/* $OpenBSD: bn_mont.c,v 1.28 2022/02/07 19:44:23 tb Exp $ */

/* 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 <stdint.h>

#include "bn_lcl.h"

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

#ifdef MONT_WORD

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 (bn_mul_mont(r->d, a->d, b->d, mont->N.d, mont->n0, num)) {

      r->neg = a->neg^b->neg;

      r->top = num;

      bn_correct_top(r);

      return (1);

    }

  }

#endif

  BN_CTX_start(ctx);

  if ((tmp = BN_CTX_get(ctx)) == 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_WORD

  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);

}

int

BN_to_montgomery(BIGNUM *r, const BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx)

{

  return BN_mod_mul_montgomery(r, a, &mont->RR, mont, ctx);

}

#ifdef MONT_WORD

static int

BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)

{

  BIGNUM *n;

  BN_ULONG *ap, *np, *rp, n0, v, carry;

  int nl, max, i;

  n = &(mont->N);

  nl = n->top;

  if (nl == 0) {

    ret->top = 0;

    return (1);

  }

  max = (2 * nl); /* carry is stored separately */

  if (bn_wexpand(r, max) == NULL)

    return (0);

  r->neg ^= n->neg;

  np = n->d;

  rp = r->d;

  /* clear the top words of T */

#if 1

  for (i=r->top; i<max; i++) /* memset? XXX */

    rp[i] = 0;

#else

  memset(&(rp[r->top]), 0, (max - r->top) * sizeof(BN_ULONG));

#endif

  r->top = max;

  n0 = mont->n0[0];

#ifdef BN_COUNT

  fprintf(stderr, "word BN_from_montgomery_word %d * %d\n", nl, nl);

#endif

  for (carry = 0, i = 0; i < nl; i++, rp++) {

    v = bn_mul_add_words(rp, np, nl, (rp[0] * n0) & BN_MASK2);

    v = (v + carry + rp[nl]) & BN_MASK2;

    carry |= (v != rp[nl]);

    carry &= (v <= rp[nl]);

    rp[nl] = v;

  }

  if (bn_wexpand(ret, nl) == NULL)

    return (0);

  ret->top = nl;

  ret->neg = r->neg;

  rp = ret->d;

  ap = &(r->d[nl]);

#define BRANCH_FREE 1

#if BRANCH_FREE

  {

    BN_ULONG *nrp;

    size_t m;

    v = bn_sub_words(rp, ap, np, nl) - carry;

    /* if subtraction result is real, then

     * trick unconditional memcpy below to perform in-place

     * "refresh" instead of actual copy. */

    m = (0 - (size_t)v);

    nrp = (BN_ULONG *)(((uintptr_t)rp & ~m)|((uintptr_t)ap & m));

    for (i = 0, nl -= 4; i < nl; 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 (nl += 4; i < nl; i++)

      rp[i] = nrp[i], ap[i] = 0;

  }

#else

  if (bn_sub_words (rp, ap, np, nl) - carry)

    memcpy(rp, ap, nl*sizeof(BN_ULONG));

#endif

  bn_correct_top(r);

  bn_correct_top(ret);

  bn_check_top(ret);

  return (1);

}

#endif  /* MONT_WORD */

int

BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx)

{

  int retn = 0;

#ifdef MONT_WORD

  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);

#else /* !MONT_WORD */

  BIGNUM *t1, *t2;

  BN_CTX_start(ctx);

  if ((t1 = BN_CTX_get(ctx)) == NULL)

    goto err;

  if ((t2 = BN_CTX_get(ctx)) == 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;

  if (BN_ucmp(ret, &(mont->N)) >= 0) {

    if (!BN_usub(ret, ret, &(mont->N)))

      goto err;

  }

  retn = 1;

  bn_check_top(ret);

err:

  BN_CTX_end(ctx);

#endif /* MONT_WORD */

  return (retn);

}

BN_MONT_CTX *

BN_MONT_CTX_new(void)

{

  BN_MONT_CTX *ret;

  if ((ret = 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));

  ctx->n0[0] = ctx->n0[1] = 0;

  ctx->flags = 0;

}

void

BN_MONT_CTX_free(BN_MONT_CTX *mont)

{

  if (mont == NULL)

    return;

  BN_clear_free(&(mont->RR));

  BN_clear_free(&(mont->N));

  BN_clear_free(&(mont->Ni));

  if (mont->flags & BN_FLG_MALLOCED)

    free(mont);

}

int

BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)

{

  int ret = 0;

  BIGNUM *Ri, *R;

  if (BN_is_zero(mod))

    return 0;

  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];

    BN_init(&tmod);

    tmod.d = buf;

    tmod.dmax = 2;

    tmod.neg = 0;

    mont->ri = (BN_num_bits(mod) +

        (BN_BITS2 - 1)) / BN_BITS2 * BN_BITS2;

#if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)

    /* Only certain BN_BITS2<=32 platforms actually make use of

     * n0[1], and we could use the #else case (with a shorter R

     * value) for the others.  However, currently only the assembler

     * files do know which is which. */

    BN_zero(R);

    if (!(BN_set_bit(R, 2 * BN_BITS2)))

      goto err;

    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_ct(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_ct(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

    BN_zero(R);

    if (!(BN_set_bit(R, BN_BITS2)))

      goto err; /* R */

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

    buf[1] = 0;

    tmod.top = buf[0] != 0 ? 1 : 0;

    /* Ri = R^-1 mod N*/

    if ((BN_mod_inverse_ct(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_ct(Ri, NULL, Ri, &tmod, ctx))

      goto err;

    /* Ni = (R*Ri-1)/N,

     * keep only least significant word: */

    mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;

    mont->n0[1] = 0;

#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_ct(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_ct(&(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_ct(&(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;

  to->n0[0] = from->n0[0];

  to->n0[1] = from->n0[1];

  return (to);

}

BN_MONT_CTX *

BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock, const BIGNUM *mod,

    BN_CTX *ctx)

{

  int got_write_lock = 0;

  BN_MONT_CTX *ret;

  CRYPTO_r_lock(lock);

  if (!*pmont) {

    CRYPTO_r_unlock(lock);

    CRYPTO_w_lock(lock);

    got_write_lock = 1;

    if (!*pmont) {

      ret = BN_MONT_CTX_new();

      if (ret && !BN_MONT_CTX_set(ret, mod, ctx))

        BN_MONT_CTX_free(ret);

      else

        *pmont = ret;

    }

  }

  ret = *pmont;

  if (got_write_lock)

    CRYPTO_w_unlock(lock);

  else

    CRYPTO_r_unlock(lock);

  return ret;

}