/* $OpenBSD: bn_gf2m.c,v 1.23 2017/01/29 17:49:22 beck Exp $ */

/* ====================================================================

 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.

 *

 * The Elliptic Curve Public-Key Crypto Library (ECC Code) included

 * herein is developed by SUN MICROSYSTEMS, INC., and is contributed

 * to the OpenSSL project.

 *

 * The ECC Code is licensed pursuant to the OpenSSL open source

 * license provided below.

 *

 * In addition, Sun covenants to all licensees who provide a reciprocal

 * covenant with respect to their own patents if any, not to sue under

 * current and future patent claims necessarily infringed by the making,

 * using, practicing, selling, offering for sale and/or otherwise

 * disposing of the ECC Code as delivered hereunder (or portions thereof),

 * provided that such covenant shall not apply:

 *  1) for code that a licensee deletes from the ECC Code;

 *  2) separates from the ECC Code; or

 *  3) for infringements caused by:

 *       i) the modification of the ECC Code or

 *      ii) the combination of the ECC Code with other software or

 *          devices where such combination causes the infringement.

 *

 * The software is originally written by Sheueling Chang Shantz and

 * Douglas Stebila of Sun Microsystems Laboratories.

 *

 */

/* NOTE: This file is licensed pursuant to the OpenSSL license below

 * and may be modified; but after modifications, the above covenant

 * may no longer apply!  In such cases, the corresponding paragraph

 * ["In addition, Sun covenants ... causes the infringement."] and

 * this note can be edited out; but please keep the Sun copyright

 * notice and attribution. */

/* ====================================================================

 * Copyright (c) 1998-2002 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).

 *

 */

#include <limits.h>

#include <stdio.h>

#include <openssl/opensslconf.h>

#include <openssl/err.h>

#include "bn_lcl.h"

#ifndef OPENSSL_NO_EC2M

/* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should fail. */

#define MAX_ITERATIONS 50

static const BN_ULONG SQR_tb[16] =

  {     0,     1,     4,     5,    16,    17,    20,    21,

64,    65,    68,    69,    80,    81,    84,    85 };

/* Platform-specific macros to accelerate squaring. */

#ifdef _LP64

#define SQR1(w) \

    SQR_tb[(w) >> 60 & 0xF] << 56 | SQR_tb[(w) >> 56 & 0xF] << 48 | \

    SQR_tb[(w) >> 52 & 0xF] << 40 | SQR_tb[(w) >> 48 & 0xF] << 32 | \

    SQR_tb[(w) >> 44 & 0xF] << 24 | SQR_tb[(w) >> 40 & 0xF] << 16 | \

    SQR_tb[(w) >> 36 & 0xF] <<  8 | SQR_tb[(w) >> 32 & 0xF]

#define SQR0(w) \

    SQR_tb[(w) >> 28 & 0xF] << 56 | SQR_tb[(w) >> 24 & 0xF] << 48 | \

    SQR_tb[(w) >> 20 & 0xF] << 40 | SQR_tb[(w) >> 16 & 0xF] << 32 | \

    SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >>  8 & 0xF] << 16 | \

    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]

#else

#define SQR1(w) \

    SQR_tb[(w) >> 28 & 0xF] << 24 | SQR_tb[(w) >> 24 & 0xF] << 16 | \

    SQR_tb[(w) >> 20 & 0xF] <<  8 | SQR_tb[(w) >> 16 & 0xF]

#define SQR0(w) \

    SQR_tb[(w) >> 12 & 0xF] << 24 | SQR_tb[(w) >>  8 & 0xF] << 16 | \

    SQR_tb[(w) >>  4 & 0xF] <<  8 | SQR_tb[(w)       & 0xF]

#endif

#if !defined(OPENSSL_BN_ASM_GF2m)

/* Product of two polynomials a, b each with degree < BN_BITS2 - 1,

 * result is a polynomial r with degree < 2 * BN_BITS - 1

 * The caller MUST ensure that the variables have the right amount

 * of space allocated.

 */

static void

bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a, const BN_ULONG b)

{

#ifndef _LP64

  BN_ULONG h, l, s;

  BN_ULONG tab[8], top2b = a >> 30;

  BN_ULONG a1, a2, a4;

  a1 = a & (0x3FFFFFFF);

  a2 = a1 << 1;

  a4 = a2 << 1;

  tab[0] = 0;

  tab[1] = a1;

  tab[2] = a2;

  tab[3] = a1 ^ a2;

  tab[4] = a4;

  tab[5] = a1 ^ a4;

  tab[6] = a2 ^ a4;

  tab[7] = a1 ^ a2 ^ a4;

  s = tab[b & 0x7];

  l = s;

  s = tab[b >> 3 & 0x7];

  l ^= s << 3;

  h = s >> 29;

  s = tab[b >> 6 & 0x7];

  l ^= s <<  6;

  h ^= s >> 26;

  s = tab[b >> 9 & 0x7];

  l ^= s <<  9;

  h ^= s >> 23;

  s = tab[b >> 12 & 0x7];

  l ^= s << 12;

  h ^= s >> 20;

  s = tab[b >> 15 & 0x7];

  l ^= s << 15;

  h ^= s >> 17;

  s = tab[b >> 18 & 0x7];

  l ^= s << 18;

  h ^= s >> 14;

  s = tab[b >> 21 & 0x7];

  l ^= s << 21;

  h ^= s >> 11;

  s = tab[b >> 24 & 0x7];

  l ^= s << 24;

  h ^= s >>  8;

  s = tab[b >> 27 & 0x7];

  l ^= s << 27;

  h ^= s >>  5;

  s = tab[b >> 30];

  l ^= s << 30;

  h ^= s >> 2;

  /* compensate for the top two bits of a */

  if (top2b & 01) {

    l ^= b << 30;

    h ^= b >> 2;

  }

  if (top2b & 02) {

    l ^= b << 31;

    h ^= b >> 1;

  }

  *r1 = h;

  *r0 = l;

#else

  BN_ULONG h, l, s;

  BN_ULONG tab[16], top3b = a >> 61;

  BN_ULONG a1, a2, a4, a8;

  a1 = a & (0x1FFFFFFFFFFFFFFFULL);

  a2 = a1 << 1;

  a4 = a2 << 1;

  a8 = a4 << 1;

  tab[0] = 0;

  tab[1] = a1;

  tab[2] = a2;

  tab[3] = a1 ^ a2;

  tab[4] = a4;

  tab[5] = a1 ^ a4;

  tab[6] = a2 ^ a4;

  tab[7] = a1 ^ a2 ^ a4;

  tab[8] = a8;

  tab[9] = a1 ^ a8;

  tab[10] = a2 ^ a8;

  tab[11] = a1 ^ a2 ^ a8;

  tab[12] = a4 ^ a8;

  tab[13] = a1 ^ a4 ^ a8;

  tab[14] = a2 ^ a4 ^ a8;

  tab[15] = a1 ^ a2 ^ a4 ^ a8;

  s = tab[b & 0xF];

  l = s;

  s = tab[b >> 4 & 0xF];

  l ^= s << 4;

  h = s >> 60;

  s = tab[b >> 8 & 0xF];

  l ^= s << 8;

  h ^= s >> 56;

  s = tab[b >> 12 & 0xF];

  l ^= s << 12;

  h ^= s >> 52;

  s = tab[b >> 16 & 0xF];

  l ^= s << 16;

  h ^= s >> 48;

  s = tab[b >> 20 & 0xF];

  l ^= s << 20;

  h ^= s >> 44;

  s = tab[b >> 24 & 0xF];

  l ^= s << 24;

  h ^= s >> 40;

  s = tab[b >> 28 & 0xF];

  l ^= s << 28;

  h ^= s >> 36;

  s = tab[b >> 32 & 0xF];

  l ^= s << 32;

  h ^= s >> 32;

  s = tab[b >> 36 & 0xF];

  l ^= s << 36;

  h ^= s >> 28;

  s = tab[b >> 40 & 0xF];

  l ^= s << 40;

  h ^= s >> 24;

  s = tab[b >> 44 & 0xF];

  l ^= s << 44;

  h ^= s >> 20;

  s = tab[b >> 48 & 0xF];

  l ^= s << 48;

  h ^= s >> 16;

  s = tab[b >> 52 & 0xF];

  l ^= s << 52;

  h ^= s >> 12;

  s = tab[b >> 56 & 0xF];

  l ^= s << 56;

  h ^= s >>  8;

  s = tab[b >> 60];

  l ^= s << 60;

  h ^= s >>  4;

  /* compensate for the top three bits of a */

  if (top3b & 01) {

    l ^= b << 61;

    h ^= b >> 3;

  }

  if (top3b & 02) {

    l ^= b << 62;

    h ^= b >> 2;

  }

  if (top3b & 04) {

    l ^= b << 63;

    h ^= b >> 1;

  }

  *r1 = h;

  *r0 = l;

#endif

}

/* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,

 * result is a polynomial r with degree < 4 * BN_BITS2 - 1

 * The caller MUST ensure that the variables have the right amount

 * of space allocated.

 */

static void

bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0,

    const BN_ULONG b1, const BN_ULONG b0)

{

  BN_ULONG m1, m0;

  /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */

  bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1);

  bn_GF2m_mul_1x1(r + 1, r, a0, b0);

  bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);

  /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */

  r[2] ^= m1 ^ r[1] ^ r[3];  /* h0 ^= m1 ^ l1 ^ h1; */

  r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0;  /* l1 ^= l0 ^ h0 ^ m0; */

}

#else

void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1,

    BN_ULONG b0);

#endif

/* Add polynomials a and b and store result in r; r could be a or b, a and b

 * could be equal; r is the bitwise XOR of a and b.

 */

int

BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)

{

  int i;

  const BIGNUM *at, *bt;

  bn_check_top(a);

  bn_check_top(b);

  if (a->top < b->top) {

    at = b;

    bt = a;

  } else {

    at = a;

    bt = b;

  }

  if (bn_wexpand(r, at->top) == NULL)

    return 0;

  for (i = 0; i < bt->top; i++) {

    r->d[i] = at->d[i] ^ bt->d[i];

  }

  for (; i < at->top; i++) {

    r->d[i] = at->d[i];

  }

  r->top = at->top;

  bn_correct_top(r);

  return 1;

}

/* Some functions allow for representation of the irreducible polynomials

 * as an int[], say p.  The irreducible f(t) is then of the form:

 *     t^p[0] + t^p[1] + ... + t^p[k]

 * where m = p[0] > p[1] > ... > p[k] = 0.

 */

/* Performs modular reduction of a and store result in r.  r could be a. */

int

BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])

{

  int j, k;

  int n, dN, d0, d1;

  BN_ULONG zz, *z;

  bn_check_top(a);

  if (!p[0]) {

    /* reduction mod 1 => return 0 */

    BN_zero(r);

    return 1;

  }

  /* Since the algorithm does reduction in the r value, if a != r, copy

   * the contents of a into r so we can do reduction in r.

   */

  if (a != r) {

    if (!bn_wexpand(r, a->top))

      return 0;

    for (j = 0; j < a->top; j++) {

      r->d[j] = a->d[j];

    }

    r->top = a->top;

  }

  z = r->d;

  /* start reduction */

  dN = p[0] / BN_BITS2;

  for (j = r->top - 1; j > dN; ) {

    zz = z[j];

    if (z[j] == 0) {

      j--;

      continue;

    }

    z[j] = 0;

    for (k = 1; p[k] != 0; k++) {

      /* reducing component t^p[k] */

      n = p[0] - p[k];

      d0 = n % BN_BITS2;

      d1 = BN_BITS2 - d0;

      n /= BN_BITS2;

      z[j - n] ^= (zz >> d0);

      if (d0)

        z[j - n - 1] ^= (zz << d1);

    }

    /* reducing component t^0 */

    n = dN;

    d0 = p[0] % BN_BITS2;

    d1 = BN_BITS2 - d0;

    z[j - n] ^= (zz >> d0);

    if (d0)

      z[j - n - 1] ^= (zz << d1);

  }

  /* final round of reduction */

  while (j == dN) {

    d0 = p[0] % BN_BITS2;

    zz = z[dN] >> d0;

    if (zz == 0)

      break;

    d1 = BN_BITS2 - d0;

    /* clear up the top d1 bits */

    if (d0)

      z[dN] = (z[dN] << d1) >> d1;

    else

      z[dN] = 0;

    z[0] ^= zz; /* reduction t^0 component */

    for (k = 1; p[k] != 0; k++) {

      BN_ULONG tmp_ulong;

      /* reducing component t^p[k]*/

      n = p[k] / BN_BITS2;

      d0 = p[k] % BN_BITS2;

      d1 = BN_BITS2 - d0;

      z[n] ^= (zz << d0);

      if (d0 && (tmp_ulong = zz >> d1))

        z[n + 1] ^= tmp_ulong;

    }

  }

  bn_correct_top(r);

  return 1;

}

/* Performs modular reduction of a by p and store result in r.  r could be a.

 *

 * This function calls down to the BN_GF2m_mod_arr implementation; this wrapper

 * function is only provided for convenience; for best performance, use the

 * BN_GF2m_mod_arr function.

 */

int

BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)

{

  int ret = 0;

  int arr[6];

  bn_check_top(a);

  bn_check_top(p);

  ret = BN_GF2m_poly2arr(p, arr, sizeof(arr) / sizeof(arr[0]));

  if (!ret || ret > (int)(sizeof(arr) / sizeof(arr[0]))) {

    BNerror(BN_R_INVALID_LENGTH);

    return 0;

  }

  ret = BN_GF2m_mod_arr(r, a, arr);

  bn_check_top(r);

  return ret;

}

/* Compute the product of two polynomials a and b, reduce modulo p, and store

 * the result in r.  r could be a or b; a could be b.

 */

int

BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const int p[],

    BN_CTX *ctx)

{

  int zlen, i, j, k, ret = 0;

  BIGNUM *s;

  BN_ULONG x1, x0, y1, y0, zz[4];

  bn_check_top(a);

  bn_check_top(b);

  if (a == b) {

    return BN_GF2m_mod_sqr_arr(r, a, p, ctx);

  }

  BN_CTX_start(ctx);

  if ((s = BN_CTX_get(ctx)) == NULL)

    goto err;

  zlen = a->top + b->top + 4;

  if (!bn_wexpand(s, zlen))

    goto err;

  s->top = zlen;

  for (i = 0; i < zlen; i++)

    s->d[i] = 0;

  for (j = 0; j < b->top; j += 2) {

    y0 = b->d[j];

    y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1];

    for (i = 0; i < a->top; i += 2) {

      x0 = a->d[i];

      x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1];

      bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);

      for (k = 0; k < 4; k++)

        s->d[i + j + k] ^= zz[k];

    }

  }

  bn_correct_top(s);

  if (BN_GF2m_mod_arr(r, s, p))

    ret = 1;

  bn_check_top(r);

err:

  BN_CTX_end(ctx);

  return ret;

}

/* Compute the product of two polynomials a and b, reduce modulo p, and store

 * the result in r.  r could be a or b; a could equal b.

 *

 * This function calls down to the BN_GF2m_mod_mul_arr implementation; this wrapper

 * function is only provided for convenience; for best performance, use the

 * BN_GF2m_mod_mul_arr function.

 */

int

BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p,

    BN_CTX *ctx)

{

  int ret = 0;

  const int max = BN_num_bits(p) + 1;

  int *arr = NULL;

  bn_check_top(a);

  bn_check_top(b);

  bn_check_top(p);

  if ((arr = reallocarray(NULL, max, sizeof(int))) == NULL)

    goto err;

  ret = BN_GF2m_poly2arr(p, arr, max);

  if (!ret || ret > max) {

    BNerror(BN_R_INVALID_LENGTH);

    goto err;

  }

  ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);

  bn_check_top(r);

err:

  free(arr);

  return ret;

}

/* Square a, reduce the result mod p, and store it in a.  r could be a. */

int

BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[], BN_CTX *ctx)

{

  int i, ret = 0;

  BIGNUM *s;

  bn_check_top(a);

  BN_CTX_start(ctx);

  if ((s = BN_CTX_get(ctx)) == NULL)

    goto err;

  if (!bn_wexpand(s, 2 * a->top))

    goto err;

  for (i = a->top - 1; i >= 0; i--) {

    s->d[2 * i + 1] = SQR1(a->d[i]);

    s->d[2 * i] = SQR0(a->d[i]);

  }

  s->top = 2 * a->top;

  bn_correct_top(s);

  if (!BN_GF2m_mod_arr(r, s, p))

    goto err;

  bn_check_top(r);

  ret = 1;

err:

  BN_CTX_end(ctx);

  return ret;

}

/* Square a, reduce the result mod p, and store it in a.  r could be a.

 *

 * This function calls down to the BN_GF2m_mod_sqr_arr implementation; this wrapper

 * function is only provided for convenience; for best performance, use the

 * BN_GF2m_mod_sqr_arr function.

 */

int

BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)

{

  int ret = 0;

  const int max = BN_num_bits(p) + 1;

  int *arr = NULL;

  bn_check_top(a);

  bn_check_top(p);

  if ((arr = reallocarray(NULL, max, sizeof(int))) == NULL)

    goto err;

  ret = BN_GF2m_poly2arr(p, arr, max);

  if (!ret || ret > max) {

    BNerror(BN_R_INVALID_LENGTH);

    goto err;

  }

  ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);

  bn_check_top(r);

err:

  free(arr);

  return ret;

}

/* Invert a, reduce modulo p, and store the result in r. r could be a.

 * Uses Modified Almost Inverse Algorithm (Algorithm 10) from

 *     Hankerson, D., Hernandez, J.L., and Menezes, A.  "Software Implementation

 *     of Elliptic Curve Cryptography Over Binary Fields".

 */

int

BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)

{

  BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp;

  int ret = 0;

  bn_check_top(a);

  bn_check_top(p);

  BN_CTX_start(ctx);

  if ((b = BN_CTX_get(ctx)) == NULL)

    goto err;

  if ((c = BN_CTX_get(ctx)) == NULL)

    goto err;

  if ((u = BN_CTX_get(ctx)) == NULL)

    goto err;

  if ((v = BN_CTX_get(ctx)) == NULL)

    goto err;

  if (!BN_GF2m_mod(u, a, p))

    goto err;

  if (BN_is_zero(u))

    goto err;

  if (!BN_copy(v, p))

    goto err;

#if 0

  if (!BN_one(b))

    goto err;

  while (1) {

    while (!BN_is_odd(u)) {

      if (BN_is_zero(u))

        goto err;

      if (!BN_rshift1(u, u))

        goto err;

      if (BN_is_odd(b)) {

        if (!BN_GF2m_add(b, b, p))

          goto err;

      }

      if (!BN_rshift1(b, b))

        goto err;

    }

    if (BN_abs_is_word(u, 1))

      break;

    if (BN_num_bits(u) < BN_num_bits(v)) {

      tmp = u;

      u = v;

      v = tmp;

      tmp = b;

      b = c;

      c = tmp;

    }

    if (!BN_GF2m_add(u, u, v))

      goto err;

    if (!BN_GF2m_add(b, b, c))

      goto err;

  }

#else

  {

    int i,  ubits = BN_num_bits(u),

    vbits = BN_num_bits(v), /* v is copy of p */

    top = p->top;

    BN_ULONG *udp, *bdp, *vdp, *cdp;

    if (!bn_wexpand(u, top))

                        goto err;

    udp = u->d;

    for (i = u->top; i < top; i++)

      udp[i] = 0;

    u->top = top;

    if (!bn_wexpand(b, top))

                        goto err;

    bdp = b->d;

    bdp[0] = 1;

    for (i = 1; i < top; i++)

      bdp[i] = 0;

    b->top = top;

    if (!bn_wexpand(c, top))

                        goto err;

    cdp = c->d;

    for (i = 0; i < top; i++)

      cdp[i] = 0;

    c->top = top;

    vdp = v->d; /* It pays off to "cache" *->d pointers, because

         * it allows optimizer to be more aggressive.

         * But we don't have to "cache" p->d, because *p

         * is declared 'const'... */

    while (1) {

      while (ubits && !(udp[0]&1)) {

        BN_ULONG u0, u1, b0, b1, mask;

        u0 = udp[0];

        b0 = bdp[0];

        mask = (BN_ULONG)0 - (b0 & 1);

        b0  ^= p->d[0] & mask;

        for (i = 0; i < top - 1; i++) {

          u1 = udp[i + 1];

          udp[i] = ((u0 >> 1) |

              (u1 << (BN_BITS2 - 1))) & BN_MASK2;

          u0 = u1;

          b1 = bdp[i + 1] ^ (p->d[i + 1] & mask);

          bdp[i] = ((b0 >> 1) |

              (b1 << (BN_BITS2 - 1))) & BN_MASK2;

          b0 = b1;

        }

        udp[i] = u0 >> 1;

        bdp[i] = b0 >> 1;

        ubits--;

      }

      if (ubits <= BN_BITS2) {

        /* See if poly was reducible. */

        if (udp[0] == 0)

          goto err;

        if (udp[0] == 1)

          break;

      }

      if (ubits < vbits) {

        i = ubits;

        ubits = vbits;

        vbits = i;

        tmp = u;

        u = v;

        v = tmp;

        tmp = b;

        b = c;

        c = tmp;

        udp = vdp;

        vdp = v->d;

        bdp = cdp;

        cdp = c->d;

      }

      for (i = 0; i < top; i++) {

        udp[i] ^= vdp[i];

        bdp[i] ^= cdp[i];

      }

      if (ubits == vbits) {

        BN_ULONG ul;

        int utop = (ubits - 1) / BN_BITS2;

        while ((ul = udp[utop]) == 0 && utop)

          utop--;

        ubits = utop*BN_BITS2 + BN_num_bits_word(ul);

      }

    }

    bn_correct_top(b);

  }

#endif

  if (!BN_copy(r, b))

    goto err;

  bn_check_top(r);

  ret = 1;

err:

#ifdef BN_DEBUG /* BN_CTX_end would complain about the expanded form */

  bn_correct_top(c);

  bn_correct_top(u);

  bn_correct_top(v);

#endif

  BN_CTX_end(ctx);

  return ret;

}

/* Invert xx, reduce modulo p, and store the result in r. r could be xx.

 *

 * This function calls down to the BN_GF2m_mod_inv implementation; this wrapper

 * function is only provided for convenience; for best performance, use the

 * BN_GF2m_mod_inv function.

 */

int

BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[], BN_CTX *ctx)

{

  BIGNUM *field;

  int ret = 0;

  bn_check_top(xx);

  BN_CTX_start(ctx);

  if ((field = BN_CTX_get(ctx)) == NULL)

    goto err;

  if (!BN_GF2m_arr2poly(p, field))

    goto err;

  ret = BN_GF2m_mod_inv(r, xx, field, ctx);

  bn_check_top(r);

err:

  BN_CTX_end(ctx);

  return ret;

}

#ifndef OPENSSL_SUN_GF2M_DIV

/* Divide y by x, reduce modulo p, and store the result in r. r could be x

 * or y, x could equal y.

 */

int

BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p,

    BN_CTX *ctx)

{

  BIGNUM *xinv = NULL;

  int ret = 0;

  bn_check_top(y);

  bn_check_top(x);

  bn_check_top(p);

  BN_CTX_start(ctx);

  if ((xinv = BN_CTX_get(ctx)) == NULL)

    goto err;

  if (!BN_GF2m_mod_inv(xinv, x, p, ctx))

    goto err;

  if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx))

    goto err;

  bn_check_top(r);

  ret = 1;

err:

  BN_CTX_end(ctx);

  return ret;

}

#else

/* Divide y by x, reduce modulo p, and store the result in r. r could be x

 * or y, x could equal y.

 * Uses algorithm Modular_Division_GF(2^m) from

 *     Chang-Shantz, S.  "From Euclid's GCD to Montgomery Multiplication to

 *     the Great Divide".

 */

int

BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x, const BIGNUM *p,

    BN_CTX *ctx)

{

  BIGNUM *a, *b, *u, *v;

  int ret = 0;

  bn_check_top(y);

  bn_check_top(x);

  bn_check_top(p);

  BN_CTX_start(ctx);

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

    goto err;

  if ((b = BN_CTX_get(ctx)) == NULL)

    goto err;

  if ((u = BN_CTX_get(ctx)) == NULL)

    goto err;

  if ((v = BN_CTX_get(ctx)) == NULL)

    goto err;

  /* reduce x and y mod p */

  if (!BN_GF2m_mod(u, y, p))

    goto err;

  if (!BN_GF2m_mod(a, x, p))

    goto err;

  if (!BN_copy(b, p))

    goto err;

  while (!BN_is_odd(a)) {

    if (!BN_rshift1(a, a))

      goto err;

    if (BN_is_odd(u))

      if (!BN_GF2m_add(u, u, p))

        goto err;

    if (!BN_rshift1(u, u))

      goto err;

  }

  do {

    if (BN_GF2m_cmp(b, a) > 0) {

      if (!BN_GF2m_add(b, b, a))

        goto err;

      if (!BN_GF2m_add(v, v, u))

        goto err;

      do {

        if (!BN_rshift1(b, b))

          goto err;

        if (BN_is_odd(v))

          if (!BN_GF2m_add(v, v, p))

            goto err;

        if (!BN_rshift1(v, v))

          goto err;

      } while (!BN_is_odd(b));

    } else if (BN_abs_is_word(a, 1))

      break;

    else {

      if (!BN_GF2m_add(a, a, b))

        goto err;

      if (!BN_GF2m_add(u, u, v))

        goto err;

      do {

        if (!BN_rshift1(a, a))

          goto err;

        if (BN_is_odd(u))

          if (!BN_GF2m_add(u, u, p))

            goto err;

        if (!BN_rshift1(u, u))

          goto err;

      } while (!BN_is_odd(a));

    }

  } while (1);

  if (!BN_copy(r, u))

    goto err;

  bn_check_top(r);

  ret = 1;

err:

  BN_CTX_end(ctx);

  return ret;

}

#endif

/* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx

 * or yy, xx could equal yy.

 *

 * This function calls down to the BN_GF2m_mod_div implementation; this wrapper

 * function is only provided for convenience; for best performance, use the

 * BN_GF2m_mod_div function.

 */

int

BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx,

    const int p[], BN_CTX *ctx)

{

  BIGNUM *field;

  int ret = 0;

  bn_check_top(yy);

  bn_check_top(xx);

  BN_CTX_start(ctx);