crypto/bn/bn_mont.c

/* crypto/bn/bn_mont.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 *
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 *
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 *
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */
/* ====================================================================
 * Copyright (c) 1998-2006 The OpenSSL Project.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

/*
 * Details about Montgomery multiplication algorithms can be found at
 * http://security.ece.orst.edu/publications.html, e.g.
 * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
 * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
 */

#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"

#define MONT_WORD               /* use the faster word-based algorithm */

#if defined(MONT_WORD) && defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
/*
 * This condition means we have a specific non-default build: In the 0.9.8
 * branch, OPENSSL_BN_ASM_MONT is normally not set for any BN_BITS2<=32
 * platform; an explicit "enable-montasm" is required. I.e., if we are here,
 * the user intentionally deviates from the normal stable build to get better
 * Montgomery performance from the 0.9.9-dev backport. In this case only, we
 * also enable BN_from_montgomery_word() (another non-stable feature from
 * 0.9.9-dev).
 */
# define MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD
#endif

#ifdef MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD
static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
#endif

int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                          BN_MONT_CTX *mont, BN_CTX *ctx)
{
    BIGNUM *tmp;
    int ret = 0;
#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
    int num = mont->N.top;

    if (num > 1 && a->top == num && b->top == num) {
        if (bn_wexpand(r, num) == NULL)
            return (0);
# if 0                          /* for OpenSSL 0.9.9 mont->n0 */
        if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num))
# else
        if (bn_mul_mont(r->d, a->d, b->d, mont->N.d, &mont->n0, num))
# endif
        {
            r->neg = a->neg ^ b->neg;
            r->top = num;
            bn_correct_top(r);
            return (1);
        }
    }
#endif

    BN_CTX_start(ctx);
    tmp = BN_CTX_get(ctx);
    if (tmp == NULL)
        goto err;

    bn_check_top(tmp);
    if (a == b) {
        if (!BN_sqr(tmp, a, ctx))
            goto err;
    } else {
        if (!BN_mul(tmp, a, b, ctx))
            goto err;
    }
    /* reduce from aRR to aR */
#ifdef MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD
    if (!BN_from_montgomery_word(r, tmp, mont))
        goto err;
#else
    if (!BN_from_montgomery(r, tmp, mont, ctx))
        goto err;
#endif
    bn_check_top(r);
    ret = 1;
 err:
    BN_CTX_end(ctx);
    return (ret);
}

#ifdef MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD
static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
{
    BIGNUM *n;
    BN_ULONG *ap, *np, *rp, n0, v, *nrp;
    int al, nl, max, i, x, ri;

    n = &(mont->N);
    /*
     * mont->ri is the size of mont->N in bits (rounded up to the word size)
     */
    al = ri = mont->ri / BN_BITS2;

    nl = n->top;
    if ((al == 0) || (nl == 0)) {
        ret->top = 0;
        return (1);
    }

    max = (nl + al + 1);        /* allow for overflow (no?) XXX */
    if (bn_wexpand(r, max) == NULL)
        return (0);

    r->neg ^= n->neg;
    np = n->d;
    rp = r->d;
    nrp = &(r->d[nl]);

    /* clear the top words of T */
    for (i = r->top; i < max; i++) /* memset? XXX */
        r->d[i] = 0;

    r->top = max;
# if 0                          /* for OpenSSL 0.9.9 mont->n0 */
    n0 = mont->n0[0];
# else
    n0 = mont->n0;
# endif

# ifdef BN_COUNT
    fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl);
# endif
    for (i = 0; i < nl; i++) {
# ifdef __TANDEM
        {
            long long t1;
            long long t2;
            long long t3;
            t1 = rp[0] * (n0 & 0177777);
            t2 = 037777600000l;
            t2 = n0 & t2;
            t3 = rp[0] & 0177777;
            t2 = (t3 * t2) & BN_MASK2;
            t1 = t1 + t2;
            v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1);
        }
# else
        v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
# endif
        nrp++;
        rp++;
        if (((nrp[-1] += v) & BN_MASK2) >= v)
            continue;
        else {
            if (((++nrp[0]) & BN_MASK2) != 0)
                continue;
            if (((++nrp[1]) & BN_MASK2) != 0)
                continue;
            for (x = 2; (((++nrp[x]) & BN_MASK2) == 0); x++) ;
        }
    }
    bn_correct_top(r);

    /*
     * mont->ri will be a multiple of the word size and below code is kind of
     * BN_rshift(ret,r,mont->ri) equivalent
     */
    if (r->top <= ri) {
        ret->top = 0;
        return (1);
    }
    al = r->top - ri;

    if (bn_wexpand(ret, ri) == NULL)
        return (0);
    x = 0 - (((al - ri) >> (sizeof(al) * 8 - 1)) & 1);
    ret->top = x = (ri & ~x) | (al & x); /* min(ri,al) */
    ret->neg = r->neg;

    rp = ret->d;
    ap = &(r->d[ri]);

    {
        size_t m1, m2;

        v = bn_sub_words(rp, ap, np, ri);
        /*
         * this ----------------^^ works even in al<ri case thanks to zealous
         * zeroing of top of the vector in the beginning.
         */

        /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
        /*
         * in other words if subtraction result is real, then trick
         * unconditional memcpy below to perform in-place "refresh" instead
         * of actual copy.
         */
        m1 = 0 - (size_t)(((al - ri) >> (sizeof(al) * 8 - 1)) & 1); /* al<ri */
        m2 = 0 - (size_t)(((ri - al) >> (sizeof(al) * 8 - 1)) & 1); /* al>ri */
        m1 |= m2;               /* (al!=ri) */
        m1 |= (0 - (size_t)v);  /* (al!=ri || v) */
        m1 &= ~m2;              /* (al!=ri || v) && !al>ri */
        nrp = (BN_ULONG *)(((size_t)rp & ~m1) | ((size_t)ap & m1));
    }

    /*
     * 'i<ri' is chosen to eliminate dependency on input data, even though it
     * results in redundant copy in al<ri case.
     */
    for (i = 0, ri -= 4; i < ri; i += 4) {
        BN_ULONG t1, t2, t3, t4;

        t1 = nrp[i + 0];
        t2 = nrp[i + 1];
        t3 = nrp[i + 2];
        ap[i + 0] = 0;
        t4 = nrp[i + 3];
        ap[i + 1] = 0;
        rp[i + 0] = t1;
        ap[i + 2] = 0;
        rp[i + 1] = t2;
        ap[i + 3] = 0;
        rp[i + 2] = t3;
        rp[i + 3] = t4;
    }
    for (ri += 4; i < ri; i++)
        rp[i] = nrp[i], ap[i] = 0;
    bn_correct_top(r);
    bn_correct_top(ret);
    bn_check_top(ret);

    return (1);
}

int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
                       BN_CTX *ctx)
{
    int retn = 0;
    BIGNUM *t;

    BN_CTX_start(ctx);
    if ((t = BN_CTX_get(ctx)) && BN_copy(t, a))
        retn = BN_from_montgomery_word(ret, t, mont);
    BN_CTX_end(ctx);
    return retn;
}

#else                           /* !MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD */

int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
                       BN_CTX *ctx)
{
    int retn = 0;

# ifdef MONT_WORD
    BIGNUM *n, *r;
    BN_ULONG *ap, *np, *rp, n0, v, *nrp;
    int al, nl, max, i, x, ri;

    BN_CTX_start(ctx);
    if ((r = BN_CTX_get(ctx)) == NULL)
        goto err;

    if (!BN_copy(r, a))
        goto err;
    n = &(mont->N);

    ap = a->d;
    /*
     * mont->ri is the size of mont->N in bits (rounded up to the word size)
     */
    al = ri = mont->ri / BN_BITS2;

    nl = n->top;
    if ((al == 0) || (nl == 0)) {
        r->top = 0;
        return (1);
    }

    max = (nl + al + 1);        /* allow for overflow (no?) XXX */
    if (bn_wexpand(r, max) == NULL)
        goto err;

    r->neg = a->neg ^ n->neg;
    np = n->d;
    rp = r->d;
    nrp = &(r->d[nl]);

    /* clear the top words of T */
#  if 1
    for (i = r->top; i < max; i++) /* memset? XXX */
        r->d[i] = 0;
#  else
    memset(&(r->d[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));
#  endif

    r->top = max;
    n0 = mont->n0;

#  ifdef BN_COUNT
    fprintf(stderr, "word BN_from_montgomery %d * %d\n", nl, nl);
#  endif
    for (i = 0; i < nl; i++) {
#  ifdef __TANDEM
        {
            long long t1;
            long long t2;
            long long t3;
            t1 = rp[0] * (n0 & 0177777);
            t2 = 037777600000l;
            t2 = n0 & t2;
            t3 = rp[0] & 0177777;
            t2 = (t3 * t2) & BN_MASK2;
            t1 = t1 + t2;
            v = bn_mul_add_words(rp, np, nl, (BN_ULONG)t1);
        }
#  else
        v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);
#  endif
        nrp++;
        rp++;
        if (((nrp[-1] += v) & BN_MASK2) >= v)
            continue;
        else {
            if (((++nrp[0]) & BN_MASK2) != 0)
                continue;
            if (((++nrp[1]) & BN_MASK2) != 0)
                continue;
            for (x = 2; (((++nrp[x]) & BN_MASK2) == 0); x++) ;
        }
    }
    bn_correct_top(r);

    /*
     * mont->ri will be a multiple of the word size and below code is kind of
     * BN_rshift(ret,r,mont->ri) equivalent
     */
    if (r->top <= ri) {
        ret->top = 0;
        retn = 1;
        goto err;
    }
    al = r->top - ri;

#  define BRANCH_FREE 1
#  if BRANCH_FREE
    if (bn_wexpand(ret, ri) == NULL)
        goto err;
    x = 0 - (((al - ri) >> (sizeof(al) * 8 - 1)) & 1);
    ret->top = x = (ri & ~x) | (al & x); /* min(ri,al) */
    ret->neg = r->neg;

    rp = ret->d;
    ap = &(r->d[ri]);

    {
        size_t m1, m2;

        v = bn_sub_words(rp, ap, np, ri);
        /*
         * this ----------------^^ works even in al<ri case thanks to zealous
         * zeroing of top of the vector in the beginning.
         */

        /* if (al==ri && !v) || al>ri) nrp=rp; else nrp=ap; */
        /*
         * in other words if subtraction result is real, then trick
         * unconditional memcpy below to perform in-place "refresh" instead
         * of actual copy.
         */
        m1 = 0 - (size_t)(((al - ri) >> (sizeof(al) * 8 - 1)) & 1); /* al<ri */
        m2 = 0 - (size_t)(((ri - al) >> (sizeof(al) * 8 - 1)) & 1); /* al>ri */
        m1 |= m2;               /* (al!=ri) */
        m1 |= (0 - (size_t)v);  /* (al!=ri || v) */
        m1 &= ~m2;              /* (al!=ri || v) && !al>ri */
        nrp = (BN_ULONG *)(((size_t)rp & ~m1) | ((size_t)ap & m1));
    }

    /*
     * 'i<ri' is chosen to eliminate dependency on input data, even though it
     * results in redundant copy in al<ri case.
     */
    for (i = 0, ri -= 4; i < ri; i += 4) {
        BN_ULONG t1, t2, t3, t4;

        t1 = nrp[i + 0];
        t2 = nrp[i + 1];
        t3 = nrp[i + 2];
        ap[i + 0] = 0;
        t4 = nrp[i + 3];
        ap[i + 1] = 0;
        rp[i + 0] = t1;
        ap[i + 2] = 0;
        rp[i + 1] = t2;
        ap[i + 3] = 0;
        rp[i + 2] = t3;
        rp[i + 3] = t4;
    }
    for (ri += 4; i < ri; i++)
        rp[i] = nrp[i], ap[i] = 0;
    bn_correct_top(r);
    bn_correct_top(ret);
#  else
    if (bn_wexpand(ret, al) == NULL)
        goto err;
    ret->top = al;
    ret->neg = r->neg;

    rp = ret->d;
    ap = &(r->d[ri]);
    al -= 4;
    for (i = 0; i < al; i += 4) {
        BN_ULONG t1, t2, t3, t4;

        t1 = ap[i + 0];
        t2 = ap[i + 1];
        t3 = ap[i + 2];
        t4 = ap[i + 3];
        rp[i + 0] = t1;
        rp[i + 1] = t2;
        rp[i + 2] = t3;
        rp[i + 3] = t4;
    }
    al += 4;
    for (; i < al; i++)
        rp[i] = ap[i];
#  endif
# else                          /* !MONT_WORD */
    BIGNUM *t1, *t2;

    BN_CTX_start(ctx);
    t1 = BN_CTX_get(ctx);
    t2 = BN_CTX_get(ctx);
    if (t1 == NULL || t2 == NULL)
        goto err;

    if (!BN_copy(t1, a))
        goto err;
    BN_mask_bits(t1, mont->ri);

    if (!BN_mul(t2, t1, &mont->Ni, ctx))
        goto err;
    BN_mask_bits(t2, mont->ri);

    if (!BN_mul(t1, t2, &mont->N, ctx))
        goto err;
    if (!BN_add(t2, a, t1))
        goto err;
    if (!BN_rshift(ret, t2, mont->ri))
        goto err;
# endif                         /* MONT_WORD */

# if !defined(BRANCH_FREE) || BRANCH_FREE==0
    if (BN_ucmp(ret, &(mont->N)) >= 0) {
        if (!BN_usub(ret, ret, &(mont->N)))
            goto err;
    }
# endif
    retn = 1;
    bn_check_top(ret);
 err:
    BN_CTX_end(ctx);
    return (retn);
}
#endif                          /* MONT_FROM_WORD___NON_DEFAULT_0_9_8_BUILD */

BN_MONT_CTX *BN_MONT_CTX_new(void)
{
    BN_MONT_CTX *ret;

    if ((ret = (BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
        return (NULL);

    BN_MONT_CTX_init(ret);
    ret->flags = BN_FLG_MALLOCED;
    return (ret);
}

void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
{
    ctx->ri = 0;
    BN_init(&(ctx->RR));
    BN_init(&(ctx->N));
    BN_init(&(ctx->Ni));
#if 0                           /* for OpenSSL 0.9.9 mont->n0 */
    ctx->n0[0] = ctx->n0[1] = 0;
#else
    ctx->n0 = 0;
#endif
    ctx->flags = 0;
}

void BN_MONT_CTX_free(BN_MONT_CTX *mont)
{
    if (mont == NULL)
        return;

    BN_free(&(mont->RR));
    BN_free(&(mont->N));
    BN_free(&(mont->Ni));
    if (mont->flags & BN_FLG_MALLOCED)
        OPENSSL_free(mont);
}

int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
{
    int ret = 0;
    BIGNUM *Ri, *R;

    BN_CTX_start(ctx);
    if ((Ri = BN_CTX_get(ctx)) == NULL)
        goto err;
    R = &(mont->RR);            /* grab RR as a temp */
    if (!BN_copy(&(mont->N), mod))
        goto err;               /* Set N */
    mont->N.neg = 0;

#ifdef MONT_WORD
    {
        BIGNUM tmod;
        BN_ULONG buf[2];

        mont->ri = (BN_num_bits(mod) + (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;
        BN_zero(R);
# if 0                          /* for OpenSSL 0.9.9 mont->n0, would be "#if
                                 * defined(OPENSSL_BN_ASM_MONT) &&
                                 * (BN_BITS2<=32)", only certain BN_BITS2<=32
                                 * platforms actually need this */
        if (!(BN_set_bit(R, 2 * BN_BITS2)))
            goto err;           /* R */
# else
        if (!(BN_set_bit(R, BN_BITS2)))
            goto err;           /* R */
# endif

        buf[0] = mod->d[0];     /* tmod = N mod word size */
        buf[1] = 0;

        BN_init(&tmod);
        tmod.d = buf;
        tmod.top = buf[0] != 0 ? 1 : 0;
        tmod.dmax = 2;
        tmod.neg = 0;

# if 0                          /* for OpenSSL 0.9.9 mont->n0, would be "#if
                                 * defined(OPENSSL_BN_ASM_MONT) &&
                                 * (BN_BITS2<=32)"; only certain BN_BITS2<=32
                                 * platforms actually need this */
        tmod.top = 0;
        if ((buf[0] = mod->d[0]))
            tmod.top = 1;
        if ((buf[1] = mod->top > 1 ? mod->d[1] : 0))
            tmod.top = 2;

        if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
            goto err;
        if (!BN_lshift(Ri, Ri, 2 * BN_BITS2))
            goto err;           /* R*Ri */
        if (!BN_is_zero(Ri)) {
            if (!BN_sub_word(Ri, 1))
                goto err;
        } else {                /* if N mod word size == 1 */

            if (bn_expand(Ri, (int)sizeof(BN_ULONG) * 2) == NULL)
                goto err;
            /* Ri-- (mod double word size) */
            Ri->neg = 0;
            Ri->d[0] = BN_MASK2;
            Ri->d[1] = BN_MASK2;
            Ri->top = 2;
        }
        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
            goto err;
        /*
         * Ni = (R*Ri-1)/N, keep only couple of least significant words:
         */
        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
        mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
# else
        /* Ri = R^-1 mod N */
        if ((BN_mod_inverse(Ri, R, &tmod, ctx)) == NULL)
            goto err;
        if (!BN_lshift(Ri, Ri, BN_BITS2))
            goto err;           /* R*Ri */
        if (!BN_is_zero(Ri)) {
            if (!BN_sub_word(Ri, 1))
                goto err;
        } else {                /* if N mod word size == 1 */

            if (!BN_set_word(Ri, BN_MASK2))
                goto err;       /* Ri-- (mod word size) */
        }
        if (!BN_div(Ri, NULL, Ri, &tmod, ctx))
            goto err;
        /*
         * Ni = (R*Ri-1)/N, keep only least significant word:
         */
#  if 0                         /* for OpenSSL 0.9.9 mont->n0 */
        mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
        mont->n0[1] = 0;
#  else
        mont->n0 = (Ri->top > 0) ? Ri->d[0] : 0;
#  endif
# endif
    }
#else                           /* !MONT_WORD */
    {                           /* bignum version */
        mont->ri = BN_num_bits(&mont->N);
        BN_zero(R);
        if (!BN_set_bit(R, mont->ri))
            goto err;           /* R = 2^ri */
        /* Ri = R^-1 mod N */
        if ((BN_mod_inverse(Ri, R, &mont->N, ctx)) == NULL)
            goto err;
        if (!BN_lshift(Ri, Ri, mont->ri))
            goto err;           /* R*Ri */
        if (!BN_sub_word(Ri, 1))
            goto err;
        /*
         * Ni = (R*Ri-1) / N
         */
        if (!BN_div(&(mont->Ni), NULL, Ri, &mont->N, ctx))
            goto err;
    }
#endif

    /* setup RR for conversions */
    BN_zero(&(mont->RR));
    if (!BN_set_bit(&(mont->RR), mont->ri * 2))
        goto err;
    if (!BN_mod(&(mont->RR), &(mont->RR), &(mont->N), ctx))
        goto err;

    ret = 1;
 err:
    BN_CTX_end(ctx);
    return ret;
}

BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
{
    if (to == from)
        return (to);

    if (!BN_copy(&(to->RR), &(from->RR)))
        return NULL;
    if (!BN_copy(&(to->N), &(from->N)))
        return NULL;
    if (!BN_copy(&(to->Ni), &(from->Ni)))
        return NULL;
    to->ri = from->ri;
#if 0                           /* for OpenSSL 0.9.9 mont->n0 */
    to->n0[0] = from->n0[0];
    to->n0[1] = from->n0[1];
#else
    to->n0 = from->n0;
#endif
    return (to);
}

BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
                                    const BIGNUM *mod, BN_CTX *ctx)
{
    BN_MONT_CTX *ret;

    CRYPTO_r_lock(lock);
    ret = *pmont;
    CRYPTO_r_unlock(lock);
    if (ret)
        return ret;

    /*
     * We don't want to serialise globally while doing our lazy-init math in
     * BN_MONT_CTX_set. That punishes threads that are doing independent
     * things. Instead, punish the case where more than one thread tries to
     * lazy-init the same 'pmont', by having each do the lazy-init math work
     * independently and only use the one from the thread that wins the race
     * (the losers throw away the work they've done).
     */
    ret = BN_MONT_CTX_new();
    if (!ret)
        return NULL;
    if (!BN_MONT_CTX_set(ret, mod, ctx)) {
        BN_MONT_CTX_free(ret);
        return NULL;
    }

    /* The locked compare-and-set, after the local work is done. */
    CRYPTO_w_lock(lock);
    if (*pmont) {
        BN_MONT_CTX_free(ret);
        ret = *pmont;
    } else
        *pmont = ret;
    CRYPTO_w_unlock(lock);
    return ret;
}