ring 0.3.0

/* 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 <openssl/bn.h>

#include <assert.h>
#include <limits.h>
#include <openssl/err.h>

#include "internal.h"


#if !defined(BN_ULLONG)
/* bn_div_words divides a double-width |h|,|l| by |d| and returns the result,
 * which must fit in a |BN_ULONG|. */
static BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) {
  BN_ULONG dh, dl, q, ret = 0, th, tl, t;
  int i, count = 2;

  if (d == 0) {
    return BN_MASK2;
  }

  i = BN_num_bits_word(d);
  assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));

  i = BN_BITS2 - i;
  if (h >= d) {
    h -= d;
  }

  if (i) {
    d <<= i;
    h = (h << i) | (l >> (BN_BITS2 - i));
    l <<= i;
  }
  dh = (d & BN_MASK2h) >> BN_BITS4;
  dl = (d & BN_MASK2l);
  for (;;) {
    if ((h >> BN_BITS4) == dh) {
      q = BN_MASK2l;
    } else {
      q = h / dh;
    }

    th = q * dh;
    tl = dl * q;
    for (;;) {
      t = h - th;
      if ((t & BN_MASK2h) ||
          ((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4)))) {
        break;
      }
      q--;
      th -= dh;
      tl -= dl;
    }
    t = (tl >> BN_BITS4);
    tl = (tl << BN_BITS4) & BN_MASK2h;
    th += t;

    if (l < tl) {
      th++;
    }
    l -= tl;
    if (h < th) {
      h += d;
      q--;
    }
    h -= th;

    if (--count == 0) {
      break;
    }

    ret = q << BN_BITS4;
    h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2;
    l = (l & BN_MASK2l) << BN_BITS4;
  }

  ret |= q;
  return ret;
}
#endif /* !defined(BN_ULLONG) */

static inline void bn_div_rem_words(BN_ULONG *quotient_out, BN_ULONG *rem_out,
                                    BN_ULONG n0, BN_ULONG n1, BN_ULONG d0) {
  /* GCC and Clang generate function calls to |__udivdi3| and |__umoddi3| when
   * the |BN_ULLONG|-based C code is used.
   *
   * GCC bugs:
   *   * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=14224
   *   * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=43721
   *   * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=54183
   *   * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=58897
   *   * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=65668
   *
   * Clang bugs:
   *   * https://llvm.org/bugs/show_bug.cgi?id=6397
   *   * https://llvm.org/bugs/show_bug.cgi?id=12418
   *
   * These issues aren't specific to x86 and x86_64, so it might be worthwhile
   * to add more assembly language implementations. */
#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86) && defined(__GNUC__)
  __asm__ volatile (
    "divl %4"
    : "=a"(*quotient_out), "=d"(*rem_out)
    : "a"(n1), "d"(n0), "g"(d0)
    : "cc" );
#elif !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && defined(__GNUC__)
  __asm__ volatile (
    "divq %4"
    : "=a"(*quotient_out), "=d"(*rem_out)
    : "a"(n1), "d"(n0), "g"(d0)
    : "cc" );
#else
#if defined(BN_ULLONG)
  BN_ULLONG n = (((BN_ULLONG)n0) << BN_BITS2) | n1;
  *quotient_out = (BN_ULONG)(n / d0);
#else
  *quotient_out = bn_div_words(n0, n1, d0);
#endif
  *rem_out = n1 - (*quotient_out * d0);
#endif
}

/* BN_div computes  dv := num / divisor,  rounding towards
 * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
 * Thus:
 *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 *     rm->neg == num->neg                 (unless the remainder is zero)
 * If 'dv' or 'rm' is NULL, the respective value is not returned.
 *
 * This was specifically designed to contain fewer branches that may leak
 * sensitive information; see "New Branch Prediction Vulnerabilities in OpenSSL
 * and Necessary Software Countermeasures" by Onur Acıçmez, Shay Gueron, and
 * Jean-Pierre Seifert. */
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor) {
  int norm_shift, i, loop;
  BN_ULONG *resp, *wnump;
  BN_ULONG d0, d1;
  int num_n, div_n;

  /* Invalid zero-padding would have particularly bad consequences
   * so don't just rely on bn_check_top() here */
  if ((num->top > 0 && num->d[num->top - 1] == 0) ||
      (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
    OPENSSL_PUT_ERROR(BN, BN_R_NOT_INITIALIZED);
    return 0;
  }

  if (BN_is_zero(divisor)) {
    OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
    return 0;
  }

  BIGNUM snum;
  BN_init(&snum);

  BIGNUM sdiv;
  BN_init(&sdiv);

  BIGNUM tmp;
  BN_init(&tmp);

  BIGNUM res_tmp;
  BN_init(&res_tmp);

  BIGNUM wnum; /* Weak; do not |BN_free|. */

  BIGNUM *res; /* weak pointer */
  if (dv == NULL) {
    res = &res_tmp;
  } else {
    res = dv;
  }

  int ret = 0;

  /* First we normalise the numbers */
  norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
  if (!(BN_lshift(&sdiv, divisor, norm_shift))) {
    goto err;
  }
  sdiv.neg = 0;
  norm_shift += BN_BITS2;
  if (!(BN_lshift(&snum, num, norm_shift))) {
    goto err;
  }
  snum.neg = 0;

  /* Since we don't want to have special-case logic for the case where snum is
   * larger than sdiv, we pad snum with enough zeroes without changing its
   * value. */
  if (snum.top <= sdiv.top + 1) {
    if (bn_wexpand(&snum, sdiv.top + 2) == NULL) {
      goto err;
    }
    for (i = snum.top; i < sdiv.top + 2; i++) {
      snum.d[i] = 0;
    }
    snum.top = sdiv.top + 2;
  } else {
    if (bn_wexpand(&snum, snum.top + 1) == NULL) {
      goto err;
    }
    snum.d[snum.top] = 0;
    snum.top++;
  }

  div_n = sdiv.top;
  num_n = snum.top;
  loop = num_n - div_n;
  /* Lets setup a 'window' into snum
   * This is the part that corresponds to the current
   * 'area' being divided */

  wnum.neg = 0;
  wnum.d = &(snum.d[loop]);
  wnum.top = div_n;
  /* only needed when BN_ucmp messes up the values between top and max */
  wnum.dmax = snum.dmax - loop; /* so we don't step out of bounds */

  /* Get the top 2 words of sdiv */
  /* div_n=sdiv.top; */
  d0 = sdiv.d[div_n - 1];
  d1 = (div_n == 1) ? 0 : sdiv.d[div_n - 2];

  /* pointer to the 'top' of snum */
  wnump = &(snum.d[num_n - 1]);

  /* Setup to 'res' */
  res->neg = (num->neg ^ divisor->neg);
  if (!bn_wexpand(res, (loop + 1))) {
    goto err;
  }
  res->top = loop - 1;
  resp = &(res->d[loop - 1]);

  /* space for temp */
  if (!bn_wexpand(&tmp, (div_n + 1))) {
    goto err;
  }

  /* if res->top == 0 then clear the neg value otherwise decrease
   * the resp pointer */
  if (res->top == 0) {
    res->neg = 0;
  } else {
    resp--;
  }

  for (i = 0; i < loop - 1; i++, wnump--, resp--) {
    BN_ULONG q, l0;
    /* the first part of the loop uses the top two words of snum and sdiv to
     * calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv */
    BN_ULONG n0, n1, rem = 0;

    n0 = wnump[0];
    n1 = wnump[-1];
    if (n0 == d0) {
      q = BN_MASK2;
    } else {
      /* n0 < d0 */
      bn_div_rem_words(&q, &rem, n0, n1, d0);

#ifdef BN_ULLONG
      BN_ULLONG t2 = (BN_ULLONG)d1 * q;
      for (;;) {
        if (t2 <= ((((BN_ULLONG)rem) << BN_BITS2) | wnump[-2])) {
          break;
        }
        q--;
        rem += d0;
        if (rem < d0) {
          break; /* don't let rem overflow */
        }
        t2 -= d1;
      }
#else /* !BN_ULLONG */
      BN_ULONG t2l, t2h;
      bn_umult_lohi(&t2l, &t2h, d1, q);
      for (;;) {
        if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2]))) {
          break;
        }
        q--;
        rem += d0;
        if (rem < d0) {
          break; /* don't let rem overflow */
        }
        if (t2l < d1) {
          t2h--;
        }
        t2l -= d1;
      }
#endif /* !BN_ULLONG */
    }

    l0 = bn_mul_words(tmp.d, sdiv.d, div_n, q);
    tmp.d[div_n] = l0;
    wnum.d--;
    /* ingore top values of the bignums just sub the two
     * BN_ULONG arrays with bn_sub_words */
    if (bn_sub_words(wnum.d, wnum.d, tmp.d, div_n + 1)) {
      /* Note: As we have considered only the leading
       * two BN_ULONGs in the calculation of q, sdiv * q
       * might be greater than wnum (but then (q-1) * sdiv
       * is less or equal than wnum)
       */
      q--;
      if (bn_add_words(wnum.d, wnum.d, sdiv.d, div_n)) {
        /* we can't have an overflow here (assuming
         * that q != 0, but if q == 0 then tmp is
         * zero anyway) */
        (*wnump)++;
      }
    }
    /* store part of the result */
    *resp = q;
  }
  bn_correct_top(&snum);
  if (rm != NULL) {
    /* Keep a copy of the neg flag in num because if rm==num
     * BN_rshift() will overwrite it.
     */
    int neg = num->neg;
    if (!BN_rshift(rm, &snum, norm_shift)) {
      goto err;
    }
    if (!BN_is_zero(rm)) {
      rm->neg = neg;
    }
  }
  bn_correct_top(res);
  ret = 1;

err:
  BN_free(&tmp);
  BN_free(&snum);
  BN_free(&sdiv);
  BN_free(&res_tmp);

  return ret;
}

int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d) {
  if (!(BN_mod(r, m, d))) {
    return 0;
  }
  if (!r->neg) {
    return 1;
  }

  /* now -|d| < r < 0, so we have to set r := r + |d|. */
  return (d->neg ? BN_sub : BN_add)(r, r, d);
}

int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
                     const BIGNUM *m) {
  if (!BN_sub(r, a, b)) {
    return 0;
  }
  if (r->neg) {
    return BN_add(r, r, m);
  }
  return 1;
}