/* crypto/bn/bn_gf2m.c */

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

  * 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 <assert.h>

 #include <limits.h>

 #include <stdio.h>

 #include "cryptlib.h"

 #include "bn_lcl.h"

 /* 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. */

 #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)

 #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]

 #endif

 #ifdef THIRTY_TWO_BIT

 #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

 #ifdef SIXTEEN_BIT

 #define SQR1(w) \

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

 #define SQR0(w) \

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

 #endif

 #ifdef EIGHT_BIT

 #define SQR1(w) \

     SQR_tb[(w) >>  4 & 0xF]

 #define SQR0(w) \

     SQR_tb[(w)       & 15]

 #endif

 /* 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.

  */

 #ifdef EIGHT_BIT

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

 	{

 	register BN_ULONG h, l, s;

 	BN_ULONG tab[4], top1b = a >> 7;

 	register BN_ULONG a1, a2;

 	a1 = a & (0x7F); a2 = a1 << 1;

 	tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;

 	s = tab[b      & 0x3]; l  = s;

 	s = tab[b >> 2 & 0x3]; l ^= s << 2; h  = s >> 6;

 	s = tab[b >> 4 & 0x3]; l ^= s << 4; h ^= s >> 4;

 	s = tab[b >> 6      ]; l ^= s << 6; h ^= s >> 2;

 	/* compensate for the top bit of a */

 	if (top1b & 01) { l ^= b << 7; h ^= b >> 1; } 

 	*r1 = h; *r0 = l;

 	} 

 #endif

 #ifdef SIXTEEN_BIT

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

 	{

 	register BN_ULONG h, l, s;

 	BN_ULONG tab[4], top1b = a >> 15; 

 	register BN_ULONG a1, a2;

 	a1 = a & (0x7FFF); a2 = a1 << 1;

 	tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;

 	s = tab[b      & 0x3]; l  = s;

 	s = tab[b >> 2 & 0x3]; l ^= s <<  2; h  = s >> 14;

 	s = tab[b >> 4 & 0x3]; l ^= s <<  4; h ^= s >> 12;

 	s = tab[b >> 6 & 0x3]; l ^= s <<  6; h ^= s >> 10;

 	s = tab[b >> 8 & 0x3]; l ^= s <<  8; h ^= s >>  8;

 	s = tab[b >>10 & 0x3]; l ^= s << 10; h ^= s >>  6;

 	s = tab[b >>12 & 0x3]; l ^= s << 12; h ^= s >>  4;

 	s = tab[b >>14      ]; l ^= s << 14; h ^= s >>  2;

 	/* compensate for the top bit of a */

 	if (top1b & 01) { l ^= b << 15; h ^= b >> 1; } 

 	*r1 = h; *r0 = l;

 	} 

 #endif

 #ifdef THIRTY_TWO_BIT

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

 	{

 	register BN_ULONG h, l, s;

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

 	register 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;

 	} 

 #endif

 #if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)

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

 	{

 	register BN_ULONG h, l, s;

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

 	register 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; */

 	}

 /* 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.

  */

 EXPORT_C 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; }

 	bn_wexpand(r, at->top);

 	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. */

 EXPORT_C int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const unsigned 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;

 		if (d0) z[dN] = (z[dN] << d1) >> d1; /* clear up the top d1 bits */

 		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);

 			tmp_ulong = zz >> d1;

                         if (d0 && tmp_ulong)

                                 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.

  */

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

 	{

 	int ret = 0;

 	const int max = BN_num_bits(p);

 	unsigned int *arr=NULL;

 	bn_check_top(a);

 	bn_check_top(p);

 	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;

 	ret = BN_GF2m_poly2arr(p, arr, max);

 	if (!ret || ret > max)

 		{

 		BNerr(BN_F_BN_GF2M_MOD,BN_R_INVALID_LENGTH);

 		goto err;

 		}

 	ret = BN_GF2m_mod_arr(r, a, arr);

 	bn_check_top(r);

 err:

 	if (arr) OPENSSL_free(arr);

 	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.

  */

 EXPORT_C int	BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned 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.

  */

 EXPORT_C 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);

 	unsigned int *arr=NULL;

 	bn_check_top(a);

 	bn_check_top(b);

 	bn_check_top(p);

 	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;

 	ret = BN_GF2m_poly2arr(p, arr, max);

 	if (!ret || ret > max)

 		{

 		BNerr(BN_F_BN_GF2M_MOD_MUL,BN_R_INVALID_LENGTH);

 		goto err;

 		}

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

 	bn_check_top(r);

 err:

 	if (arr) OPENSSL_free(arr);

 	return ret;

 	}

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

 EXPORT_C int	BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const unsigned 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) return 0;

 	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.

  */

 EXPORT_C 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);

 	unsigned int *arr=NULL;

 	bn_check_top(a);

 	bn_check_top(p);

 	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;

 	ret = BN_GF2m_poly2arr(p, arr, max);

 	if (!ret || ret > max)

 		{

 		BNerr(BN_F_BN_GF2M_MOD_SQR,BN_R_INVALID_LENGTH);

 		goto err;

 		}

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

 	bn_check_top(r);

 err:

 	if (arr) OPENSSL_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".

  */

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

 	{

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

 	int ret = 0;

 	bn_check_top(a);

 	bn_check_top(p);

 	BN_CTX_start(ctx);

 	b = BN_CTX_get(ctx);

 	c = BN_CTX_get(ctx);

 	u = BN_CTX_get(ctx);

 	v = BN_CTX_get(ctx);

 	if (v == NULL) goto err;

 	if (!BN_one(b)) goto err;

 	if (!BN_GF2m_mod(u, a, p)) goto err;

 	if (!BN_copy(v, p)) goto err;

 	if (BN_is_zero(u)) goto err;

 	while (1)

 		{

 		while (!BN_is_odd(u))

 			{

 			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;

 		}

 	if (!BN_copy(r, b)) goto err;

 	bn_check_top(r);

 	ret = 1;

 err:

   	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.

  */

 EXPORT_C int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const unsigned 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.

  */

 EXPORT_C 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);

 	xinv = BN_CTX_get(ctx);

 	if (xinv == 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".

  */

 EXPORT_C 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);

 	a = BN_CTX_get(ctx);

 	b = BN_CTX_get(ctx);

 	u = BN_CTX_get(ctx);

 	v = BN_CTX_get(ctx);

 	if (v == 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.

  */

 EXPORT_C int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx, const unsigned int p[], BN_CTX *ctx)

 	{

 	BIGNUM *field;

 	int ret = 0;

 	bn_check_top(yy);

 	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_div(r, yy, xx, field, ctx);

 	bn_check_top(r);

 err:

 	BN_CTX_end(ctx);

 	return ret;

 	}

 /* Compute the bth power of a, reduce modulo p, and store

  * the result in r.  r could be a.

  * Uses simple square-and-multiply algorithm A.5.1 from IEEE P1363.

  */

 EXPORT_C int	BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const unsigned int p[], BN_CTX *ctx)

 	{

 	int ret = 0, i, n;

 	BIGNUM *u;

 	bn_check_top(a);

 	bn_check_top(b);

 	if (BN_is_zero(b))

 		return(BN_one(r));

 	if (BN_abs_is_word(b, 1))

 		return (BN_copy(r, a) != NULL);

 	BN_CTX_start(ctx);

 	if ((u = BN_CTX_get(ctx)) == NULL) goto err;

 	if (!BN_GF2m_mod_arr(u, a, p)) goto err;

 	n = BN_num_bits(b) - 1;

 	for (i = n - 1; i >= 0; i--)

 		{

 		if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx)) goto err;

 		if (BN_is_bit_set(b, i))

 			{

 			if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx)) goto err;

 			}

 		}

 	if (!BN_copy(r, u)) goto err;

 	bn_check_top(r);

 	ret = 1;

 err:

 	BN_CTX_end(ctx);

 	return ret;

 	}

 /* Compute the bth power of a, reduce modulo p, and store

  * the result in r.  r could be a.

  *

  * This function calls down to the BN_GF2m_mod_exp_arr implementation; this wrapper

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

  * BN_GF2m_mod_exp_arr function.

  */

 EXPORT_C int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *p, BN_CTX *ctx)

 	{

 	int ret = 0;

 	const int max = BN_num_bits(p);

 	unsigned int *arr=NULL;

 	bn_check_top(a);

 	bn_check_top(b);

 	bn_check_top(p);

 	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;

 	ret = BN_GF2m_poly2arr(p, arr, max);

 	if (!ret || ret > max)

 		{

 		BNerr(BN_F_BN_GF2M_MOD_EXP,BN_R_INVALID_LENGTH);

 		goto err;

 		}

 	ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);

 	bn_check_top(r);

 err:

 	if (arr) OPENSSL_free(arr);

 	return ret;

 	}

 /* Compute the square root of a, reduce modulo p, and store

  * the result in r.  r could be a.

  * Uses exponentiation as in algorithm A.4.1 from IEEE P1363.

  */

 EXPORT_C int	BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const unsigned int p[], BN_CTX *ctx)

 	{

 	int ret = 0;

 	BIGNUM *u;

 	bn_check_top(a);

 	if (!p[0])

 		{

 		/* reduction mod 1 => return 0 */

 		BN_zero(r);

 		return 1;

 		}

 	BN_CTX_start(ctx);

 	if ((u = BN_CTX_get(ctx)) == NULL) goto err;

 	if (!BN_set_bit(u, p[0] - 1)) goto err;

 	ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);

 	bn_check_top(r);

 err:

 	BN_CTX_end(ctx);

 	return ret;

 	}

 /* Compute the square root of a, reduce modulo p, and store

  * the result in r.  r could be a.

  *

  * This function calls down to the BN_GF2m_mod_sqrt_arr implementation; this wrapper

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

  * BN_GF2m_mod_sqrt_arr function.

  */

 EXPORT_C int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)

 	{

 	int ret = 0;

 	const int max = BN_num_bits(p);

 	unsigned int *arr=NULL;

 	bn_check_top(a);

 	bn_check_top(p);

 	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) * max)) == NULL) goto err;

 	ret = BN_GF2m_poly2arr(p, arr, max);

 	if (!ret || ret > max)

 		{

 		BNerr(BN_F_BN_GF2M_MOD_SQRT,BN_R_INVALID_LENGTH);

 		goto err;

 		}

 	ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);

 	bn_check_top(r);

 err:

 	if (arr) OPENSSL_free(arr);

 	return ret;

 	}

 /* Find r such that r^2 + r = a mod p.  r could be a. If no r exists returns 0.

  * Uses algorithms A.4.7 and A.4.6 from IEEE P1363.

  */

 EXPORT_C int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const unsigned int p[], BN_CTX *ctx)

 	{

 	int ret = 0, count = 0;

 	unsigned int j;

 	BIGNUM *a, *z, *rho, *w, *w2, *tmp;

 	bn_check_top(a_);

 	if (!p[0])

 		{

 		/* reduction mod 1 => return 0 */

 		BN_zero(r);

 		return 1;

 		}

 	BN_CTX_start(ctx);

 	a = BN_CTX_get(ctx);

 	z = BN_CTX_get(ctx);

 	w = BN_CTX_get(ctx);

 	if (w == NULL) goto err;

 	if (!BN_GF2m_mod_arr(a, a_, p)) goto err;

 	if (BN_is_zero(a))

 		{

 		BN_zero(r);

 		ret = 1;

 		goto err;

 		}

 	if (p[0] & 0x1) /* m is odd */

 		{

 		/* compute half-trace of a */

 		if (!BN_copy(z, a)) goto err;

 		for (j = 1; j <= (p[0] - 1) / 2; j++)

 			{

 			if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;

 			if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;

 			if (!BN_GF2m_add(z, z, a)) goto err;

 			}

 		}

 	else /* m is even */

 		{

 		rho = BN_CTX_get(ctx);

 		w2 = BN_CTX_get(ctx);

 		tmp = BN_CTX_get(ctx);

 		if (tmp == NULL) goto err;

 		do

 			{

 			if (!BN_rand(rho, p[0], 0, 0)) goto err;

 			if (!BN_GF2m_mod_arr(rho, rho, p)) goto err;

 			BN_zero(z);

 			if (!BN_copy(w, rho)) goto err;

 			for (j = 1; j <= p[0] - 1; j++)

 				{

 				if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx)) goto err;

 				if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx)) goto err;

 				if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx)) goto err;

 				if (!BN_GF2m_add(z, z, tmp)) goto err;

 				if (!BN_GF2m_add(w, w2, rho)) goto err;

 				}

 			count++;

 			} while (BN_is_zero(w) && (count < MAX_ITERATIONS));

 		if (BN_is_zero(w))

 			{

 			BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR,BN_R_TOO_MANY_ITERATIONS);

 			goto err;

 			}

 		}

 	if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx)) goto err;

 	if (!BN_GF2m_add(w, z, w)) goto err;

 	if (BN_GF2m_cmp(w, a))

 		{

 		BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD_ARR, BN_R_NO_SOLUTION);

 		goto err;

 		}

 	if (!BN_copy(r, z)) goto err;

 	bn_check_top(r);

 	ret = 1;

 err:

 	BN_CTX_end(ctx);

 	return ret;

 	}

 /* Find r such that r^2 + r = a mod p.  r could be a. If no r exists returns 0.

  *

  * This function calls down to the BN_GF2m_mod_solve_quad_arr implementation; this wrapper

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

  * BN_GF2m_mod_solve_quad_arr function.

  */

 EXPORT_C int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)

 	{

 	int ret = 0;

 	const int max = BN_num_bits(p);

 	unsigned int *arr=NULL;

 	bn_check_top(a);

 	bn_check_top(p);

 	if ((arr = (unsigned int *)OPENSSL_malloc(sizeof(unsigned int) *

 						max)) == NULL) goto err;

 	ret = BN_GF2m_poly2arr(p, arr, max);

 	if (!ret || ret > max)

 		{

 		BNerr(BN_F_BN_GF2M_MOD_SOLVE_QUAD,BN_R_INVALID_LENGTH);

 		goto err;

 		}

 	ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);

 	bn_check_top(r);

 err:

 	if (arr) OPENSSL_free(arr);

 	return ret;

 	}

 /* Convert the bit-string representation of a polynomial

  * ( \sum_{i=0}^n a_i * x^i , where a_0 is *not* zero) into an array

  * of integers corresponding to the bits with non-zero coefficient.

  * Up to max elements of the array will be filled.  Return value is total

  * number of coefficients that would be extracted if array was large enough.

  */

 EXPORT_C int BN_GF2m_poly2arr(const BIGNUM *a, unsigned int p[], int max)

 	{

 	int i, j, k = 0;

 	BN_ULONG mask;

 	if (BN_is_zero(a) || !BN_is_bit_set(a, 0))

 		/* a_0 == 0 => return error (the unsigned int array

 		 * must be terminated by 0)

 		 */

 		return 0;

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

 		{

 		if (!a->d[i])

 			/* skip word if a->d[i] == 0 */

 			continue;

 		mask = BN_TBIT;

 		for (j = BN_BITS2 - 1; j >= 0; j--)

 			{

 			if (a->d[i] & mask) 

 				{

 				if (k < max) p[k] = BN_BITS2 * i + j;

 				k++;

 				}

 			mask >>= 1;

 			}

 		}

 	return k;

 	}

 /* Convert the coefficient array representation of a polynomial to a 

  * bit-string.  The array must be terminated by 0.

  */

 EXPORT_C int BN_GF2m_arr2poly(const unsigned int p[], BIGNUM *a)

 	{

 	int i;

 	bn_check_top(a);

 	BN_zero(a);

 	for (i = 0; p[i] != 0; i++)

 		{

   		if (BN_set_bit(a, p[i]) == 0)

 			return 0;

 		}

 	BN_set_bit(a, 0);

 	bn_check_top(a);

 	return 1;

 	}