crypto/bn/rsaz_exp.c - third_party/openssl - Git at Google

 /*****************************************************************************
 *                                                                            *
 *  Copyright (c) 2012, Intel Corporation                                     *
 *                                                                            *
 *  All rights reserved.                                                      *
 *                                                                            *
 *  Redistribution and use in source and binary forms, with or without        *
 *  modification, are permitted provided that the following conditions are    *
 *  met:                                                                      *
 *                                                                            *
 *  *  Redistributions of source code must retain the above copyright         *
 *     notice, this list of conditions and the following disclaimer.          *
 *                                                                            *
 *  *  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.                                                          *
 *                                                                            *
 *  *  Neither the name of the Intel Corporation nor the names of its         *
 *     contributors may be used to endorse or promote products derived from   *
 *     this software without specific prior written permission.               *
 *                                                                            *
 *                                                                            *
 *  THIS SOFTWARE IS PROVIDED BY INTEL CORPORATION ""AS IS"" AND ANY          *
 *  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE         *
 *  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR        *
 *  PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL CORPORATION OR            *
 *  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,     *
 *  EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,       *
 *  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR        *
 *  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF    *
 *  LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING      *
 *  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS        *
 *  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              *
 *                                                                            *
 ******************************************************************************
 * Developers and authors:                                                    *
 * Shay Gueron (1, 2), and Vlad Krasnov (1)                                   *
 * (1) Intel Corporation, Israel Development Center, Haifa, Israel            *
 * (2) University of Haifa, Israel                                            *
 *****************************************************************************/

 #include "rsaz_exp.h"

 /*
  * See crypto/bn/asm/rsaz-avx2.pl for further details.
  */
 void rsaz_1024_norm2red_avx2(void *red, const void *norm);
 void rsaz_1024_mul_avx2(void *ret, const void *a, const void *b,
                         const void *n, BN_ULONG k);
 void rsaz_1024_sqr_avx2(void *ret, const void *a, const void *n, BN_ULONG k,
                         int cnt);
 void rsaz_1024_scatter5_avx2(void *tbl, const void *val, int i);
 void rsaz_1024_gather5_avx2(void *val, const void *tbl, int i);
 void rsaz_1024_red2norm_avx2(void *norm, const void *red);

 #if defined(__GNUC__)
 # define ALIGN64        __attribute__((aligned(64)))
 #elif defined(_MSC_VER)
 # define ALIGN64        __declspec(align(64))
 #elif defined(__SUNPRO_C)
 # define ALIGN64
 # pragma align 64(one,two80)
 #else
 /* not fatal, might hurt performance a little */
 # define ALIGN64
 #endif

 ALIGN64 static const BN_ULONG one[40] = {
     1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
 };

 ALIGN64 static const BN_ULONG two80[40] = {
     0, 0, 1 << 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
 };

 void RSAZ_1024_mod_exp_avx2(BN_ULONG result_norm[16],
                             const BN_ULONG base_norm[16],
                             const BN_ULONG exponent[16],
                             const BN_ULONG m_norm[16], const BN_ULONG RR[16],
                             BN_ULONG k0)
 {
     unsigned char storage[320 * 3 + 32 * 9 * 16 + 64]; /* 5.5KB */
     unsigned char *p_str = storage + (64 - ((size_t)storage % 64));
     unsigned char *a_inv, *m, *result;
     unsigned char *table_s = p_str + 320 * 3;
     unsigned char *R2 = table_s; /* borrow */
     int index;
     int wvalue;

     if ((((size_t)p_str & 4095) + 320) >> 12) {
         result = p_str;
         a_inv = p_str + 320;
         m = p_str + 320 * 2;    /* should not cross page */
     } else {
         m = p_str;              /* should not cross page */
         result = p_str + 320;
         a_inv = p_str + 320 * 2;
     }

     rsaz_1024_norm2red_avx2(m, m_norm);
     rsaz_1024_norm2red_avx2(a_inv, base_norm);
     rsaz_1024_norm2red_avx2(R2, RR);

     rsaz_1024_mul_avx2(R2, R2, R2, m, k0);
     rsaz_1024_mul_avx2(R2, R2, two80, m, k0);

     /* table[0] = 1 */
     rsaz_1024_mul_avx2(result, R2, one, m, k0);
     /* table[1] = a_inv^1 */
     rsaz_1024_mul_avx2(a_inv, a_inv, R2, m, k0);

     rsaz_1024_scatter5_avx2(table_s, result, 0);
     rsaz_1024_scatter5_avx2(table_s, a_inv, 1);

     /* table[2] = a_inv^2 */
     rsaz_1024_sqr_avx2(result, a_inv, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 2);
 #if 0
     /* this is almost 2x smaller and less than 1% slower */
     for (index = 3; index < 32; index++) {
         rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
         rsaz_1024_scatter5_avx2(table_s, result, index);
     }
 #else
     /* table[4] = a_inv^4 */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 4);
     /* table[8] = a_inv^8 */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 8);
     /* table[16] = a_inv^16 */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 16);
     /* table[17] = a_inv^17 */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 17);

     /* table[3] */
     rsaz_1024_gather5_avx2(result, table_s, 2);
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 3);
     /* table[6] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 6);
     /* table[12] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 12);
     /* table[24] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 24);
     /* table[25] */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 25);

     /* table[5] */
     rsaz_1024_gather5_avx2(result, table_s, 4);
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 5);
     /* table[10] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 10);
     /* table[20] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 20);
     /* table[21] */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 21);

     /* table[7] */
     rsaz_1024_gather5_avx2(result, table_s, 6);
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 7);
     /* table[14] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 14);
     /* table[28] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 28);
     /* table[29] */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 29);

     /* table[9] */
     rsaz_1024_gather5_avx2(result, table_s, 8);
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 9);
     /* table[18] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 18);
     /* table[19] */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 19);

     /* table[11] */
     rsaz_1024_gather5_avx2(result, table_s, 10);
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 11);
     /* table[22] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 22);
     /* table[23] */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 23);

     /* table[13] */
     rsaz_1024_gather5_avx2(result, table_s, 12);
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 13);
     /* table[26] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 26);
     /* table[27] */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 27);

     /* table[15] */
     rsaz_1024_gather5_avx2(result, table_s, 14);
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 15);
     /* table[30] */
     rsaz_1024_sqr_avx2(result, result, m, k0, 1);
     rsaz_1024_scatter5_avx2(table_s, result, 30);
     /* table[31] */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     rsaz_1024_scatter5_avx2(table_s, result, 31);
 #endif

     /* load first window */
     p_str = (unsigned char *)exponent;
     wvalue = p_str[127] >> 3;
     rsaz_1024_gather5_avx2(result, table_s, wvalue);

     index = 1014;

     while (index > -1) {        /* loop for the remaining 127 windows */

         rsaz_1024_sqr_avx2(result, result, m, k0, 5);

         wvalue = *((unsigned short *)&p_str[index / 8]);
         wvalue = (wvalue >> (index % 8)) & 31;
         index -= 5;

         rsaz_1024_gather5_avx2(a_inv, table_s, wvalue); /* borrow a_inv */
         rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
     }

     /* square four times */
     rsaz_1024_sqr_avx2(result, result, m, k0, 4);

     wvalue = p_str[0] & 15;

     rsaz_1024_gather5_avx2(a_inv, table_s, wvalue); /* borrow a_inv */
     rsaz_1024_mul_avx2(result, result, a_inv, m, k0);

     /* from Montgomery */
     rsaz_1024_mul_avx2(result, result, one, m, k0);

     rsaz_1024_red2norm_avx2(result_norm, result);

     OPENSSL_cleanse(storage, sizeof(storage));
 }

 /*
  * See crypto/bn/rsaz-x86_64.pl for further details.
  */
 void rsaz_512_mul(void *ret, const void *a, const void *b, const void *n,
                   BN_ULONG k);
 void rsaz_512_mul_scatter4(void *ret, const void *a, const void *n,
                            BN_ULONG k, const void *tbl, unsigned int power);
 void rsaz_512_mul_gather4(void *ret, const void *a, const void *tbl,
                           const void *n, BN_ULONG k, unsigned int power);
 void rsaz_512_mul_by_one(void *ret, const void *a, const void *n, BN_ULONG k);
 void rsaz_512_sqr(void *ret, const void *a, const void *n, BN_ULONG k,
                   int cnt);
 void rsaz_512_scatter4(void *tbl, const BN_ULONG *val, int power);
 void rsaz_512_gather4(BN_ULONG *val, const void *tbl, int power);

 void RSAZ_512_mod_exp(BN_ULONG result[8],
                       const BN_ULONG base[8], const BN_ULONG exponent[8],
                       const BN_ULONG m[8], BN_ULONG k0, const BN_ULONG RR[8])
 {
     unsigned char storage[16 * 8 * 8 + 64 * 2 + 64]; /* 1.2KB */
     unsigned char *table = storage + (64 - ((size_t)storage % 64));
     BN_ULONG *a_inv = (BN_ULONG *)(table + 16 * 8 * 8);
     BN_ULONG *temp = (BN_ULONG *)(table + 16 * 8 * 8 + 8 * 8);
     unsigned char *p_str = (unsigned char *)exponent;
     int index;
     unsigned int wvalue;

     /* table[0] = 1_inv */
     temp[0] = 0 - m[0];
     temp[1] = ~m[1];
     temp[2] = ~m[2];
     temp[3] = ~m[3];
     temp[4] = ~m[4];
     temp[5] = ~m[5];
     temp[6] = ~m[6];
     temp[7] = ~m[7];
     rsaz_512_scatter4(table, temp, 0);

     /* table [1] = a_inv^1 */
     rsaz_512_mul(a_inv, base, RR, m, k0);
     rsaz_512_scatter4(table, a_inv, 1);

     /* table [2] = a_inv^2 */
     rsaz_512_sqr(temp, a_inv, m, k0, 1);
     rsaz_512_scatter4(table, temp, 2);

     for (index = 3; index < 16; index++)
         rsaz_512_mul_scatter4(temp, a_inv, m, k0, table, index);

     /* load first window */
     wvalue = p_str[63];

     rsaz_512_gather4(temp, table, wvalue >> 4);
     rsaz_512_sqr(temp, temp, m, k0, 4);
     rsaz_512_mul_gather4(temp, temp, table, m, k0, wvalue & 0xf);

     for (index = 62; index >= 0; index--) {
         wvalue = p_str[index];

         rsaz_512_sqr(temp, temp, m, k0, 4);
         rsaz_512_mul_gather4(temp, temp, table, m, k0, wvalue >> 4);

         rsaz_512_sqr(temp, temp, m, k0, 4);
         rsaz_512_mul_gather4(temp, temp, table, m, k0, wvalue & 0x0f);
     }

     /* from Montgomery */
     rsaz_512_mul_by_one(result, temp, m, k0);

     OPENSSL_cleanse(storage, sizeof(storage));
 }
	/*****************************************************************************
	* *
	* Copyright (c) 2012, Intel Corporation *
	* *
	* All rights reserved. *
	* *
	* Redistribution and use in source and binary forms, with or without *
	* modification, are permitted provided that the following conditions are *
	* met: *
	* *
	* * Redistributions of source code must retain the above copyright *
	* notice, this list of conditions and the following disclaimer. *
	* *
	* * 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. *
	* *
	* * Neither the name of the Intel Corporation nor the names of its *
	* contributors may be used to endorse or promote products derived from *
	* this software without specific prior written permission. *
	* *
	* *
	* THIS SOFTWARE IS PROVIDED BY INTEL CORPORATION ""AS IS"" AND ANY *
	* EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE *
	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR *
	* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL CORPORATION OR *
	* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, *
	* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, *
	* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR *
	* PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF *
	* LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING *
	* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS *
	* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. *
	* *
	******************************************************************************
	* Developers and authors: *
	* Shay Gueron (1, 2), and Vlad Krasnov (1) *
	* (1) Intel Corporation, Israel Development Center, Haifa, Israel *
	* (2) University of Haifa, Israel *
	*****************************************************************************/

	#include "rsaz_exp.h"

	/*
	* See crypto/bn/asm/rsaz-avx2.pl for further details.
	*/
	void rsaz_1024_norm2red_avx2(void red, const void norm);
	void rsaz_1024_mul_avx2(void ret, const void a, const void *b,
	const void *n, BN_ULONG k);
	void rsaz_1024_sqr_avx2(void ret, const void a, const void *n, BN_ULONG k,
	int cnt);
	void rsaz_1024_scatter5_avx2(void tbl, const void val, int i);
	void rsaz_1024_gather5_avx2(void val, const void tbl, int i);
	void rsaz_1024_red2norm_avx2(void norm, const void red);

	#if defined(__GNUC__)
	# define ALIGN64 __attribute__((aligned(64)))
	#elif defined(_MSC_VER)
	# define ALIGN64 __declspec(align(64))
	#elif defined(__SUNPRO_C)
	# define ALIGN64
	# pragma align 64(one,two80)
	#else
	/* not fatal, might hurt performance a little */
	# define ALIGN64
	#endif

	ALIGN64 static const BN_ULONG one[40] = {
	1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
	};

	ALIGN64 static const BN_ULONG two80[40] = {
	0, 0, 1 << 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
	};

	void RSAZ_1024_mod_exp_avx2(BN_ULONG result_norm[16],
	const BN_ULONG base_norm[16],
	const BN_ULONG exponent[16],
	const BN_ULONG m_norm[16], const BN_ULONG RR[16],
	BN_ULONG k0)
	{
	unsigned char storage[320 * 3 + 32 * 9 * 16 + 64]; /* 5.5KB */
	unsigned char *p_str = storage + (64 - ((size_t)storage % 64));
	unsigned char a_inv, m, *result;
	unsigned char table_s = p_str + 320 3;
	unsigned char R2 = table_s; / borrow */
	int index;
	int wvalue;

	if ((((size_t)p_str & 4095) + 320) >> 12) {
	result = p_str;
	a_inv = p_str + 320;
	m = p_str + 320 * 2; /* should not cross page */
	} else {
	m = p_str; /* should not cross page */
	result = p_str + 320;
	a_inv = p_str + 320 * 2;
	}

	rsaz_1024_norm2red_avx2(m, m_norm);
	rsaz_1024_norm2red_avx2(a_inv, base_norm);
	rsaz_1024_norm2red_avx2(R2, RR);

	rsaz_1024_mul_avx2(R2, R2, R2, m, k0);
	rsaz_1024_mul_avx2(R2, R2, two80, m, k0);

	/* table[0] = 1 */
	rsaz_1024_mul_avx2(result, R2, one, m, k0);
	/* table[1] = a_inv^1 */
	rsaz_1024_mul_avx2(a_inv, a_inv, R2, m, k0);

	rsaz_1024_scatter5_avx2(table_s, result, 0);
	rsaz_1024_scatter5_avx2(table_s, a_inv, 1);

	/* table[2] = a_inv^2 */
	rsaz_1024_sqr_avx2(result, a_inv, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 2);
	#if 0
	/* this is almost 2x smaller and less than 1% slower */
	for (index = 3; index < 32; index++) {
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, index);
	}
	#else
	/* table[4] = a_inv^4 */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 4);
	/* table[8] = a_inv^8 */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 8);
	/* table[16] = a_inv^16 */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 16);
	/* table[17] = a_inv^17 */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 17);

	/* table[3] */
	rsaz_1024_gather5_avx2(result, table_s, 2);
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 3);
	/* table[6] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 6);
	/* table[12] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 12);
	/* table[24] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 24);
	/* table[25] */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 25);

	/* table[5] */
	rsaz_1024_gather5_avx2(result, table_s, 4);
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 5);
	/* table[10] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 10);
	/* table[20] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 20);
	/* table[21] */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 21);

	/* table[7] */
	rsaz_1024_gather5_avx2(result, table_s, 6);
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 7);
	/* table[14] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 14);
	/* table[28] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 28);
	/* table[29] */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 29);

	/* table[9] */
	rsaz_1024_gather5_avx2(result, table_s, 8);
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 9);
	/* table[18] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 18);
	/* table[19] */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 19);

	/* table[11] */
	rsaz_1024_gather5_avx2(result, table_s, 10);
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 11);
	/* table[22] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 22);
	/* table[23] */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 23);

	/* table[13] */
	rsaz_1024_gather5_avx2(result, table_s, 12);
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 13);
	/* table[26] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 26);
	/* table[27] */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 27);

	/* table[15] */
	rsaz_1024_gather5_avx2(result, table_s, 14);
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 15);
	/* table[30] */
	rsaz_1024_sqr_avx2(result, result, m, k0, 1);
	rsaz_1024_scatter5_avx2(table_s, result, 30);
	/* table[31] */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	rsaz_1024_scatter5_avx2(table_s, result, 31);
	#endif

	/* load first window */
	p_str = (unsigned char *)exponent;
	wvalue = p_str[127] >> 3;
	rsaz_1024_gather5_avx2(result, table_s, wvalue);

	index = 1014;

	while (index > -1) { /* loop for the remaining 127 windows */

	rsaz_1024_sqr_avx2(result, result, m, k0, 5);

	wvalue = ((unsigned short )&p_str[index / 8]);
	wvalue = (wvalue >> (index % 8)) & 31;
	index -= 5;

	rsaz_1024_gather5_avx2(a_inv, table_s, wvalue); /* borrow a_inv */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);
	}

	/* square four times */
	rsaz_1024_sqr_avx2(result, result, m, k0, 4);

	wvalue = p_str[0] & 15;

	rsaz_1024_gather5_avx2(a_inv, table_s, wvalue); /* borrow a_inv */
	rsaz_1024_mul_avx2(result, result, a_inv, m, k0);

	/* from Montgomery */
	rsaz_1024_mul_avx2(result, result, one, m, k0);

	rsaz_1024_red2norm_avx2(result_norm, result);

	OPENSSL_cleanse(storage, sizeof(storage));
	}

	/*
	* See crypto/bn/rsaz-x86_64.pl for further details.
	*/
	void rsaz_512_mul(void ret, const void a, const void b, const void n,
	BN_ULONG k);
	void rsaz_512_mul_scatter4(void ret, const void a, const void *n,
	BN_ULONG k, const void *tbl, unsigned int power);
	void rsaz_512_mul_gather4(void ret, const void a, const void *tbl,
	const void *n, BN_ULONG k, unsigned int power);
	void rsaz_512_mul_by_one(void ret, const void a, const void *n, BN_ULONG k);
	void rsaz_512_sqr(void ret, const void a, const void *n, BN_ULONG k,
	int cnt);
	void rsaz_512_scatter4(void tbl, const BN_ULONG val, int power);
	void rsaz_512_gather4(BN_ULONG val, const void tbl, int power);

	void RSAZ_512_mod_exp(BN_ULONG result[8],
	const BN_ULONG base[8], const BN_ULONG exponent[8],
	const BN_ULONG m[8], BN_ULONG k0, const BN_ULONG RR[8])
	{
	unsigned char storage[16 * 8 * 8 + 64 * 2 + 64]; /* 1.2KB */
	unsigned char *table = storage + (64 - ((size_t)storage % 64));
	BN_ULONG a_inv = (BN_ULONG )(table + 16 * 8 * 8);
	BN_ULONG temp = (BN_ULONG )(table + 16 * 8 * 8 + 8 * 8);
	unsigned char p_str = (unsigned char )exponent;
	int index;
	unsigned int wvalue;

	/* table[0] = 1_inv */
	temp[0] = 0 - m[0];
	temp[1] = ~m[1];
	temp[2] = ~m[2];
	temp[3] = ~m[3];
	temp[4] = ~m[4];
	temp[5] = ~m[5];
	temp[6] = ~m[6];
	temp[7] = ~m[7];
	rsaz_512_scatter4(table, temp, 0);

	/* table [1] = a_inv^1 */
	rsaz_512_mul(a_inv, base, RR, m, k0);
	rsaz_512_scatter4(table, a_inv, 1);

	/* table [2] = a_inv^2 */
	rsaz_512_sqr(temp, a_inv, m, k0, 1);
	rsaz_512_scatter4(table, temp, 2);

	for (index = 3; index < 16; index++)
	rsaz_512_mul_scatter4(temp, a_inv, m, k0, table, index);

	/* load first window */
	wvalue = p_str[63];

	rsaz_512_gather4(temp, table, wvalue >> 4);
	rsaz_512_sqr(temp, temp, m, k0, 4);
	rsaz_512_mul_gather4(temp, temp, table, m, k0, wvalue & 0xf);

	for (index = 62; index >= 0; index--) {
	wvalue = p_str[index];

	rsaz_512_sqr(temp, temp, m, k0, 4);
	rsaz_512_mul_gather4(temp, temp, table, m, k0, wvalue >> 4);

	rsaz_512_sqr(temp, temp, m, k0, 4);
	rsaz_512_mul_gather4(temp, temp, table, m, k0, wvalue & 0x0f);
	}

	/* from Montgomery */
	rsaz_512_mul_by_one(result, temp, m, k0);

	OPENSSL_cleanse(storage, sizeof(storage));
	}