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else if (smallExp & 0x20) {
                SQR(pa1, pa2);
                MUL(smallExp / 64, pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SWAPPA;
            } else {
                abort();
            }
        } else {
            abort();
        }
    }

    res = s_mp_redc(pa1, mmm);
    mp_exch(pa1, result);

CLEANUP:
    mp_clear(&accum1);
    mp_clear(&accum2);
    mp_clear(&power2);
    for (i = 0; i < odd_ints; ++i) {
        mp_clear(oddPowers + i);
    }
    return res;
}
#undef SQR
#undef MUL

#ifdef MP_USING_CACHE_SAFE_MOD_EXP
unsigned int mp_using_cache_safe_exp = 1;
#endif

mp_err
mp_set_safe_modexp(int value)
{
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
    mp_using_cache_safe_exp = value;
    return MP_OKAY;
#else
    if (value == 0) {
        return MP_OKAY;
    }
    return MP_BADARG;
#endif
}

#ifdef MP_USING_CACHE_SAFE_MOD_EXP
#define WEAVE_WORD_SIZE 4

/*
 * mpi_to_weave takes an array of bignums, a matrix in which each bignum
 * occupies all the columns of a row, and transposes it into a matrix in
 * which each bignum occupies a column of every row.  The first row of the
 * input matrix becomes the first column of the output matrix.  The n'th
 * row of input becomes the n'th column of output.  The input data is said
 * to be "interleaved" or "woven" into the output matrix.
 *
 * The array of bignums is left in this woven form.  Each time a single
 * bignum value is needed, it is recreated by fetching the n'th column,
 * forming a single row which is the new bignum.
 *
 * The purpose of this interleaving is make it impossible to determine which
 * of the bignums is being used in any one operation by examining the pattern
 * of cache misses.
 *
 * The weaving function does not transpose the entire input matrix in one call.
 * It transposes 4 rows of mp_ints into their respective columns of output.
 *
 * This implementation treats each mp_int bignum as an array of mp_digits,
 * It stores those bytes as a column of mp_digits in the output matrix.  It
 * doesn't care if the machine uses big-endian or little-endian byte ordering
 * within mp_digits.
 *
 * "bignums" is an array of mp_ints.
 * It points to four rows, four mp_ints, a subset of a larger array of mp_ints.
 *
 * "weaved" is the weaved output matrix.
 * The first byte of bignums[0] is stored in weaved[0].
 *
 * "nBignums" is the total number of bignums in the array of which "bignums"
 * is a part.
 *
 * "nDigits" is the size in mp_digits of each mp_int in the "bignums" array.
 * mp_ints that use less than nDigits digits are logically padded with zeros
 * while being stored in the weaved array.
 */
mp_err
mpi_to_weave(const mp_int *bignums,
             mp_digit *weaved,
             mp_size nDigits,  /* in each mp_int of input */
             mp_size nBignums) /* in the entire source array */
{
    mp_size i;
    mp_digit *endDest = weaved + (nDigits * nBignums);

    for (i = 0; i < WEAVE_WORD_SIZE; i++) {
        mp_size used = MP_USED(&bignums[i]);
        mp_digit *pSrc = MP_DIGITS(&bignums[i]);
        mp_digit *endSrc = pSrc + used;
        mp_digit *pDest = weaved + i;

        ARGCHK(MP_SIGN(&bignums[i]) == MP_ZPOS, MP_BADARG);
        ARGCHK(used <= nDigits, MP_BADARG);

        for (; pSrc < endSrc; pSrc++) {
            *pDest = *pSrc;
            pDest += nBignums;
        }
        while (pDest < endDest) {
            *pDest = 0;
            pDest += nBignums;
        }
    }

    return MP_OKAY;
}

/*
 * These functions return 0xffffffff if the output is true, and 0 otherwise.
 */
#define CONST_TIME_MSB(x) (0L - ((x) >> (8 * sizeof(x) - 1)))
#define CONST_TIME_EQ_Z(x) CONST_TIME_MSB(~(x) & ((x)-1))
#define CONST_TIME_EQ(a, b) CONST_TIME_EQ_Z((a) ^ (b))

/* Reverse the operation above for one mp_int.
 * Reconstruct one mp_int from its column in the weaved array.
 * Every read accesses every element of the weaved array, in order to
 * avoid timing attacks based on patterns of memory accesses.
 */
mp_err
weave_to_mpi(mp_int *a,              /* out, result */
             const mp_digit *weaved, /* in, byte matrix */
             mp_size index,          /* which column to read */
             mp_size nDigits,        /* number of mp_digits in each bignum */
             mp_size nBignums)       /* width of the matrix */
{
    /* these are indices, but need to be the same size as mp_digit
     * because of the CONST_TIME operations */
    mp_digit i, j;
    mp_digit d;
    mp_digit *pDest = MP_DIGITS(a);

    MP_SIGN(a) = MP_ZPOS;
    MP_USED(a) = nDigits;

    assert(weaved != NULL);

    /* Fetch the proper column in constant time, indexing over the whole array */
    for (i = 0; i < nDigits; ++i) {
        d = 0;
        for (j = 0; j < nBignums; ++j) {
            d |= weaved[i * nBignums + j] & CONST_TIME_EQ(j, index);
        }
        pDest[i] = d;
    }

    s_mp_clamp(a);
    return MP_OKAY;
}

#define SQR(a, b)             \
    MP_CHECKOK(mp_sqr(a, b)); \
    MP_CHECKOK(s_mp_redc(b, mmm))

#if defined(MP_MONT_USE_MP_MUL)
#define MUL_NOWEAVE(x, a, b)     \
    MP_CHECKOK(mp_mul(a, x, b)); \
    MP_CHECKOK(s_mp_redc(b, mmm))
#else
#define MUL_NOWEAVE(x, a, b) \
    MP_CHECKOK(s_mp_mul_mont(a, x, b, mmm))
#endif

#define MUL(x, a, b)                                               \
    MP_CHECKOK(weave_to_mpi(&tmp, powers, (x), nLen, num_powers)); \
    MUL_NOWEAVE(&tmp, a, b)

#define SWAPPA  \
    ptmp = pa1; \
    pa1 = pa2;  \
    pa2 = ptmp
#define MP_ALIGN(x, y) ((((ptrdiff_t)(x)) + ((y)-1)) & (((ptrdiff_t)0) - (y)))

/* Do modular exponentiation using integer multiply code. */
mp_err
mp_exptmod_safe_i(const mp_int *montBase,
                  const mp_int *exponent,
                  const mp_int *modulus,
                  mp_int *result,
                  mp_mont_modulus *mmm,
                  int nLen,
                  mp_size bits_in_exponent,
                  mp_size window_bits,
                  mp_size num_powers)
{
    mp_int *pa1, *pa2, *ptmp;
    mp_size i;
    mp_size first_window;
    mp_err res;
    int expOff;
    mp_int accum1, accum2, accum[WEAVE_WORD_SIZE];
    mp_int tmp;
    mp_digit *powersArray = NULL;
    mp_digit *powers = NULL;

    MP_DIGITS(&accum1) = 0;
    MP_DIGITS(&accum2) = 0;
    MP_DIGITS(&accum[0]) = 0;
    MP_DIGITS(&accum[1]) = 0;
    MP_DIGITS(&accum[2]) = 0;
    MP_DIGITS(&accum[3]) = 0;
    MP_DIGITS(&tmp) = 0;

    /* grab the first window value. This allows us to preload accumulator1
   * and save a conversion, some squares and a multiple*/
    MP_CHECKOK(mpl_get_bits(exponent,
                            bits_in_exponent - window_bits, window_bits));
    first_window = (mp_size)res;

    MP_CHECKOK(mp_init_size(&accum1, 3 * nLen + 2));
    MP_CHECKOK(mp_init_size(&accum2, 3 * nLen + 2));

    /* build the first WEAVE_WORD powers inline */
    /* if WEAVE_WORD_SIZE is not 4, this code will have to change */
    if (num_powers > 2) {
        MP_CHECKOK(mp_init_size(&accum[0], 3 * nLen + 2));
        MP_CHECKOK(mp_init_size(&accum[1], 3 * nLen + 2));
        MP_CHECKOK(mp_init_size(&accum[2], 3 * nLen + 2));
        MP_CHECKOK(mp_init_size(&accum[3], 3 * nLen + 2));
        mp_set(&accum[0], 1);
        MP_CHECKOK(mp_to_mont(&accum[0], &(mmm->N), &accum[0]));
        MP_CHECKOK(mp_copy(montBase, &accum[1]));
        SQR(montBase, &accum[2]);
        MUL_NOWEAVE(montBase, &accum[2], &accum[3]);
        powersArray = (mp_digit *)malloc(num_powers * (nLen * sizeof(mp_digit) + 1));
        if (!powersArray) {
            res = MP_MEM;
            goto CLEANUP;
        }
        /* powers[i] = base ** (i); */
        powers = (mp_digit *)MP_ALIGN(powersArray, num_powers);
        MP_CHECKOK(mpi_to_weave(accum, powers, nLen, num_powers));
        if (first_window < 4) {
            MP_CHECKOK(mp_copy(&accum[first_window], &accum1));
            first_window = num_powers;
        }
    } else {
        if (first_window == 0) {
            mp_set(&accum1, 1);
            MP_CHECKOK(mp_to_mont(&accum1, &(mmm->N), &accum1));
        } else {
            /* assert first_window == 1? */
            MP_CHECKOK(mp_copy(montBase, &accum1));
        }
    }

    /*
     * calculate all the powers in the powers array.
     * this adds 2**(k-1)-2 square operations over just calculating the
     * odd powers where k is the window size in the two other mp_modexpt
     * implementations in this file. We will get some of that
     * back by not needing the first 'k' squares and one multiply for the
     * first window.
     * Given the value of 4 for WEAVE_WORD_SIZE, this loop will only execute if
     * num_powers > 2, in which case powers will have been allocated.
     */
    for (i = WEAVE_WORD_SIZE; i < num_powers; i++) {
        int acc_index = i & (WEAVE_WORD_SIZE - 1); /* i % WEAVE_WORD_SIZE */
        if (i & 1) {
            MUL_NOWEAVE(montBase, &accum[acc_index - 1], &accum[acc_index]);
            /* we've filled the array do our 'per array' processing */
            if (acc_index == (WEAVE_WORD_SIZE - 1)) {
                MP_CHECKOK(mpi_to_weave(accum, powers + i - (WEAVE_WORD_SIZE - 1),
                                        nLen, num_powers));

                if (first_window <= i) {
                    MP_CHECKOK(mp_copy(&accum[first_window & (WEAVE_WORD_SIZE - 1)],
                                       &accum1));
                    first_window = num_powers;
                }
            }
        } else {
            /* up to 8 we can find 2^i-1 in the accum array, but at 8 we our source
             * and target are the same so we need to copy.. After that, the
             * value is overwritten, so we need to fetch it from the stored
             * weave array */
            if (i > 2 * WEAVE_WORD_SIZE) {
                MP_CHECKOK(weave_to_mpi(&accum2, powers, i / 2, nLen, num_powers));
                SQR(&accum2, &accum[acc_index]);
            } else {
                int half_power_index = (i / 2) & (WEAVE_WORD_SIZE - 1);
                if (half_power_index == acc_index) {
                    /* copy is cheaper than weave_to_mpi */
                    MP_CHECKOK(mp_copy(&accum[half_power_index], &accum2));
                    SQR(&accum2, &accum[acc_index]);
                } else {
                    SQR(&accum[half_power_index], &accum[acc_index]);
                }
            }
        }
    }
/* if the accum1 isn't set, Then there is something wrong with our logic
   * above and is an internal programming error.
   */
#if MP_ARGCHK == 2
    assert(MP_USED(&accum1) != 0);
#endif

    /* set accumulator to montgomery residue of 1 */
    pa1 = &accum1;
    pa2 = &accum2;

    /* tmp is not used if window_bits == 1. */
    if (window_bits != 1) {
        MP_CHECKOK(mp_init_size(&tmp, 3 * nLen + 2));
    }

    for (expOff = bits_in_exponent - window_bits * 2; expOff >= 0; expOff -= window_bits) {
        mp_size smallExp;
        MP_CHECKOK(mpl_get_bits(exponent, expOff, window_bits));
        smallExp = (mp_size)res;

        /* handle unroll the loops */
        switch (window_bits) {
            case 1:
                if (!smallExp) {
                    SQR(pa1, pa2);
                    SWAPPA;
                } else if (smallExp & 1) {
                    SQR(pa1, pa2);
                    MUL_NOWEAVE(montBase, pa2, pa1);
                } else {
                    abort();
                }
                break;
            case 6:
                SQR(pa1, pa2);
                SQR(pa2, pa1);
            /* fall through */
            case 4:
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                MUL(smallExp, pa1, pa2);
                SWAPPA;
                break;
            case 5:
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                SQR(pa2, pa1);
                SQR(pa1, pa2);
                MUL(smallExp, pa2, pa1);
                break;
            default:
                abort(); /* could do a loop? */
        }
    }

    res = s_mp_redc(pa1, mmm);
    mp_exch(pa1, result);

CLEANUP:
    mp_clear(&accum1);
    mp_clear(&accum2);
    mp_clear(&accum[0]);
    mp_clear(&accum[1]);
    mp_clear(&accum[2]);
    mp_clear(&accum[3]);
    mp_clear(&tmp);
    /* zero required by FIPS here, can't use PORT_ZFree
     * because mpi doesn't link with util */
    if (powers) {
        PORT_Memset(powers, 0, num_powers * sizeof(mp_digit));
    }
    free(powersArray);
    return res;
}
#undef SQR
#undef MUL
#endif

mp_err
mp_exptmod(const mp_int *inBase, const mp_int *exponent,
           const mp_int *modulus, mp_int *result)
{
    const mp_int *base;
    mp_size bits_in_exponent, i, window_bits, odd_ints;
    mp_err res;
    int nLen;
    mp_int montBase, goodBase;
    mp_mont_modulus mmm;
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
    static unsigned int max_window_bits;
#endif

    /* function for computing n0prime only works if n0 is odd */
    if (!mp_isodd(modulus))
        return s_mp_exptmod(inBase, exponent, modulus, result);

    MP_DIGITS(&montBase) = 0;
    MP_DIGITS(&goodBase) = 0;

    if (mp_cmp(inBase, modulus) < 0) {
        base = inBase;
    } else {
        MP_CHECKOK(mp_init(&goodBase));
        base = &goodBase;
        MP_CHECKOK(mp_mod(inBase, modulus, &goodBase));
    }

    nLen = MP_USED(modulus);
    MP_CHECKOK(mp_init_size(&montBase, 2 * nLen + 2));

    mmm.N = *modulus; /* a copy of the mp_int struct */

    /* compute n0', given n0, n0' = -(n0 ** -1) mod MP_RADIX
    **        where n0 = least significant mp_digit of N, the modulus.
    */
    mmm.n0prime = mp_calculate_mont_n0i(modulus);

    MP_CHECKOK(mp_to_mont(base, modulus, &montBase));

    bits_in_exponent = mpl_significant_bits(exponent);
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
    if (mp_using_cache_safe_exp) {
        if (bits_in_exponent > 780)
            window_bits = 6;
        else if (bits_in_exponent > 256)
            window_bits = 5;
        else if (bits_in_exponent > 20)
            window_bits = 4;
        /* RSA public key exponents are typically under 20 bits (common values
         * are: 3, 17, 65537) and a 4-bit window is inefficient
         */
        else
            window_bits = 1;
    } else
#endif
        if (bits_in_exponent > 480)
        window_bits = 6;
    else if (bits_in_exponent > 160)
        window_bits = 5;
    else if (bits_in_exponent > 20)
        window_bits = 4;
    /* RSA public key exponents are typically under 20 bits (common values
     * are: 3, 17, 65537) and a 4-bit window is inefficient
     */
    else
        window_bits = 1;

#ifdef MP_USING_CACHE_SAFE_MOD_EXP
    /*
     * clamp the window size based on
     * the cache line size.
     */
    if (!max_window_bits) {
        unsigned long cache_size = s_mpi_getProcessorLineSize();
        /* processor has no cache, use 'fast' code always */
        if (cache_size == 0) {
            mp_using_cache_safe_exp = 0;
        }
        if ((cache_size == 0) || (cache_size >= 64)) {
            max_window_bits = 6;
        } else if (cache_size >= 32) {
            max_window_bits = 5;
        } else if (cache_size >= 16) {
            max_window_bits = 4;
        } else
            max_window_bits = 1; /* should this be an assert? */
    }

    /* clamp the window size down before we caclulate bits_in_exponent */
    if (mp_using_cache_safe_exp) {
        if (window_bits > max_window_bits) {
            window_bits = max_window_bits;
        }
    }
#endif

    odd_ints = 1 << (window_bits - 1);
    i = bits_in_exponent % window_bits;
    if (i != 0) {
        bits_in_exponent += window_bits - i;
    }

#ifdef MP_USING_MONT_MULF
    if (mp_using_mont_mulf) {
        MP_CHECKOK(s_mp_pad(&montBase, nLen));
        res = mp_exptmod_f(&montBase, exponent, modulus, result, &mmm, nLen,
                           bits_in_exponent, window_bits, odd_ints);
    } else
#endif
#ifdef MP_USING_CACHE_SAFE_MOD_EXP
        if (mp_using_cache_safe_exp) {
        res = mp_exptmod_safe_i(&montBase, exponent, modulus, result, &mmm, nLen,
                                bits_in_exponent, window_bits, 1 << window_bits);
    } else
#endif
        res = mp_exptmod_i(&montBase, exponent, modulus, result, &mmm, nLen,
                           bits_in_exponent, window_bits, odd_ints);

CLEANUP:
    mp_clear(&montBase);
    mp_clear(&goodBase);
    /* Don't mp_clear mmm.N because it is merely a copy of modulus.
    ** Just zap it.
    */
    memset(&mmm, 0, sizeof mmm);
    return res;
}