/* $OpenBSD: bn_recp.c,v 1.15 2017/01/29 17:49:22 beck 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.]

 */

#include <stdio.h>

#include <openssl/err.h>

#include "bn_lcl.h"

void

BN_RECP_CTX_init(BN_RECP_CTX *recp)

{

  BN_init(&(recp->N));

  BN_init(&(recp->Nr));

  recp->num_bits = 0;

  recp->flags = 0;

}

BN_RECP_CTX *

BN_RECP_CTX_new(void)

{

  BN_RECP_CTX *ret;

  if ((ret = malloc(sizeof(BN_RECP_CTX))) == NULL)

    return (NULL);

  BN_RECP_CTX_init(ret);

  ret->flags = BN_FLG_MALLOCED;

  return (ret);

}

void

BN_RECP_CTX_free(BN_RECP_CTX *recp)

{

  if (recp == NULL)

    return;

  BN_free(&(recp->N));

  BN_free(&(recp->Nr));

  if (recp->flags & BN_FLG_MALLOCED)

    free(recp);

}

int

BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *d, BN_CTX *ctx)

{

  if (!BN_copy(&(recp->N), d))

    return 0;

  BN_zero(&(recp->Nr));

  recp->num_bits = BN_num_bits(d);

  recp->shift = 0;

  return (1);

}

int

BN_mod_mul_reciprocal(BIGNUM *r, const BIGNUM *x, const BIGNUM *y,

    BN_RECP_CTX *recp, BN_CTX *ctx)

{

  int ret = 0;

  BIGNUM *a;

  const BIGNUM *ca;

  BN_CTX_start(ctx);

  if ((a = BN_CTX_get(ctx)) == NULL)

    goto err;

  if (y != NULL) {

    if (x == y) {

      if (!BN_sqr(a, x, ctx))

        goto err;

    } else {

      if (!BN_mul(a, x, y, ctx))

        goto err;

    }

    ca = a;

  } else

    ca = x; /* Just do the mod */

  ret = BN_div_recp(NULL, r, ca, recp, ctx);

err:

  BN_CTX_end(ctx);

  bn_check_top(r);

  return (ret);

}

int

BN_div_recp(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, BN_RECP_CTX *recp,

    BN_CTX *ctx)

{

  int i, j, ret = 0;

  BIGNUM *a, *b, *d, *r;

  BN_CTX_start(ctx);

  a = BN_CTX_get(ctx);

  b = BN_CTX_get(ctx);

  if (dv != NULL)

    d = dv;

  else

    d = BN_CTX_get(ctx);

  if (rem != NULL)

    r = rem;

  else

    r = BN_CTX_get(ctx);

  if (a == NULL || b == NULL || d == NULL || r == NULL)

    goto err;

  if (BN_ucmp(m, &(recp->N)) < 0) {

    BN_zero(d);

    if (!BN_copy(r, m)) {

      BN_CTX_end(ctx);

      return 0;

    }

    BN_CTX_end(ctx);

    return (1);

  }

  /* We want the remainder

   * Given input of ABCDEF / ab

   * we need multiply ABCDEF by 3 digests of the reciprocal of ab

   *

   */

  /* i := max(BN_num_bits(m), 2*BN_num_bits(N)) */

  i = BN_num_bits(m);

  j = recp->num_bits << 1;

  if (j > i)

    i = j;

  /* Nr := round(2^i / N) */

  if (i != recp->shift)

    recp->shift = BN_reciprocal(&(recp->Nr), &(recp->N), i, ctx);

  /* BN_reciprocal returns i, or -1 for an error */

  if (recp->shift == -1)

    goto err;

  /* d := |round(round(m / 2^BN_num_bits(N)) * recp->Nr / 2^(i - BN_num_bits(N)))|

   *    = |round(round(m / 2^BN_num_bits(N)) * round(2^i / N) / 2^(i - BN_num_bits(N)))|

   *   <= |(m / 2^BN_num_bits(N)) * (2^i / N) * (2^BN_num_bits(N) / 2^i)|

   *    = |m/N|

   */

  if (!BN_rshift(a, m, recp->num_bits))

    goto err;

  if (!BN_mul(b, a,&(recp->Nr), ctx))

    goto err;

  if (!BN_rshift(d, b, i - recp->num_bits))

    goto err;

  d->neg = 0;

  if (!BN_mul(b, &(recp->N), d, ctx))

    goto err;

  if (!BN_usub(r, m, b))

    goto err;

  r->neg = 0;

#if 1

  j = 0;

  while (BN_ucmp(r, &(recp->N)) >= 0) {

    if (j++ > 2) {

      BNerror(BN_R_BAD_RECIPROCAL);

      goto err;

    }

    if (!BN_usub(r, r, &(recp->N)))

      goto err;

    if (!BN_add_word(d, 1))

      goto err;

  }

#endif

  r->neg = BN_is_zero(r) ? 0 : m->neg;

  d->neg = m->neg^recp->N.neg;

  ret = 1;

err:

  BN_CTX_end(ctx);

  bn_check_top(dv);

  bn_check_top(rem);

  return (ret);

}

/* len is the expected size of the result

 * We actually calculate with an extra word of precision, so

 * we can do faster division if the remainder is not required.

 */

/* r := 2^len / m */

int

BN_reciprocal(BIGNUM *r, const BIGNUM *m, int len, BN_CTX *ctx)

{

  int ret = -1;

  BIGNUM *t;

  BN_CTX_start(ctx);

  if ((t = BN_CTX_get(ctx)) == NULL)

    goto err;

  if (!BN_set_bit(t, len))

    goto err;

  if (!BN_div_ct(r, NULL, t,m, ctx))

    goto err;

  ret = len;

err:

  bn_check_top(r);

  BN_CTX_end(ctx);

  return (ret);

}