/* $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);
        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.
 */
int
BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const 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.
 */
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) + 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_exp_arr(r, a, b, arr, ctx);
        bn_check_top(r);

err:
        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.
 */
int
BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const 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.
 */
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) + 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_sqrt_arr(r, a, arr, ctx);
        bn_check_top(r);

err:
        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.
 */
int
BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[],
    BN_CTX *ctx)
{
        int ret = 0, count = 0, 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);
        if ((a = BN_CTX_get(ctx)) == NULL)
                goto err;
        if ((z = BN_CTX_get(ctx)) == NULL)
                goto err;
        if ((w = BN_CTX_get(ctx)) == 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 */
        {
                if ((rho = BN_CTX_get(ctx)) == NULL)
                        goto err;
                if ((w2 = BN_CTX_get(ctx)) == NULL)
                        goto err;
                if ((tmp = BN_CTX_get(ctx)) == 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)) {
                        BNerror(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)) {
                BNerror(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.
 */
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) + 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_solve_quad_arr(r, a, arr, ctx);
        bn_check_top(r);

err:
        free(arr);
        return ret;
}

/* Convert the bit-string representation of a polynomial
 * ( \sum_{i=0}^n a_i * x^i) into an array of integers corresponding
 * to the bits with non-zero coefficient.  Array is terminated with -1.
 * Up to max elements of the array will be filled.  Return value is total
 * number of array elements that would be filled if array was large enough.
 */
int
BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
{
        int i, j, k = 0;
        BN_ULONG mask;

        if (BN_is_zero(a))
                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;
                }
        }

        if (k < max) {
                p[k] = -1;
                k++;
        }

        return k;
}

/* Convert the coefficient array representation of a polynomial to a
 * bit-string.  The array must be terminated by -1.
 */
int
BN_GF2m_arr2poly(const int p[], BIGNUM *a)
{
        int i;

        bn_check_top(a);
        BN_zero(a);
        for (i = 0; p[i] != -1; i++) {
                if (BN_set_bit(a, p[i]) == 0)
                        return 0;
        }
        bn_check_top(a);

        return 1;
}

#endif