luna - wolfssl/wolfcrypt/src/sp

   1/* sp_cdsp_signed.c
   2 *
   3 * Copyright (C) 2006-2026 wolfSSL Inc.
   4 *
   5 * This file is part of wolfSSL.
   6 *
   7 * wolfSSL is free software; you can redistribute it and/or modify
   8 * it under the terms of the GNU General Public License as published by
   9 * the Free Software Foundation; either version 3 of the License, or
  10 * (at your option) any later version.
  11 *
  12 * wolfSSL is distributed in the hope that it will be useful,
  13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15 * GNU General Public License for more details.
  16 *
  17 * You should have received a copy of the GNU General Public License
  18 * along with this program; if not, write to the Free Software
  19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
  20 */
  21
  22#include <wolfssl/wolfcrypt/libwolfssl_sources.h>
  23
  24/* from wolfcrypt/src/sp_c32.c */
  25
  26#include <wolfssl/wolfcrypt/cpuid.h>
  27#ifdef NO_INLINE
  28    #include <wolfssl/wolfcrypt/misc.h>
  29#else
  30    #define WOLFSSL_MISC_INCLUDED
  31    #include <wolfcrypt/src/misc.c>
  32#endif
  33
  34#if defined(WOLFSSL_HAVE_SP_ECC)
  35#ifdef WOLFSSL_DSP
  36
  37#include <wolfssl/wolfcrypt/sp.h>
  38#include "remote.h"
  39#include "hexagon_protos.h"
  40#include "hexagon_types.h"
  41
  42#if (!defined(WC_NO_CACHE_RESISTANT) || defined(WOLFSSL_SP_SMALL)) && \
  43             (defined(WOLFSSL_HAVE_SP_ECC) || !defined(WOLFSSL_RSA_PUBLIC_ONLY))
  44/* Mask for address to obfuscate which of the two address will be used. */
  45static const size_t addr_mask[2] = { 0, (size_t)-1 };
  46#endif
  47
  48#ifdef WOLFSSL_HAVE_SP_ECC
  49#ifndef WOLFSSL_SP_NO_256
  50
  51/* Point structure to use. */
  52typedef struct sp_point {
  53    sp_digit x[2 * 10] __attribute__((aligned(128)));
  54    sp_digit y[2 * 10] __attribute__((aligned(128)));
  55    sp_digit z[2 * 10] __attribute__((aligned(128)));
  56    int infinity;
  57} sp_point;
  58
  59/* The modulus (prime) of the curve P256. */
  60static const sp_digit p256_mod[10] __attribute__((aligned(128))) = {
  61    0x3ffffff,0x3ffffff,0x3ffffff,0x003ffff,0x0000000,0x0000000,0x0000000,
  62    0x0000400,0x3ff0000,0x03fffff
  63};
  64#ifndef WOLFSSL_SP_SMALL
  65/* The Montgomery normalizer for modulus of the curve P256. */
  66static const sp_digit p256_norm_mod[10] __attribute__((aligned(128))) = {
  67    0x0000001,0x0000000,0x0000000,0x3fc0000,0x3ffffff,0x3ffffff,0x3ffffff,
  68    0x3fffbff,0x000ffff,0x0000000
  69};
  70#endif /* WOLFSSL_SP_SMALL */
  71/* The Montgomery multiplier for modulus of the curve P256. */
  72static const sp_digit p256_mp_mod __attribute__((aligned(128))) = 0x000001;
  73#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || defined(HAVE_ECC_SIGN) || \
  74                                            defined(HAVE_ECC_VERIFY)
  75/* The order of the curve P256. */
  76static const sp_digit p256_order[10] __attribute__((aligned(128))) = {
  77    0x0632551,0x272b0bf,0x1e84f3b,0x2b69c5e,0x3bce6fa,0x3ffffff,0x3ffffff,
  78    0x00003ff,0x3ff0000,0x03fffff
  79};
  80#endif
  81#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
  82/* The Montgomery normalizer for order of the curve P256. */
  83static const sp_digit p256_norm_order[10] __attribute__((aligned(128))) = {
  84    0x39cdaaf,0x18d4f40,0x217b0c4,0x14963a1,0x0431905,0x0000000,0x0000000,
  85    0x3fffc00,0x000ffff,0x0000000
  86};
  87#endif
  88#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
  89/* The Montgomery multiplier for order of the curve P256. */
  90static const sp_digit p256_mp_order __attribute__((aligned(128))) = 0x200bc4f;
  91#endif
  92/* The base point of curve P256. */
  93static const sp_point p256_base __attribute__((aligned(128))) = {
  94    /* X ordinate */
  95    {
  96        0x098c296,0x04e5176,0x33a0f4a,0x204b7ac,0x277037d,0x0e9103c,0x3ce6e56,
  97        0x1091fe2,0x1f2e12c,0x01ac5f4, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
  98    },
  99    /* Y ordinate */
 100    {
 101        0x3bf51f5,0x1901a0d,0x1ececbb,0x15dacc5,0x22bce33,0x303e785,0x27eb4a7,
 102        0x1fe6e3b,0x2e2fe1a,0x013f8d0, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
 103    },
 104    /* Z ordinate */
 105    {
 106        0x0000001,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,
 107        0x0000000,0x0000000,0x0000000, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L
 108    },
 109    /* infinity */
 110    0
 111};
 112
 113static int sp_ecc_point_new_ex(void* heap, sp_point* sp, sp_point** p)
 114{
 115    int ret = MP_OKAY;
 116
 117    if (p == NULL) {
 118        ret = MEMORY_E;
 119    } else {
 120#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
 121        (void)sp;
 122        *p = (sp_point*)XMALLOC(sizeof(sp_point), heap, DYNAMIC_TYPE_ECC);
 123        if (*p == NULL) {
 124            ret = MEMORY_E;
 125        }
 126#else
 127        (void)heap;
 128        if (sp == NULL) {
 129            ret = MEMORY_E;
 130        } else {
 131            *p = sp;
 132        }
 133#endif
 134    }
 135
 136    return ret;
 137}
 138
 139#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
 140/* Allocate memory for point and return error. */
 141#define sp_ecc_point_new(heap, sp, p) sp_ecc_point_new_ex((heap), NULL, &(p))
 142#else
 143/* Set pointer to data and return no error. */
 144#define sp_ecc_point_new(heap, sp, p) sp_ecc_point_new_ex((heap), &(sp), &(p))
 145#endif
 146
 147
 148static void sp_ecc_point_free(sp_point* p, int clear, void* heap)
 149{
 150#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
 151/* If valid pointer then clear point data if requested and free data. */
 152    if (p != NULL) {
 153        if (clear != 0) {
 154            XMEMSET(p, 0, sizeof(*p));
 155        }
 156        XFREE(p, heap, DYNAMIC_TYPE_ECC);
 157    }
 158#else
 159/* Clear point data if requested. */
 160    if (clear != 0) {
 161        XMEMSET(p, 0, sizeof(*p));
 162    }
 163#endif
 164    (void)heap;
 165}
 166
 167/* Multiply a number by Montgomery normalizer mod modulus (prime).
 168 *
 169 * r  The resulting Montgomery form number.
 170 * a  The number to convert.
 171 * m  The modulus (prime).
 172 * returns MEMORY_E when memory allocation fails and MP_OKAY otherwise.
 173 */
 174static int sp_256_mod_mul_norm_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
 175{
 176#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
 177    int64_t* td;
 178#else
 179    int64_t td[8];
 180    int64_t a32d[8];
 181#endif
 182    int64_t* t;
 183    int64_t* a32;
 184    int64_t o;
 185    int err = MP_OKAY;
 186
 187    (void)m;
 188
 189#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
 190    td = (int64_t*)XMALLOC(sizeof(int64_t) * 2 * 8, NULL, DYNAMIC_TYPE_ECC);
 191    if (td == NULL) {
 192        err = MEMORY_E;
 193    }
 194#endif
 195
 196    if (err == MP_OKAY) {
 197#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
 198        t = td;
 199        a32 = td + 8;
 200#else
 201        t = td;
 202        a32 = a32d;
 203#endif
 204
 205        a32[0] = a[0];
 206        a32[0] |= a[1] << 26U;
 207        a32[0] &= 0xffffffffL;
 208        a32[1] = (sp_digit)(a[1] >> 6);
 209        a32[1] |= a[2] << 20U;
 210        a32[1] &= 0xffffffffL;
 211        a32[2] = (sp_digit)(a[2] >> 12);
 212        a32[2] |= a[3] << 14U;
 213        a32[2] &= 0xffffffffL;
 214        a32[3] = (sp_digit)(a[3] >> 18);
 215        a32[3] |= a[4] << 8U;
 216        a32[3] &= 0xffffffffL;
 217        a32[4] = (sp_digit)(a[4] >> 24);
 218        a32[4] |= a[5] << 2U;
 219        a32[4] |= a[6] << 28U;
 220        a32[4] &= 0xffffffffL;
 221        a32[5] = (sp_digit)(a[6] >> 4);
 222        a32[5] |= a[7] << 22U;
 223        a32[5] &= 0xffffffffL;
 224        a32[6] = (sp_digit)(a[7] >> 10);
 225        a32[6] |= a[8] << 16U;
 226        a32[6] &= 0xffffffffL;
 227        a32[7] = (sp_digit)(a[8] >> 16);
 228        a32[7] |= a[9] << 10U;
 229        a32[7] &= 0xffffffffL;
 230
 231        /*  1  1  0 -1 -1 -1 -1  0 */
 232        t[0] = 0 + a32[0] + a32[1] - a32[3] - a32[4] - a32[5] - a32[6];
 233        /*  0  1  1  0 -1 -1 -1 -1 */
 234        t[1] = 0 + a32[1] + a32[2] - a32[4] - a32[5] - a32[6] - a32[7];
 235        /*  0  0  1  1  0 -1 -1 -1 */
 236        t[2] = 0 + a32[2] + a32[3] - a32[5] - a32[6] - a32[7];
 237        /* -1 -1  0  2  2  1  0 -1 */
 238        t[3] = 0 - a32[0] - a32[1] + 2 * a32[3] + 2 * a32[4] + a32[5] - a32[7];
 239        /*  0 -1 -1  0  2  2  1  0 */
 240        t[4] = 0 - a32[1] - a32[2] + 2 * a32[4] + 2 * a32[5] + a32[6];
 241        /*  0  0 -1 -1  0  2  2  1 */
 242        t[5] = 0 - a32[2] - a32[3] + 2 * a32[5] + 2 * a32[6] + a32[7];
 243        /* -1 -1  0  0  0  1  3  2 */
 244        t[6] = 0 - a32[0] - a32[1] + a32[5] + 3 * a32[6] + 2 * a32[7];
 245        /*  1  0 -1 -1 -1 -1  0  3 */
 246        t[7] = 0 + a32[0] - a32[2] - a32[3] - a32[4] - a32[5] + 3 * a32[7];
 247
 248        t[1] += t[0] >> 32U; t[0] &= 0xffffffffL;
 249        t[2] += t[1] >> 32U; t[1] &= 0xffffffffL;
 250        t[3] += t[2] >> 32U; t[2] &= 0xffffffffL;
 251        t[4] += t[3] >> 32U; t[3] &= 0xffffffffL;
 252        t[5] += t[4] >> 32U; t[4] &= 0xffffffffL;
 253        t[6] += t[5] >> 32U; t[5] &= 0xffffffffL;
 254        t[7] += t[6] >> 32U; t[6] &= 0xffffffffL;
 255        o     = t[7] >> 32U; t[7] &= 0xffffffffL;
 256        t[0] += o;
 257        t[3] -= o;
 258        t[6] -= o;
 259        t[7] += o;
 260        t[1] += t[0] >> 32U; t[0] &= 0xffffffffL;
 261        t[2] += t[1] >> 32U; t[1] &= 0xffffffffL;
 262        t[3] += t[2] >> 32U; t[2] &= 0xffffffffL;
 263        t[4] += t[3] >> 32U; t[3] &= 0xffffffffL;
 264        t[5] += t[4] >> 32U; t[4] &= 0xffffffffL;
 265        t[6] += t[5] >> 32U; t[5] &= 0xffffffffL;
 266        t[7] += t[6] >> 32U; t[6] &= 0xffffffffL;
 267
 268        r[0] = (sp_digit)(t[0]) & 0x3ffffffL;
 269        r[1] = (sp_digit)(t[0] >> 26U);
 270        r[1] |= t[1] << 6U;
 271        r[1] &= 0x3ffffffL;
 272        r[2] = (sp_digit)(t[1] >> 20U);
 273        r[2] |= t[2] << 12U;
 274        r[2] &= 0x3ffffffL;
 275        r[3] = (sp_digit)(t[2] >> 14U);
 276        r[3] |= t[3] << 18U;
 277        r[3] &= 0x3ffffffL;
 278        r[4] = (sp_digit)(t[3] >> 8U);
 279        r[4] |= t[4] << 24U;
 280        r[4] &= 0x3ffffffL;
 281        r[5] = (sp_digit)(t[4] >> 2U) & 0x3ffffffL;
 282        r[6] = (sp_digit)(t[4] >> 28U);
 283        r[6] |= t[5] << 4U;
 284        r[6] &= 0x3ffffffL;
 285        r[7] = (sp_digit)(t[5] >> 22U);
 286        r[7] |= t[6] << 10U;
 287        r[7] &= 0x3ffffffL;
 288        r[8] = (sp_digit)(t[6] >> 16U);
 289        r[8] |= t[7] << 16U;
 290        r[8] &= 0x3ffffffL;
 291        r[9] = (sp_digit)(t[7] >> 10U);
 292    }
 293
 294#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
 295    XFREE(td, NULL, DYNAMIC_TYPE_ECC);
 296#endif
 297
 298    return err;
 299}
 300
 301
 302/* Compare a with b in constant time.
 303 *
 304 * a  A single precision integer.
 305 * b  A single precision integer.
 306 * return -ve, 0 or +ve if a is less than, equal to or greater than b
 307 * respectively.
 308 */
 309static sp_digit sp_256_cmp_10(const sp_digit* a, const sp_digit* b)
 310{
 311    sp_digit r = 0;
 312#ifdef WOLFSSL_SP_SMALL
 313    int i;
 314
 315    for (i=9; i>=0; i--) {
 316        r |= (a[i] - b[i]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 317    }
 318#else
 319    r |= (a[ 9] - b[ 9]) & (0 - (sp_digit)1);
 320    r |= (a[ 8] - b[ 8]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 321    r |= (a[ 7] - b[ 7]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 322    r |= (a[ 6] - b[ 6]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 323    r |= (a[ 5] - b[ 5]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 324    r |= (a[ 4] - b[ 4]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 325    r |= (a[ 3] - b[ 3]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 326    r |= (a[ 2] - b[ 2]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 327    r |= (a[ 1] - b[ 1]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 328    r |= (a[ 0] - b[ 0]) & (0 - ((r == 0) ? (sp_digit)1 : (sp_digit)0));
 329#endif /* WOLFSSL_SP_SMALL */
 330
 331    return r;
 332}
 333
 334/* Normalize the values in each word to 26.
 335 *
 336 * a  Array of sp_digit to normalize.
 337 */
 338static void sp_256_norm_10(sp_digit* a)
 339{
 340#ifdef WOLFSSL_SP_SMALL
 341    int i;
 342    for (i = 0; i < 9; i++) {
 343        a[i+1] += a[i] >> 26;
 344        a[i] &= 0x3ffffff;
 345    }
 346#else
 347    a[1] += a[0] >> 26; a[0] = Q6_R_and_RR(a[0], 0x3ffffff);
 348    a[2] += a[1] >> 26; a[1] = Q6_R_and_RR(a[1], 0x3ffffff);
 349    a[3] += a[2] >> 26; a[2] = Q6_R_and_RR(a[2], 0x3ffffff);
 350    a[4] += a[3] >> 26; a[3] = Q6_R_and_RR(a[3], 0x3ffffff);
 351    a[5] += a[4] >> 26; a[4] = Q6_R_and_RR(a[4], 0x3ffffff);
 352    a[6] += a[5] >> 26; a[5] = Q6_R_and_RR(a[5], 0x3ffffff);
 353    a[7] += a[6] >> 26; a[6] = Q6_R_and_RR(a[6], 0x3ffffff);
 354    a[8] += a[7] >> 26; a[7] = Q6_R_and_RR(a[7], 0x3ffffff);
 355    a[9] += a[8] >> 26; a[8] = Q6_R_and_RR(a[8], 0x3ffffff);
 356#endif
 357}
 358
 359/* Conditionally subtract b from a using the mask m.
 360 * m is -1 to subtract and 0 when not.
 361 *
 362 * r  A single precision number representing condition subtract result.
 363 * a  A single precision number to subtract from.
 364 * b  A single precision number to subtract.
 365 * m  Mask value to apply.
 366 */
 367static void sp_256_cond_sub_10(sp_digit* r, const sp_digit* a,
 368        const sp_digit* b, const sp_digit m)
 369{
 370#ifdef WOLFSSL_SP_SMALL
 371    int i;
 372
 373    for (i = 0; i < 10; i++) {
 374        r[i] = a[i] - (b[i] & m);
 375    }
 376#else
 377    r[ 0] = Q6_R_sub_RR(a[ 0], Q6_R_and_RR(b[ 0], m));
 378    r[ 1] = Q6_R_sub_RR(a[ 1], Q6_R_and_RR(b[ 1], m));
 379    r[ 2] = Q6_R_sub_RR(a[ 2], Q6_R_and_RR(b[ 2], m));
 380    r[ 3] = Q6_R_sub_RR(a[ 3], Q6_R_and_RR(b[ 3], m));
 381    r[ 4] = Q6_R_sub_RR(a[ 4], Q6_R_and_RR(b[ 4], m));
 382    r[ 5] = Q6_R_sub_RR(a[ 5], Q6_R_and_RR(b[ 5], m));
 383    r[ 6] = Q6_R_sub_RR(a[ 6], Q6_R_and_RR(b[ 6], m));
 384    r[ 7] = Q6_R_sub_RR(a[ 7], Q6_R_and_RR(b[ 7], m));
 385    r[ 8] = Q6_R_sub_RR(a[ 8], Q6_R_and_RR(b[ 8], m));
 386    r[ 9] = Q6_R_sub_RR(a[ 9], Q6_R_and_RR(b[ 9], m));
 387#endif /* WOLFSSL_SP_SMALL */
 388}
 389
 390#define sp_256_mont_reduce_order_10         sp_256_mont_reduce_10
 391
 392/* Mul a by scalar b and add into r. (r += a * b)
 393 *
 394 * r  A single precision integer.
 395 * a  A single precision integer.
 396 * b  A scalar.
 397 */
 398SP_NOINLINE static void sp_256_mul_add_10(sp_digit* r, const sp_digit* a,
 399        const sp_digit b)
 400{
 401#ifdef WOLFSSL_SP_SMALL
 402    int64_t tb = b;
 403    int64_t t = 0;
 404    int i;
 405
 406    for (i = 0; i < 10; i++) {
 407        t += (tb * a[i]) + r[i];
 408        r[i] = t & 0x3ffffff;
 409        t >>= 26;
 410    }
 411    r[10] += t;
 412#else
 413    int64_t tb = b;
 414    int64_t t[10];
 415
 416    t[ 0] = Q6_P_mpy_RR(tb, a[ 0]);
 417    t[ 1] = Q6_P_mpy_RR(tb, a[ 1]);
 418    t[ 2] = Q6_P_mpy_RR(tb, a[ 2]);
 419    t[ 3] = Q6_P_mpy_RR(tb, a[ 3]);
 420    t[ 4] = Q6_P_mpy_RR(tb, a[ 4]);
 421    t[ 5] = Q6_P_mpy_RR(tb, a[ 5]);
 422    t[ 6] = Q6_P_mpy_RR(tb, a[ 6]);
 423    t[ 7] = Q6_P_mpy_RR(tb, a[ 7]);
 424    t[ 8] = Q6_P_mpy_RR(tb, a[ 8]);
 425    t[ 9] = Q6_P_mpy_RR(tb, a[ 9]);
 426    r[ 0] +=                 (t[ 0] & 0x3ffffff);
 427    r[ 1] += (t[ 0] >> 26) + (t[ 1] & 0x3ffffff);
 428    r[ 2] += (t[ 1] >> 26) + (t[ 2] & 0x3ffffff);
 429    r[ 3] += (t[ 2] >> 26) + (t[ 3] & 0x3ffffff);
 430    r[ 4] += (t[ 3] >> 26) + (t[ 4] & 0x3ffffff);
 431    r[ 5] += (t[ 4] >> 26) + (t[ 5] & 0x3ffffff);
 432    r[ 6] += (t[ 5] >> 26) + (t[ 6] & 0x3ffffff);
 433    r[ 7] += (t[ 6] >> 26) + (t[ 7] & 0x3ffffff);
 434    r[ 8] += (t[ 7] >> 26) + (t[ 8] & 0x3ffffff);
 435    r[ 9] += (t[ 8] >> 26) + (t[ 9] & 0x3ffffff);
 436    r[10] +=  t[ 9] >> 26;
 437#endif /* WOLFSSL_SP_SMALL */
 438}
 439
 440/* Shift the result in the high 256 bits down to the bottom.
 441 *
 442 * r  A single precision number.
 443 * a  A single precision number.
 444 */
 445static void sp_256_mont_shift_10(sp_digit* r, const sp_digit* a)
 446{
 447#ifdef WOLFSSL_SP_SMALL
 448    int i;
 449    sp_digit n, s;
 450
 451    s = a[10];
 452    n = a[9] >> 22;
 453    for (i = 0; i < 9; i++) {
 454        n += (s & 0x3ffffff) << 4;
 455        r[i] = n & 0x3ffffff;
 456        n >>= 26;
 457        s = a[11 + i] + (s >> 26);
 458    }
 459    n += s << 4;
 460    r[9] = n;
 461#else
 462    sp_digit n, s;
 463
 464    s = a[10]; n = a[9] >> 22;
 465    n += (s & 0x3ffffff) << 4; r[ 0] = Q6_R_and_RR(n, 0x3ffffff);
 466    n >>= 26; s = a[11] + (s >> 26);
 467    n += (s & 0x3ffffff) << 4; r[ 1] = Q6_R_and_RR(n, 0x3ffffff);
 468    n >>= 26; s = a[12] + (s >> 26);
 469    n += (s & 0x3ffffff) << 4; r[ 2] = Q6_R_and_RR(n, 0x3ffffff);
 470    n >>= 26; s = a[13] + (s >> 26);
 471    n += (s & 0x3ffffff) << 4; r[ 3] = Q6_R_and_RR(n, 0x3ffffff);
 472    n >>= 26; s = a[14] + (s >> 26);
 473    n += (s & 0x3ffffff) << 4; r[ 4] = Q6_R_and_RR(n, 0x3ffffff);
 474    n >>= 26; s = a[15] + (s >> 26);
 475    n += (s & 0x3ffffff) << 4; r[ 5] = Q6_R_and_RR(n, 0x3ffffff);
 476    n >>= 26; s = a[16] + (s >> 26);
 477    n += (s & 0x3ffffff) << 4; r[ 6] = Q6_R_and_RR(n, 0x3ffffff);
 478    n >>= 26; s = a[17] + (s >> 26);
 479    n += (s & 0x3ffffff) << 4; r[ 7] = Q6_R_and_RR(n, 0x3ffffff);
 480    n >>= 26; s = a[18] + (s >> 26);
 481    n += (s & 0x3ffffff) << 4; r[ 8] = Q6_R_and_RR(n, 0x3ffffff);
 482    n >>= 26; s = a[19] + (s >> 26);
 483    n += s << 4;              r[ 9] = n;
 484#endif /* WOLFSSL_SP_SMALL */
 485    XMEMSET(&r[10], 0, sizeof(*r) * 10U);
 486}
 487
 488
 489/* Reduce the number back to 256 bits using Montgomery reduction.
 490 *
 491 * a   A single precision number to reduce in place.
 492 * m   The single precision number representing the modulus.
 493 * mp  The digit representing the negative inverse of m mod 2^n.
 494 */
 495static void sp_256_mont_reduce_10(sp_digit* a, const sp_digit* m, sp_digit mp)
 496{
 497    sp_digit mu;
 498
 499
 500    /* unrolled for loops due to unexpected behavior with -O optimizations */
 501    if (mp != 1) {
 502        mu = Q6_P_mpy_RR(a[0], mp) & 0x3ffffff;
 503        sp_256_mul_add_10(a+0, m, mu);
 504        a[0+1] += a[0] >> 26;
 505
 506        mu = Q6_P_mpy_RR(a[1], mp) & 0x3ffffff;
 507        sp_256_mul_add_10(a+1, m, mu);
 508        a[1+1] += a[1] >> 26;
 509
 510        mu = Q6_P_mpy_RR(a[2], mp) & 0x3ffffff;
 511        sp_256_mul_add_10(a+2, m, mu);
 512        a[2+1] += a[2] >> 26;
 513
 514        mu = Q6_P_mpy_RR(a[3], mp) & 0x3ffffff;
 515        sp_256_mul_add_10(a+3, m, mu);
 516        a[3+1] += a[3] >> 26;
 517
 518        mu = Q6_P_mpy_RR(a[4], mp) & 0x3ffffff;
 519        sp_256_mul_add_10(a+4, m, mu);
 520        a[4+1] += a[4] >> 26;
 521
 522        mu = Q6_P_mpy_RR(a[5], mp) & 0x3ffffff;
 523        sp_256_mul_add_10(a+5, m, mu);
 524        a[5+1] += a[5] >> 26;
 525
 526        mu = Q6_P_mpy_RR(a[6], mp) & 0x3ffffff;
 527        sp_256_mul_add_10(a+6, m, mu);
 528        a[6+1] += a[6] >> 26;
 529
 530        mu = Q6_P_mpy_RR(a[7], mp) & 0x3ffffff;
 531        sp_256_mul_add_10(a+7, m, mu);
 532        a[7+1] += a[7] >> 26;
 533
 534        mu = Q6_P_mpy_RR(a[8], mp) & 0x3ffffff;
 535        sp_256_mul_add_10(a+8, m, mu);
 536        a[8+1] += a[8] >> 26;
 537
 538        mu = Q6_P_mpy_RR(a[9], mp) & 0x3fffffL;
 539        sp_256_mul_add_10(a+9, m, mu);
 540        a[9+1] += a[9] >> 26;
 541        a[9] &= 0x3ffffff;
 542    }
 543    else {
 544        mu = Q6_P_mpy_RR(a[0], mp) & 0x3ffffff;
 545        sp_256_mul_add_10(a+0, p256_mod, mu);
 546        a[0+1] += a[0] >> 26;
 547
 548        mu = Q6_P_mpy_RR(a[1], mp) & 0x3ffffff;
 549        sp_256_mul_add_10(a+1, p256_mod, mu);
 550        a[1+1] += a[1] >> 26;
 551
 552        mu = Q6_P_mpy_RR(a[2], mp) & 0x3ffffff;
 553        sp_256_mul_add_10(a+2, p256_mod, mu);
 554        a[2+1] += a[2] >> 26;
 555
 556        mu = Q6_P_mpy_RR(a[3], mp) & 0x3ffffff;
 557        sp_256_mul_add_10(a+3, p256_mod, mu);
 558        a[3+1] += a[3] >> 26;
 559
 560        mu = Q6_P_mpy_RR(a[4], mp) & 0x3ffffff;
 561        sp_256_mul_add_10(a+4, p256_mod, mu);
 562        a[4+1] += a[4] >> 26;
 563
 564        mu = Q6_P_mpy_RR(a[5], mp) & 0x3ffffff;
 565        sp_256_mul_add_10(a+5, p256_mod, mu);
 566        a[5+1] += a[5] >> 26;
 567
 568        mu = Q6_P_mpy_RR(a[6], mp) & 0x3ffffff;
 569        sp_256_mul_add_10(a+6, p256_mod, mu);
 570        a[6+1] += a[6] >> 26;
 571
 572        mu = Q6_P_mpy_RR(a[7], mp) & 0x3ffffff;
 573        sp_256_mul_add_10(a+7, p256_mod, mu);
 574        a[7+1] += a[7] >> 26;
 575
 576        mu = Q6_P_mpy_RR(a[8], mp) & 0x3ffffff;
 577        sp_256_mul_add_10(a+8, p256_mod, mu);
 578        a[8+1] += a[8] >> 26;
 579
 580        mu = Q6_P_mpy_RR(a[9], mp) & 0x3fffffL;
 581        sp_256_mul_add_10(a+9, p256_mod, mu);
 582        a[9+1] += a[9] >> 26;
 583        a[9] &= 0x3ffffff;
 584    }
 585
 586
 587    sp_256_mont_shift_10(a, a);
 588    sp_256_cond_sub_10(a, a, m, 0 - (((a[9] >> 22) > 0) ?
 589            (sp_digit)1 : (sp_digit)0));
 590    sp_256_norm_10(a);
 591}
 592
 593/* Multiply a and b into r. (r = a * b)
 594 *
 595 * r  A single precision integer.
 596 * a  A single precision integer.
 597 * b  A single precision integer.
 598 */
 599SP_NOINLINE static void sp_256_mul_10(sp_digit* r, const sp_digit* a,
 600    const sp_digit* b)
 601{
 602#if 1
 603    int64_t t0   = Q6_P_mpy_RR(a[0], b[0]);
 604    int64_t t1   = Q6_P_mpy_RR(a[0], b[1])
 605                 + Q6_P_mpy_RR(a[1], b[0]);
 606    int64_t t2   = Q6_P_mpy_RR(a[0], b[2])
 607                 + Q6_P_mpy_RR(a[1], b[1])
 608                 + Q6_P_mpy_RR(a[2], b[0]);
 609    int64_t t3   = Q6_P_mpy_RR(a[0], b[3])
 610                 + Q6_P_mpy_RR(a[1], b[2])
 611                 + Q6_P_mpy_RR(a[2], b[1])
 612                 + Q6_P_mpy_RR(a[3], b[0]);
 613    int64_t t4   = Q6_P_mpy_RR(a[0], b[4])
 614                 + Q6_P_mpy_RR(a[1], b[3])
 615                 + Q6_P_mpy_RR(a[2], b[2])
 616                 + Q6_P_mpy_RR(a[3], b[1])
 617                 + Q6_P_mpy_RR(a[4], b[0]);
 618    int64_t t5   = Q6_P_mpy_RR(a[0], b[5])
 619                 + Q6_P_mpy_RR(a[1], b[4])
 620                 + Q6_P_mpy_RR(a[2], b[3])
 621                 + Q6_P_mpy_RR(a[3], b[2])
 622                 + Q6_P_mpy_RR(a[4], b[1])
 623                 + Q6_P_mpy_RR(a[5], b[0]);
 624    int64_t t6   = Q6_P_mpy_RR(a[0], b[6])
 625                 + Q6_P_mpy_RR(a[1], b[5])
 626                 + Q6_P_mpy_RR(a[2], b[4])
 627                 + Q6_P_mpy_RR(a[3], b[3])
 628                 + Q6_P_mpy_RR(a[4], b[2])
 629                 + Q6_P_mpy_RR(a[5], b[1])
 630                 + Q6_P_mpy_RR(a[6], b[0]);
 631    int64_t t7   = Q6_P_mpy_RR(a[0], b[7])
 632                 + Q6_P_mpy_RR(a[1], b[6])
 633                 + Q6_P_mpy_RR(a[2], b[5])
 634                 + Q6_P_mpy_RR(a[3], b[4])
 635                 + Q6_P_mpy_RR(a[4], b[3])
 636                 + Q6_P_mpy_RR(a[5], b[2])
 637                 + Q6_P_mpy_RR(a[6], b[1])
 638                 + Q6_P_mpy_RR(a[7], b[0]);
 639    int64_t t8   = Q6_P_mpy_RR(a[0], b[8])
 640                 + Q6_P_mpy_RR(a[1], b[7])
 641                 + Q6_P_mpy_RR(a[2], b[6])
 642                 + Q6_P_mpy_RR(a[3], b[5])
 643                 + Q6_P_mpy_RR(a[4], b[4])
 644                 + Q6_P_mpy_RR(a[5], b[3])
 645                 + Q6_P_mpy_RR(a[6], b[2])
 646                 + Q6_P_mpy_RR(a[7], b[1])
 647                 + Q6_P_mpy_RR(a[8], b[0]);
 648    int64_t t9   = Q6_P_mpy_RR(a[0], b[9])
 649                 + Q6_P_mpy_RR(a[1], b[8])
 650                 + Q6_P_mpy_RR(a[2], b[7])
 651                 + Q6_P_mpy_RR(a[3], b[6])
 652                 + Q6_P_mpy_RR(a[4], b[5])
 653                 + Q6_P_mpy_RR(a[5], b[4])
 654                 + Q6_P_mpy_RR(a[6], b[3])
 655                 + Q6_P_mpy_RR(a[7], b[2])
 656                 + Q6_P_mpy_RR(a[8], b[1])
 657                 + Q6_P_mpy_RR(a[9], b[0]);
 658    int64_t t10  = Q6_P_mpy_RR(a[1], b[9])
 659                 + Q6_P_mpy_RR(a[2], b[8])
 660                 + Q6_P_mpy_RR(a[3], b[7])
 661                 + Q6_P_mpy_RR(a[4], b[6])
 662                 + Q6_P_mpy_RR(a[5], b[5])
 663                 + Q6_P_mpy_RR(a[6], b[4])
 664                 + Q6_P_mpy_RR(a[7], b[3])
 665                 + Q6_P_mpy_RR(a[8], b[2])
 666                 + Q6_P_mpy_RR(a[9], b[1]);
 667    int64_t t11  = Q6_P_mpy_RR(a[2], b[9])
 668                 + Q6_P_mpy_RR(a[3], b[8])
 669                 + Q6_P_mpy_RR(a[4], b[7])
 670                 + Q6_P_mpy_RR(a[5], b[6])
 671                 + Q6_P_mpy_RR(a[6], b[5])
 672                 + Q6_P_mpy_RR(a[7], b[4])
 673                 + Q6_P_mpy_RR(a[8], b[3])
 674                 + Q6_P_mpy_RR(a[9], b[2]);
 675    int64_t t12  = Q6_P_mpy_RR(a[3], b[9])
 676                 + Q6_P_mpy_RR(a[4], b[8])
 677                 + Q6_P_mpy_RR(a[5], b[7])
 678                 + Q6_P_mpy_RR(a[6], b[6])
 679                 + Q6_P_mpy_RR(a[7], b[5])
 680                 + Q6_P_mpy_RR(a[8], b[4])
 681                 + Q6_P_mpy_RR(a[9], b[3]);
 682    int64_t t13  = Q6_P_mpy_RR(a[4], b[9])
 683                 + Q6_P_mpy_RR(a[5], b[8])
 684                 + Q6_P_mpy_RR(a[6], b[7])
 685                 + Q6_P_mpy_RR(a[7], b[6])
 686                 + Q6_P_mpy_RR(a[8], b[5])
 687                 + Q6_P_mpy_RR(a[9], b[4]);
 688    int64_t t14  = Q6_P_mpy_RR(a[5], b[9])
 689                 + Q6_P_mpy_RR(a[6], b[8])
 690                 + Q6_P_mpy_RR(a[7], b[7])
 691                 + Q6_P_mpy_RR(a[8], b[6])
 692                 + Q6_P_mpy_RR(a[9], b[5]);
 693    int64_t t15  = Q6_P_mpy_RR(a[6], b[9])
 694                 + Q6_P_mpy_RR(a[7], b[8])
 695                 + Q6_P_mpy_RR(a[8], b[7])
 696                 + Q6_P_mpy_RR(a[9], b[6]);
 697    int64_t t16  = Q6_P_mpy_RR(a[7], b[9])
 698                 + Q6_P_mpy_RR(a[8], b[8])
 699                 + Q6_P_mpy_RR(a[9], b[7]);
 700    int64_t t17  = Q6_P_mpy_RR(a[8], b[9])
 701                 + Q6_P_mpy_RR(a[9], b[8]);
 702    int64_t t18  = Q6_P_mpy_RR(a[9], b[9]);
 703
 704
 705    t1   += t0  >> 26; r[ 0] = t0  & 0x3ffffff;
 706    t2   += t1  >> 26; r[ 1] = t1  & 0x3ffffff;
 707    t3   += t2  >> 26; r[ 2] = t2  & 0x3ffffff;
 708    t4   += t3  >> 26; r[ 3] = t3  & 0x3ffffff;
 709    t5   += t4  >> 26; r[ 4] = t4  & 0x3ffffff;
 710    t6   += t5  >> 26; r[ 5] = t5  & 0x3ffffff;
 711    t7   += t6  >> 26; r[ 6] = t6  & 0x3ffffff;
 712    t8   += t7  >> 26; r[ 7] = t7  & 0x3ffffff;
 713    t9   += t8  >> 26; r[ 8] = t8  & 0x3ffffff;
 714    t10  += t9  >> 26; r[ 9] = t9  & 0x3ffffff;
 715    t11  += t10 >> 26; r[10] = t10 & 0x3ffffff;
 716    t12  += t11 >> 26; r[11] = t11 & 0x3ffffff;
 717    t13  += t12 >> 26; r[12] = t12 & 0x3ffffff;
 718    t14  += t13 >> 26; r[13] = t13 & 0x3ffffff;
 719    t15  += t14 >> 26; r[14] = t14 & 0x3ffffff;
 720    t16  += t15 >> 26; r[15] = t15 & 0x3ffffff;
 721    t17  += t16 >> 26; r[16] = t16 & 0x3ffffff;
 722    t18  += t17 >> 26; r[17] = t17 & 0x3ffffff;
 723    r[19] = (sp_digit)(t18 >> 26);
 724                       r[18] = t18 & 0x3ffffff;
 725#endif
 726#if 0
 727    /* Testing speeds with using HVX_Vectors */
 728    {
 729    int64_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14, t15, t16, t17, t18;
 730    HVX_Vector av, splat;
 731    HVX_Vector vlow, vhi;
 732    
 733    av = Q6_V_vzero();
 734    vlow = Q6_V_vzero();
 735    vhi = Q6_V_vzero();
 736    
 737    XMEMCPY((byte*)&av, (byte*)a, 40);
 738    
 739    splat = Q6_V_vsplat_R(b[0]);
 740    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
 741    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
 742    
 743    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
 744    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
 745    unsigned int* loi = (unsigned int*)&vlow;
 746    int* hii = (int*)&vhi;
 747    
 748    /* a[0] * b[0] */
 749    t0 = loi[0] | ((int64_t)hii[0] << 31);
 750    
 751    /* a[1] * b[0] */
 752    t1 = loi[1] | ((int64_t)hii[1] << 31);
 753    
 754    /* a[2] * b[0] */
 755    t2 = loi[2] | ((int64_t)hii[2] << 31);
 756    
 757    /* a[3] * b[0] */
 758    t3 = loi[3] | ((int64_t)hii[3] << 31);
 759    
 760    /* a[4] * b[0] */
 761    t4 = loi[4] | ((int64_t)hii[4] << 31);
 762    
 763    /* a[5] * b[0] */
 764    t5 = loi[5] | ((int64_t)hii[5] << 31);
 765    
 766    /* a[6] * b[0] */
 767    t6 = loi[6] | ((int64_t)hii[6] << 31);
 768    
 769    /* a[7] * b[0] */
 770    t7 = loi[7] | ((int64_t)hii[7] << 31);
 771    
 772    /* a[8] * b[0] */
 773    t8 = loi[8] | ((int64_t)hii[8] << 31);
 774    
 775    /* a[9] * b[0] */
 776    t9 = loi[9] | ((int64_t)hii[9] << 31);
 777    
 778    /* a[*] * b[1] */
 779    splat = Q6_V_vsplat_R(b[1]);
 780    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
 781    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
 782    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
 783    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
 784    loi = (unsigned int*)&vlow;
 785    hii = (int*)&vhi;
 786    
 787    /* a[0] * b[1] */
 788    t1 += (loi[0] | ((int64_t)hii[0] << 31));
 789    
 790    /* a[1] * b[1] */
 791    t2 += (loi[1] | ((int64_t)hii[1] << 31));
 792    
 793    /* a[2] * b[1] */
 794    t3 += (loi[2] | ((int64_t)hii[2] << 31));
 795    
 796    /* a[3] * b[1] */
 797    t4 += (loi[3] | ((int64_t)hii[3] << 31));
 798    
 799    /* a[4] * b[1] */
 800    t5 += (loi[4] | ((int64_t)hii[4] << 31));
 801    
 802    /* a[5] * b[1] */
 803    t6 += (loi[5] | ((int64_t)hii[5] << 31));
 804    
 805    /* a[6] * b[1] */
 806    t7 += (loi[6] | ((int64_t)hii[6] << 31));
 807    
 808    /* a[7] * b[1] */
 809    t8 += (loi[7] | ((int64_t)hii[7] << 31));
 810    
 811    /* a[8] * b[1] */
 812    t9 += (loi[8] | ((int64_t)hii[8] << 31));
 813    
 814    /* a[9] * b[1] */
 815    t10 = (loi[9] | ((int64_t)hii[9] << 31));
 816    
 817    /* a[*] * b[2] */
 818    splat = Q6_V_vsplat_R(b[2]);
 819    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
 820    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
 821    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
 822    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
 823    loi = (unsigned int*)&vlow;
 824    hii = (int*)&vhi;
 825    
 826    
 827    /* a[0] * b[2] */
 828    t2 += (loi[0] | ((int64_t)hii[0] << 31));
 829    
 830    /* a[1] * b[2] */
 831    t3 += (loi[1] | ((int64_t)hii[1] << 31));
 832    
 833    /* a[2] * b[2] */
 834    t4 += (loi[2] | ((int64_t)hii[2] << 31));
 835    
 836    /* a[3] * b[2] */
 837    t5 += (loi[3] | ((int64_t)hii[3] << 31));
 838    
 839    /* a[4] * b[2] */
 840    t6 += (loi[4] | ((int64_t)hii[4] << 31));
 841    
 842    /* a[5] * b[2] */
 843    t7 += (loi[5] | ((int64_t)hii[5] << 31));
 844    
 845    /* a[6] * b[2] */
 846    t8 += (loi[6] | ((int64_t)hii[6] << 31));
 847    
 848    /* a[7] * b[2] */
 849    t9 += (loi[7] | ((int64_t)hii[7] << 31));
 850    
 851    /* a[8] * b[2] */
 852    t10 += (loi[8] | ((int64_t)hii[8] << 31));
 853    
 854    /* a[9] * b[2] */
 855    t11 = (loi[9] | ((int64_t)hii[9] << 31));
 856    
 857    
 858    /* a[*] * b[3] */
 859    splat = Q6_V_vsplat_R(b[3]);
 860    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
 861    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
 862    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
 863    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
 864    loi = (unsigned int*)&vlow;
 865    hii = (int*)&vhi;
 866    
 867    
 868    /* a[0] * b[3] */
 869    t3 += (loi[0] | ((int64_t)hii[0] << 31));
 870    
 871    /* a[1] * b[3] */
 872    t4 += (loi[1] | ((int64_t)hii[1] << 31));
 873    
 874    /* a[2] * b[3] */
 875    t5 += (loi[2] | ((int64_t)hii[2] << 31));
 876    
 877    /* a[3] * b[3] */
 878    t6 += (loi[3] | ((int64_t)hii[3] << 31));
 879    
 880    /* a[4] * b[3] */
 881    t7 += (loi[4] | ((int64_t)hii[4] << 31));
 882    
 883    /* a[5] * b[3] */
 884    t8 += (loi[5] | ((int64_t)hii[5] << 31));
 885    
 886    /* a[6] * b[3] */
 887    t9 += (loi[6] | ((int64_t)hii[6] << 31));
 888    
 889    /* a[7] * b[3] */
 890    t10 += (loi[7] | ((int64_t)hii[7] << 31));
 891    
 892    /* a[8] * b[3] */
 893    t11 += (loi[8] | ((int64_t)hii[8] << 31));
 894    
 895    /* a[9] * b[3] */
 896    t12 = (loi[9] | ((int64_t)hii[9] << 31));
 897    
 898    
 899    /* a[*] * b[4] */
 900    splat = Q6_V_vsplat_R(b[4]);
 901    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
 902    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
 903    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
 904    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
 905    loi = (unsigned int*)&vlow;
 906    hii = (int*)&vhi;
 907    
 908    
 909    /* a[0] * b[4] */
 910    t4 += (loi[0] | ((int64_t)hii[0] << 31));
 911    
 912    /* a[1] * b[4] */
 913    t5 += (loi[1] | ((int64_t)hii[1] << 31));
 914    
 915    /* a[2] * b[4] */
 916    t6 += (loi[2] | ((int64_t)hii[2] << 31));
 917    
 918    /* a[3] * b[4] */
 919    t7 += (loi[3] | ((int64_t)hii[3] << 31));
 920    
 921    /* a[4] * b[4] */
 922    t8 += (loi[4] | ((int64_t)hii[4] << 31));
 923    
 924    /* a[5] * b[4] */
 925    t9 += (loi[5] | ((int64_t)hii[5] << 31));
 926    
 927    /* a[6] * b[4] */
 928    t10 += (loi[6] | ((int64_t)hii[6] << 31));
 929    
 930    /* a[7] * b[4] */
 931    t11 += (loi[7] | ((int64_t)hii[7] << 31));
 932    
 933    /* a[8] * b[4] */
 934    t12 += (loi[8] | ((int64_t)hii[8] << 31));
 935    
 936    /* a[9] * b[4] */
 937    t13 = (loi[9] | ((int64_t)hii[9] << 31));
 938    
 939    
 940    /* a[*] * b[5] */
 941    splat = Q6_V_vsplat_R(b[5]);
 942    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
 943    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
 944    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
 945    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
 946    loi = (unsigned int*)&vlow;
 947    hii = (int*)&vhi;
 948    
 949    
 950    /* a[0] * b[5] */
 951    t5 += (loi[0] | ((int64_t)hii[0] << 31));
 952    
 953    /* a[1] * b[5] */
 954    t6 += (loi[1] | ((int64_t)hii[1] << 31));
 955    
 956    /* a[2] * b[5] */
 957    t7 += (loi[2] | ((int64_t)hii[2] << 31));
 958    
 959    /* a[3] * b[5] */
 960    t8 += (loi[3] | ((int64_t)hii[3] << 31));
 961    
 962    /* a[4] * b[5] */
 963    t9 += (loi[4] | ((int64_t)hii[4] << 31));
 964    
 965    /* a[5] * b[5] */
 966    t10 += (loi[5] | ((int64_t)hii[5] << 31));
 967    
 968    /* a[6] * b[5] */
 969    t11 += (loi[6] | ((int64_t)hii[6] << 31));
 970    
 971    /* a[7] * b[5] */
 972    t12 += (loi[7] | ((int64_t)hii[7] << 31));
 973    
 974    /* a[8] * b[5] */
 975    t13 += (loi[8] | ((int64_t)hii[8] << 31));
 976    
 977    /* a[9] * b[5] */
 978    t14 = (loi[9] | ((int64_t)hii[9] << 31));
 979    
 980    
 981    /* a[*] * b[6] */
 982    splat = Q6_V_vsplat_R(b[6]);
 983    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
 984    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
 985    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
 986    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
 987    loi = (unsigned int*)&vlow;
 988    hii = (int*)&vhi;
 989    
 990    
 991    /* a[0] * b[6] */
 992    t6 += (loi[0] | ((int64_t)hii[0] << 31));
 993    
 994    /* a[1] * b[6] */
 995    t7 += (loi[1] | ((int64_t)hii[1] << 31));
 996    
 997    /* a[2] * b[6] */
 998    t8 += (loi[2] | ((int64_t)hii[2] << 31));
 999    
1000    /* a[3] * b[6] */
1001    t9 += (loi[3] | ((int64_t)hii[3] << 31));
1002    
1003    /* a[4] * b[6] */
1004    t10 += (loi[4] | ((int64_t)hii[4] << 31));
1005    
1006    /* a[5] * b[6] */
1007    t11 += (loi[5] | ((int64_t)hii[5] << 31));
1008    
1009    /* a[6] * b[6] */
1010    t12 += (loi[6] | ((int64_t)hii[6] << 31));
1011    
1012    /* a[7] * b[6] */
1013    t13 += (loi[7] | ((int64_t)hii[7] << 31));
1014    
1015    /* a[8] * b[6] */
1016    t14 += (loi[8] | ((int64_t)hii[8] << 31));
1017    
1018    /* a[9] * b[6] */
1019    t15 = (loi[9] | ((int64_t)hii[9] << 31));
1020    
1021    
1022    
1023    /* a[*] * b[7] */
1024    splat = Q6_V_vsplat_R(b[7]);
1025    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
1026    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
1027    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
1028    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
1029    loi = (unsigned int*)&vlow;
1030    hii = (int*)&vhi;
1031    
1032    
1033    /* a[0] * b[7] */
1034    t7 += (loi[0] | ((int64_t)hii[0] << 31));
1035    
1036    /* a[1] * b[7] */
1037    t8 += (loi[1] | ((int64_t)hii[1] << 31));
1038    
1039    /* a[2] * b[7] */
1040    t9 += (loi[2] | ((int64_t)hii[2] << 31));
1041    
1042    /* a[3] * b[7] */
1043    t10 += (loi[3] | ((int64_t)hii[3] << 31));
1044    
1045    /* a[4] * b[7] */
1046    t11 += (loi[4] | ((int64_t)hii[4] << 31));
1047    
1048    /* a[5] * b[7] */
1049    t12 += (loi[5] | ((int64_t)hii[5] << 31));
1050    
1051    /* a[6] * b[7] */
1052    t13 += (loi[6] | ((int64_t)hii[6] << 31));
1053    
1054    /* a[7] * b[7] */
1055    t14 += (loi[7] | ((int64_t)hii[7] << 31));
1056    
1057    /* a[8] * b[7] */
1058    t15 += (loi[8] | ((int64_t)hii[8] << 31));
1059    
1060    /* a[9] * b[7] */
1061    t16 = (loi[9] | ((int64_t)hii[9] << 31));
1062    
1063    
1064    /* a[*] * b[8] */
1065    splat = Q6_V_vsplat_R(b[8]);
1066    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
1067    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
1068    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
1069    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
1070    loi = (unsigned int*)&vlow;
1071    hii = (int*)&vhi;
1072    
1073    
1074    /* a[0] * b[8] */
1075    t8 += (loi[0] | ((int64_t)hii[0] << 31));
1076    
1077    /* a[1] * b[8] */
1078    t9 += (loi[1] | ((int64_t)hii[1] << 31));
1079    
1080    /* a[2] * b[8] */
1081    t10 += (loi[2] | ((int64_t)hii[2] << 31));
1082    
1083    /* a[3] * b[8] */
1084    t11 += (loi[3] | ((int64_t)hii[3] << 31));
1085    
1086    /* a[4] * b[8] */
1087    t12 += (loi[4] | ((int64_t)hii[4] << 31));
1088    
1089    /* a[5] * b[8] */
1090    t13 += (loi[5] | ((int64_t)hii[5] << 31));
1091    
1092    /* a[6] * b[8] */
1093    t14 += (loi[6] | ((int64_t)hii[6] << 31));
1094    
1095    /* a[7] * b[8] */
1096    t15 += (loi[7] | ((int64_t)hii[7] << 31));
1097    
1098    /* a[8] * b[8] */
1099    t16 += (loi[8] | ((int64_t)hii[8] << 31));
1100    
1101    /* a[9] * b[8] */
1102    t17 = (loi[9] | ((int64_t)hii[9] << 31));
1103    
1104    
1105    /* a[*] * b[9] */
1106    splat = Q6_V_vsplat_R(b[9]);
1107    vlow = Q6_Vw_vmpyieo_VhVh(av, splat);
1108    vlow = Q6_Vw_vmpyieacc_VwVwVuh(vlow, av, splat);
1109    vhi = Q6_Vw_vmpye_VwVuh(av, splat);
1110    vhi = Q6_Vw_vmpyoacc_VwVwVh_s1_sat_shift(vhi, av, splat);
1111    loi = (unsigned int*)&vlow;
1112    hii = (int*)&vhi;
1113    
1114    
1115    /* a[0] * b[9] */
1116    t9 += (loi[0] | ((int64_t)hii[0] << 31));
1117    
1118    /* a[1] * b[9] */
1119    t10 += (loi[1] | ((int64_t)hii[1] << 31));
1120    
1121    /* a[2] * b[9] */
1122    t11 += (loi[2] | ((int64_t)hii[2] << 31));
1123    
1124    /* a[3] * b[9] */
1125    t12 += (loi[3] | ((int64_t)hii[3] << 31));
1126    
1127    /* a[4] * b[9] */
1128    t13 += (loi[4] | ((int64_t)hii[4] << 31));
1129    
1130    /* a[5] * b[9] */
1131    t14 += (loi[5] | ((int64_t)hii[5] << 31));
1132    
1133    /* a[6] * b[9] */
1134    t15 += (loi[6] | ((int64_t)hii[6] << 31));
1135    
1136    /* a[7] * b[9] */
1137    t16 += (loi[7] | ((int64_t)hii[7] << 31));
1138    
1139    /* a[8] * b[9] */
1140    t17 += (loi[8] | ((int64_t)hii[8] << 31));
1141    
1142    /* a[9] * b[9] */
1143    t18 = (loi[9] | ((int64_t)hii[9] << 31));
1144    
1145        t1   += t0  >> 26; r[ 0] = t0  & 0x3ffffff;
1146        t2   += t1  >> 26; r[ 1] = t1  & 0x3ffffff;
1147        t3   += t2  >> 26; r[ 2] = t2  & 0x3ffffff;
1148        t4   += t3  >> 26; r[ 3] = t3  & 0x3ffffff;
1149        t5   += t4  >> 26; r[ 4] = t4  & 0x3ffffff;
1150        t6   += t5  >> 26; r[ 5] = t5  & 0x3ffffff;
1151        t7   += t6  >> 26; r[ 6] = t6  & 0x3ffffff;
1152        t8   += t7  >> 26; r[ 7] = t7  & 0x3ffffff;
1153        t9   += t8  >> 26; r[ 8] = t8  & 0x3ffffff;
1154        t10  += t9  >> 26; r[ 9] = t9  & 0x3ffffff;
1155        t11  += t10 >> 26; r[10] = t10 & 0x3ffffff;
1156        t12  += t11 >> 26; r[11] = t11 & 0x3ffffff;
1157        t13  += t12 >> 26; r[12] = t12 & 0x3ffffff;
1158        t14  += t13 >> 26; r[13] = t13 & 0x3ffffff;
1159        t15  += t14 >> 26; r[14] = t14 & 0x3ffffff;
1160        t16  += t15 >> 26; r[15] = t15 & 0x3ffffff;
1161        t17  += t16 >> 26; r[16] = t16 & 0x3ffffff;
1162        t18  += t17 >> 26; r[17] = t17 & 0x3ffffff;
1163        r[19] = (sp_digit)(t18 >> 26);
1164                           r[18] = t18 & 0x3ffffff;
1165    }
1166#endif
1167}
1168
1169
1170/* Multiply two Montgomery form numbers mod the modulus (prime).
1171 * (r = a * b mod m)
1172 *
1173 * r   Result of multiplication.
1174 * a   First number to multiply in Montgomery form.
1175 * b   Second number to multiply in Montgomery form.
1176 * m   Modulus (prime).
1177 * mp  Montgomery multiplier.
1178 */
1179static void sp_256_mont_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
1180        const sp_digit* m, sp_digit mp)
1181{
1182    sp_256_mul_10(r, a, b);
1183    sp_256_mont_reduce_10(r, m, mp);
1184}
1185
1186
1187/* Square a and put result in r. (r = a * a)
1188 *
1189 * r  A single precision integer.
1190 * a  A single precision integer.
1191 */
1192SP_NOINLINE static void sp_256_sqr_10(sp_digit* r, const sp_digit* a)
1193{
1194    int64_t t0   = Q6_P_mpy_RR(a[0], a[0]);
1195    int64_t t1   = Q6_P_mpy_RR(a[0], a[1]) * 2;
1196    int64_t t2   = Q6_P_mpy_RR(a[0], a[2]) * 2
1197                 + Q6_P_mpy_RR(a[1], a[1]);
1198    int64_t t3   = (Q6_P_mpy_RR(a[0], a[3])
1199                 + Q6_P_mpy_RR(a[1], a[2])) * 2;
1200    int64_t t4   = (Q6_P_mpy_RR(a[ 0], a[ 4])
1201                 + Q6_P_mpy_RR(a[ 1], a[ 3])) * 2
1202                 + Q6_P_mpy_RR(a[ 2], a[ 2]);
1203    int64_t t5   = (Q6_P_mpy_RR(a[ 0], a[ 5])
1204                 + Q6_P_mpy_RR(a[ 1], a[ 4])
1205                 + Q6_P_mpy_RR(a[ 2], a[ 3])) * 2;
1206    int64_t t6   = (Q6_P_mpy_RR(a[ 0], a[ 6])
1207                 + Q6_P_mpy_RR(a[ 1], a[ 5])
1208                 + Q6_P_mpy_RR(a[ 2], a[ 4])) * 2
1209                 + Q6_P_mpy_RR(a[ 3], a[ 3]);
1210    int64_t t7   = (Q6_P_mpy_RR(a[ 0], a[ 7])
1211                 + Q6_P_mpy_RR(a[ 1], a[ 6])
1212                 + Q6_P_mpy_RR(a[ 2], a[ 5])
1213                 + Q6_P_mpy_RR(a[ 3], a[ 4])) * 2;
1214    int64_t t8   = (Q6_P_mpy_RR(a[ 0], a[ 8])
1215                 + Q6_P_mpy_RR(a[ 1], a[ 7])
1216                 + Q6_P_mpy_RR(a[ 2], a[ 6])
1217                 + Q6_P_mpy_RR(a[ 3], a[ 5])) * 2
1218                 + Q6_P_mpy_RR(a[ 4], a[ 4]);
1219    int64_t t9   = (Q6_P_mpy_RR(a[ 0], a[ 9])
1220                 + Q6_P_mpy_RR(a[ 1], a[ 8])
1221                 + Q6_P_mpy_RR(a[ 2], a[ 7])
1222                 + Q6_P_mpy_RR(a[ 3], a[ 6])
1223                 + Q6_P_mpy_RR(a[ 4], a[ 5])) * 2;
1224    int64_t t10  = (Q6_P_mpy_RR(a[ 1], a[ 9])
1225                 + Q6_P_mpy_RR(a[ 2], a[ 8])
1226                 + Q6_P_mpy_RR(a[ 3], a[ 7])
1227                 + Q6_P_mpy_RR(a[ 4], a[ 6])) * 2
1228                 + Q6_P_mpy_RR(a[ 5], a[ 5]);
1229    int64_t t11  = (Q6_P_mpy_RR(a[ 2], a[ 9])
1230                 + Q6_P_mpy_RR(a[ 3], a[ 8])
1231                 + Q6_P_mpy_RR(a[ 4], a[ 7])
1232                 + Q6_P_mpy_RR(a[ 5], a[ 6])) * 2;
1233    int64_t t12  = (Q6_P_mpy_RR(a[ 3], a[ 9])
1234                 + Q6_P_mpy_RR(a[ 4], a[ 8])
1235                 + Q6_P_mpy_RR(a[ 5], a[ 7])) * 2
1236                 + Q6_P_mpy_RR(a[ 6], a[ 6]);
1237    int64_t t13  = (Q6_P_mpy_RR(a[ 4], a[ 9])
1238                 + Q6_P_mpy_RR(a[ 5], a[ 8])
1239                 + Q6_P_mpy_RR(a[ 6], a[ 7])) * 2;
1240    int64_t t14  = (Q6_P_mpy_RR(a[ 5], a[ 9])
1241                 + Q6_P_mpy_RR(a[ 6], a[ 8])) * 2
1242                 + Q6_P_mpy_RR(a[ 7], a[ 7]);
1243    int64_t t15  =( Q6_P_mpy_RR(a[ 6], a[ 9])
1244                 + Q6_P_mpy_RR(a[ 7], a[ 8])) * 2;
1245    int64_t t16  = Q6_P_mpy_RR(a[ 7], a[ 9]) * 2
1246                 + Q6_P_mpy_RR(a[ 8], a[ 8]);
1247    int64_t t17  = Q6_P_mpy_RR(a[ 8], a[ 9]) * 2;
1248    int64_t t18  = Q6_P_mpy_RR(a[ 9], a[ 9]);
1249
1250    t1   += t0  >> 26; r[ 0] = t0  & 0x3ffffff;
1251    t2   += t1  >> 26; r[ 1] = t1  & 0x3ffffff;
1252    t3   += t2  >> 26; r[ 2] = t2  & 0x3ffffff;
1253    t4   += t3  >> 26; r[ 3] = t3  & 0x3ffffff;
1254    t5   += t4  >> 26; r[ 4] = t4  & 0x3ffffff;
1255    t6   += t5  >> 26; r[ 5] = t5  & 0x3ffffff;
1256    t7   += t6  >> 26; r[ 6] = t6  & 0x3ffffff;
1257    t8   += t7  >> 26; r[ 7] = t7  & 0x3ffffff;
1258    t9   += t8  >> 26; r[ 8] = t8  & 0x3ffffff;
1259    t10  += t9  >> 26; r[ 9] = t9  & 0x3ffffff;
1260    t11  += t10 >> 26; r[10] = t10 & 0x3ffffff;
1261    t12  += t11 >> 26; r[11] = t11 & 0x3ffffff;
1262    t13  += t12 >> 26; r[12] = t12 & 0x3ffffff;
1263    t14  += t13 >> 26; r[13] = t13 & 0x3ffffff;
1264    t15  += t14 >> 26; r[14] = t14 & 0x3ffffff;
1265    t16  += t15 >> 26; r[15] = t15 & 0x3ffffff;
1266    t17  += t16 >> 26; r[16] = t16 & 0x3ffffff;
1267    t18  += t17 >> 26; r[17] = t17 & 0x3ffffff;
1268    r[19] = (sp_digit)(t18 >> 26);
1269                       r[18] = t18 & 0x3ffffff;
1270}
1271
1272
1273/* Square the Montgomery form number. (r = a * a mod m)
1274 *
1275 * r   Result of squaring.
1276 * a   Number to square in Montgomery form.
1277 * m   Modulus (prime).
1278 * mp  Montgomery multiplier.
1279 */
1280static void sp_256_mont_sqr_10(sp_digit* r, const sp_digit* a, const sp_digit* m,
1281        sp_digit mp)
1282{
1283    sp_256_sqr_10(r, a);
1284    sp_256_mont_reduce_10(r, m, mp);
1285}
1286
1287#if !defined(WOLFSSL_SP_SMALL) || defined(HAVE_COMP_KEY)
1288/* Square the Montgomery form number a number of times. (r = a ^ n mod m)
1289 *
1290 * r   Result of squaring.
1291 * a   Number to square in Montgomery form.
1292 * n   Number of times to square.
1293 * m   Modulus (prime).
1294 * mp  Montgomery multiplier.
1295 */
1296static void sp_256_mont_sqr_n_10(sp_digit* r, const sp_digit* a, int n,
1297        const sp_digit* m, sp_digit mp)
1298{
1299    sp_256_mont_sqr_10(r, a, m, mp);
1300    for (; n > 1; n--) {
1301        sp_256_mont_sqr_10(r, r, m, mp);
1302    }
1303}
1304
1305#endif /* !WOLFSSL_SP_SMALL || HAVE_COMP_KEY */
1306#ifdef WOLFSSL_SP_SMALL
1307/* Mod-2 for the P256 curve. */
1308static const word32 p256_mod_2[8] = {
1309    0xfffffffdU,0xffffffffU,0xffffffffU,0x00000000U,0x00000000U,0x00000000U,
1310    0x00000001U,0xffffffffU
1311};
1312#endif /* !WOLFSSL_SP_SMALL */
1313
1314/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
1315 * P256 curve. (r = 1 / a mod m)
1316 *
1317 * r   Inverse result.
1318 * a   Number to invert.
1319 * td  Temporary data.
1320 */
1321static void sp_256_mont_inv_10(sp_digit* r, const sp_digit* a, sp_digit* td)
1322{
1323#ifdef WOLFSSL_SP_SMALL
1324    sp_digit* t = td;
1325    int i;
1326
1327    XMEMCPY(t, a, sizeof(sp_digit) * 10);
1328    for (i=254; i>=0; i--) {
1329        sp_256_mont_sqr_10(t, t, p256_mod, p256_mp_mod);
1330        if (p256_mod_2[i / 32] & ((sp_digit)1 << (i % 32)))
1331            sp_256_mont_mul_10(t, t, a, p256_mod, p256_mp_mod);
1332    }
1333    XMEMCPY(r, t, sizeof(sp_digit) * 10);
1334#else
1335    sp_digit* t = td;
1336    sp_digit* t2 = td + Q6_P_mpy_RR(2, 10);
1337    sp_digit* t3 = td + Q6_P_mpy_RR(4, 10);
1338
1339    /* t = a^2 */
1340    sp_256_mont_sqr_10(t, a, p256_mod, p256_mp_mod);
1341    /* t = a^3 = t * a */
1342    sp_256_mont_mul_10(t, t, a, p256_mod, p256_mp_mod);
1343    /* t2= a^c = t ^ 2 ^ 2 */
1344    sp_256_mont_sqr_n_10(t2, t, 2, p256_mod, p256_mp_mod);
1345    /* t3= a^d = t2 * a */
1346    sp_256_mont_mul_10(t3, t2, a, p256_mod, p256_mp_mod);
1347    /* t = a^f = t2 * t */
1348    sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
1349    /* t2= a^f0 = t ^ 2 ^ 4 */
1350    sp_256_mont_sqr_n_10(t2, t, 4, p256_mod, p256_mp_mod);
1351    /* t3= a^fd = t2 * t3 */
1352    sp_256_mont_mul_10(t3, t2, t3, p256_mod, p256_mp_mod);
1353    /* t = a^ff = t2 * t */
1354    sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
1355    /* t2= a^ff00 = t ^ 2 ^ 8 */
1356    sp_256_mont_sqr_n_10(t2, t, 8, p256_mod, p256_mp_mod);
1357    /* t3= a^fffd = t2 * t3 */
1358    sp_256_mont_mul_10(t3, t2, t3, p256_mod, p256_mp_mod);
1359    /* t = a^ffff = t2 * t */
1360    sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
1361    /* t2= a^ffff0000 = t ^ 2 ^ 16 */
1362    sp_256_mont_sqr_n_10(t2, t, 16, p256_mod, p256_mp_mod);
1363    /* t3= a^fffffffd = t2 * t3 */
1364    sp_256_mont_mul_10(t3, t2, t3, p256_mod, p256_mp_mod);
1365    /* t = a^ffffffff = t2 * t */
1366    sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
1367    /* t = a^ffffffff00000000 = t ^ 2 ^ 32  */
1368    sp_256_mont_sqr_n_10(t2, t, 32, p256_mod, p256_mp_mod);
1369    /* t2= a^ffffffffffffffff = t2 * t */
1370    sp_256_mont_mul_10(t, t2, t, p256_mod, p256_mp_mod);
1371    /* t2= a^ffffffff00000001 = t2 * a */
1372    sp_256_mont_mul_10(t2, t2, a, p256_mod, p256_mp_mod);
1373    /* t2= a^ffffffff000000010000000000000000000000000000000000000000
1374     *   = t2 ^ 2 ^ 160 */
1375    sp_256_mont_sqr_n_10(t2, t2, 160, p256_mod, p256_mp_mod);
1376    /* t2= a^ffffffff00000001000000000000000000000000ffffffffffffffff
1377     *   = t2 * t */
1378    sp_256_mont_mul_10(t2, t2, t, p256_mod, p256_mp_mod);
1379    /* t2= a^ffffffff00000001000000000000000000000000ffffffffffffffff00000000
1380     *   = t2 ^ 2 ^ 32 */
1381    sp_256_mont_sqr_n_10(t2, t2, 32, p256_mod, p256_mp_mod);
1382    /* r = a^ffffffff00000001000000000000000000000000fffffffffffffffffffffffd
1383     *   = t2 * t3 */
1384    sp_256_mont_mul_10(r, t2, t3, p256_mod, p256_mp_mod);
1385#endif /* WOLFSSL_SP_SMALL */
1386}
1387
1388
1389/* Map the Montgomery form projective coordinate point to an affine point.
1390 *
1391 * r  Resulting affine coordinate point.
1392 * p  Montgomery form projective coordinate point.
1393 * t  Temporary ordinate data.
1394 */
1395static void sp_256_map_10(sp_point* r, const sp_point* p, sp_digit* t)
1396{
1397    sp_digit* t1 = t;
1398    sp_digit* t2 = t + Q6_P_mpy_RR(2, 10);
1399    int32_t n;
1400
1401    sp_256_mont_inv_10(t1, p->z, t + 2*10);
1402
1403    sp_256_mont_sqr_10(t2, t1, p256_mod, p256_mp_mod);
1404    sp_256_mont_mul_10(t1, t2, t1, p256_mod, p256_mp_mod);
1405
1406    /* x /= z^2 */
1407    sp_256_mont_mul_10(r->x, p->x, t2, p256_mod, p256_mp_mod);
1408    XMEMSET(r->x + 10, 0, sizeof(r->x) / 2U);
1409    sp_256_mont_reduce_10(r->x, p256_mod, p256_mp_mod);
1410    /* Reduce x to less than modulus */
1411    n = sp_256_cmp_10(r->x, p256_mod);
1412    sp_256_cond_sub_10(r->x, r->x, p256_mod, 0 - ((n >= 0) ?
1413                (sp_digit)1 : (sp_digit)0));
1414    sp_256_norm_10(r->x);
1415
1416    /* y /= z^3 */
1417    sp_256_mont_mul_10(r->y, p->y, t1, p256_mod, p256_mp_mod);
1418    XMEMSET(r->y + 10, 0, sizeof(r->y) / 2U);
1419    sp_256_mont_reduce_10(r->y, p256_mod, p256_mp_mod);
1420    /* Reduce y to less than modulus */
1421    n = sp_256_cmp_10(r->y, p256_mod);
1422    sp_256_cond_sub_10(r->y, r->y, p256_mod, 0 - ((n >= 0) ?
1423                (sp_digit)1 : (sp_digit)0));
1424    sp_256_norm_10(r->y);
1425
1426    XMEMSET(r->z, 0, sizeof(r->z));
1427    r->z[0] = 1;
1428
1429}
1430
1431
1432/* Add b to a into r. (r = a + b)
1433 *
1434 * r  A single precision integer.
1435 * a  A single precision integer.
1436 * b  A single precision integer.
1437 */
1438SP_NOINLINE static int sp_256_add_10(sp_digit* r, const sp_digit* a,
1439        const sp_digit* b)
1440{
1441#if 0
1442    r[ 0] = Q6_R_add_RR(a[0], b[0]);
1443    r[ 1] = Q6_R_add_RR(a[1], b[1]);
1444    r[ 2] = Q6_R_add_RR(a[2], b[2]);
1445    r[ 3] = Q6_R_add_RR(a[3], b[3]);
1446    r[ 4] = Q6_R_add_RR(a[4], b[4]);
1447    r[ 5] = Q6_R_add_RR(a[5], b[5]);
1448    r[ 6] = Q6_R_add_RR(a[6], b[6]);
1449    r[ 7] = Q6_R_add_RR(a[7], b[7]);
1450    r[ 8] = Q6_R_add_RR(a[8], b[8]);
1451    r[ 9] = Q6_R_add_RR(a[9], b[9]);
1452#endif
1453#if 1
1454    __asm__ __volatile__ (
1455        "{ r1 = memw(%[a]+#0)  \n"
1456        "  r2 = memw(%[b]+#0) }\n"
1457        "{ r3 = memw(%[a]+#4)  \n"
1458        "  r19 = add(r1,r2)    \n"
1459        "  r4 = memw(%[b]+#4) }\n"
1460        "{ r5 = memw(%[a]+#8)  \n"
1461        "  r20 = add(r3,r4)    \n"
1462        "  r6 = memw(%[b]+#8) }\n"
1463        "{ memw(%[r]+#0) = r19 }\n"
1464        "{ r7 = memw(%[a]+#12)  \n"
1465        "  r21 = add(r5,r6)    \n"
1466        "  r8 = memw(%[b]+#12) }\n"
1467        "{ memw(%[r]+#4) = r20 }\n"
1468        "{ r9 = memw(%[a]+#16)  \n"
1469        "  r22 = add(r7,r8)     \n"
1470        "  r10 = memw(%[b]+#16) }\n"
1471        "{ memw(%[r]+#8) = r21 }\n"
1472        "{ r11 = memw(%[a]+#20)  \n"
1473        "  r23 = add(r9,r10)     \n"
1474        "  r12 = memw(%[b]+#20) }\n"
1475        "{ memw(%[r]+#12) = r22 }\n"
1476        "{ r13 = memw(%[a]+#24)  \n"
1477        "  r24 = add(r11,r12)     \n"
1478        "  r14 = memw(%[b]+#24) }\n"
1479        "{ memw(%[r]+#16) = r23 }\n"
1480        "{ r15 = memw(%[a]+#28)  \n"
1481        "  r25 = add(r13,r14)     \n"
1482        "  r16 = memw(%[b]+#28) }\n"
1483        "{ memw(%[r]+#20) = r24 }\n"
1484        "{ r17 = memw(%[a]+#32)  \n"
1485        "  r26 = add(r15,r16)     \n"
1486        "  r18 = memw(%[b]+#32) }\n"
1487        "{ memw(%[r]+#24) = r25 }\n"
1488        "{ r5 = memw(%[a]+#36)  \n"
1489        "  r19 = add(r17,r18)    \n"
1490        "  r6 = memw(%[b]+#36) }\n"
1491        "{ memw(%[r]+#28) = r26 }\n"
1492        "{ r20 = add(r5,r6)      \n"
1493            "  memw(%[r]+#32) = r19 }\n"
1494        "{ memw(%[r]+#36) = r20 }\n"
1495        : [r] "+r" (r)
1496        : [a] "r"(a), [b] "r"(b)
1497        : "memory", "r1", "r2", "r3", "r4", "r5", "r6", "r7", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "r16", "r17", "r18", "r19", "r20", "r21", "r22", "r23", "r24", "r25", "r26"
1498    );
1499#endif
1500    return 0;
1501}
1502
1503
1504/* Add two Montgomery form numbers (r = a + b % m).
1505 *
1506 * r   Result of addition.
1507 * a   First number to add in Montgomery form.
1508 * b   Second number to add in Montgomery form.
1509 * m   Modulus (prime).
1510 */
1511static void sp_256_mont_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
1512        const sp_digit* m)
1513{
1514    (void)sp_256_add_10(r, a, b);
1515    sp_256_norm_10(r);
1516    sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
1517                (sp_digit)1 : (sp_digit)0));
1518    sp_256_norm_10(r);
1519}
1520
1521
1522/* Double a Montgomery form number (r = a + a % m).
1523 *
1524 * r   Result of doubling.
1525 * a   Number to double in Montgomery form.
1526 * m   Modulus (prime).
1527 */
1528static void sp_256_mont_dbl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
1529{
1530    (void)sp_256_add_10(r, a, a);
1531    sp_256_norm_10(r);
1532    sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
1533                (sp_digit)1 : (sp_digit)0));
1534    sp_256_norm_10(r);
1535}
1536
1537
1538/* Triple a Montgomery form number (r = a + a + a % m).
1539 *
1540 * r   Result of Tripling.
1541 * a   Number to triple in Montgomery form.
1542 * m   Modulus (prime).
1543 */
1544static void sp_256_mont_tpl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
1545{
1546    (void)sp_256_add_10(r, a, a);
1547    sp_256_norm_10(r);
1548    sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
1549                (sp_digit)1 : (sp_digit)0));
1550    sp_256_norm_10(r);
1551    (void)sp_256_add_10(r, r, a);
1552    sp_256_norm_10(r);
1553    sp_256_cond_sub_10(r, r, m, 0 - (((r[9] >> 22) > 0) ?
1554                (sp_digit)1 : (sp_digit)0));
1555    sp_256_norm_10(r);
1556}
1557
1558/* Sub b from a into r. (r = a - b)
1559 *
1560 * r  A single precision integer.
1561 * a  A single precision integer.
1562 * b  A single precision integer.
1563 */
1564SP_NOINLINE static int sp_256_sub_10(sp_digit* r, const sp_digit* a,
1565        const sp_digit* b)
1566{
1567#if 0
1568    r[ 0] = Q6_R_sub_RR(a[0], b[0]);
1569    r[ 1] = Q6_R_sub_RR(a[1], b[1]);
1570    r[ 2] = Q6_R_sub_RR(a[2], b[2]);
1571    r[ 3] = Q6_R_sub_RR(a[3], b[3]);
1572    r[ 4] = Q6_R_sub_RR(a[4], b[4]);
1573    r[ 5] = Q6_R_sub_RR(a[5], b[5]);
1574    r[ 6] = Q6_R_sub_RR(a[6], b[6]);
1575    r[ 7] = Q6_R_sub_RR(a[7], b[7]);
1576    r[ 8] = Q6_R_sub_RR(a[8], b[8]);
1577    r[ 9] = Q6_R_sub_RR(a[9], b[9]);
1578#endif
1579#if 1
1580    __asm__ __volatile__ (
1581        "{ r1 = memw(%[a]+#0)  \n"
1582        "  r2 = memw(%[b]+#0) }\n"
1583        "{ r3 = memw(%[a]+#4)  \n"
1584        "  r19 = sub(r1,r2)    \n"
1585        "  r4 = memw(%[b]+#4) }\n"
1586        "{ r5 = memw(%[a]+#8)  \n"
1587        "  r20 = sub(r3,r4)    \n"
1588        "  r6 = memw(%[b]+#8) }\n"
1589        "{ memw(%[r]+#0) = r19 }\n"
1590        "{ r7 = memw(%[a]+#12)  \n"
1591        "  r21 = sub(r5,r6)    \n"
1592        "  r8 = memw(%[b]+#12) }\n"
1593        "{ memw(%[r]+#4) = r20 }\n"
1594        "{ r9 = memw(%[a]+#16)  \n"
1595        "  r22 = sub(r7,r8)     \n"
1596        "  r10 = memw(%[b]+#16) }\n"
1597        "{ memw(%[r]+#8) = r21 }\n"
1598        "{ r11 = memw(%[a]+#20)  \n"
1599        "  r23 = sub(r9,r10)     \n"
1600        "  r12 = memw(%[b]+#20) }\n"
1601        "{ memw(%[r]+#12) = r22 }\n"
1602        "{ r13 = memw(%[a]+#24)  \n"
1603        "  r24 = sub(r11,r12)     \n"
1604        "  r14 = memw(%[b]+#24) }\n"
1605        "{ memw(%[r]+#16) = r23 }\n"
1606        "{ r15 = memw(%[a]+#28)  \n"
1607        "  r25 = sub(r13,r14)     \n"
1608        "  r16 = memw(%[b]+#28) }\n"
1609        "{ memw(%[r]+#20) = r24 }\n"
1610        "{ r17 = memw(%[a]+#32)  \n"
1611        "  r26 = sub(r15,r16)     \n"
1612        "  r18 = memw(%[b]+#32) }\n"
1613        "{ memw(%[r]+#24) = r25 }\n"
1614        "{ r5 = memw(%[a]+#36)  \n"
1615        "  r19 = sub(r17,r18)    \n"
1616        "  r6 = memw(%[b]+#36) }\n"
1617        "{ memw(%[r]+#28) = r26 }\n"
1618        "{ r20 = sub(r5,r6)      \n"
1619            "  memw(%[r]+#32) = r19 }\n"
1620        "{ memw(%[r]+#36) = r20 }\n"
1621        : [r] "+r" (r)
1622        : [a] "r"(a), [b] "r"(b)
1623        : "memory", "r1", "r2", "r3", "r4", "r5", "r6", "r7", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "r16", "r17", "r18", "r19", "r20", "r21", "r22", "r23", "r24", "r25", "r26"
1624    );
1625#endif
1626    return 0;
1627}
1628
1629/* Conditionally add a and b using the mask m.
1630 * m is -1 to add and 0 when not.
1631 *
1632 * r  A single precision number representing conditional add result.
1633 * a  A single precision number to add with.
1634 * b  A single precision number to add.
1635 * m  Mask value to apply.
1636 */
1637static void sp_256_cond_add_10(sp_digit* r, const sp_digit* a,
1638        const sp_digit* b, const sp_digit m)
1639{
1640#ifdef WOLFSSL_SP_SMALL
1641    int i;
1642
1643    for (i = 0; i < 10; i++) {
1644        r[i] = a[i] + (b[i] & m);
1645    }
1646#else
1647    r[ 0] = Q6_R_add_RR(a[ 0], Q6_R_and_RR(b[ 0], m));
1648    r[ 1] = Q6_R_add_RR(a[ 1], Q6_R_and_RR(b[ 1], m));
1649    r[ 2] = Q6_R_add_RR(a[ 2], Q6_R_and_RR(b[ 2], m));
1650    r[ 3] = Q6_R_add_RR(a[ 3], Q6_R_and_RR(b[ 3], m));
1651    r[ 4] = Q6_R_add_RR(a[ 4], Q6_R_and_RR(b[ 4], m));
1652    r[ 5] = Q6_R_add_RR(a[ 5], Q6_R_and_RR(b[ 5], m));
1653    r[ 6] = Q6_R_add_RR(a[ 6], Q6_R_and_RR(b[ 6], m));
1654    r[ 7] = Q6_R_add_RR(a[ 7], Q6_R_and_RR(b[ 7], m));
1655    r[ 8] = Q6_R_add_RR(a[ 8], Q6_R_and_RR(b[ 8], m));
1656    r[ 9] = Q6_R_add_RR(a[ 9], Q6_R_and_RR(b[ 9], m));
1657#endif /* WOLFSSL_SP_SMALL */
1658}
1659
1660
1661/* Subtract two Montgomery form numbers (r = a - b % m).
1662 *
1663 * r   Result of subtration.
1664 * a   Number to subtract from in Montgomery form.
1665 * b   Number to subtract with in Montgomery form.
1666 * m   Modulus (prime).
1667 */
1668static void sp_256_mont_sub_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
1669        const sp_digit* m)
1670{
1671    (void)sp_256_sub_10(r, a, b);
1672    sp_256_cond_add_10(r, r, m, r[9] >> 22);
1673    sp_256_norm_10(r);
1674}
1675
1676
1677/* Shift number left one bit.
1678 * Bottom bit is lost.
1679 *
1680 * r  Result of shift.
1681 * a  Number to shift.
1682 */
1683SP_NOINLINE static void sp_256_rshift1_10(sp_digit* r, sp_digit* a)
1684{
1685#ifdef WOLFSSL_SP_SMALL
1686    int i;
1687
1688    for (i=0; i<9; i++) {
1689        r[i] = ((a[i] >> 1) | (a[i + 1] << 25)) & 0x3ffffff;
1690    }
1691#else
1692    r[0] = ((a[0] >> 1) | Q6_R_and_RR((a[1] << 25), 0x3ffffff));
1693    r[1] = ((a[1] >> 1) | Q6_R_and_RR((a[2] << 25), 0x3ffffff));
1694    r[2] = ((a[2] >> 1) | Q6_R_and_RR((a[3] << 25), 0x3ffffff));
1695    r[3] = ((a[3] >> 1) | Q6_R_and_RR((a[4] << 25), 0x3ffffff));
1696    r[4] = ((a[4] >> 1) | Q6_R_and_RR((a[5] << 25), 0x3ffffff));
1697    r[5] = ((a[5] >> 1) | Q6_R_and_RR((a[6] << 25), 0x3ffffff));
1698    r[6] = ((a[6] >> 1) | Q6_R_and_RR((a[7] << 25), 0x3ffffff));
1699    r[7] = ((a[7] >> 1) | Q6_R_and_RR((a[8] << 25), 0x3ffffff));
1700    r[8] = ((a[8] >> 1) | Q6_R_and_RR((a[9] << 25), 0x3ffffff));
1701#endif
1702    r[9] = a[9] >> 1;
1703}
1704
1705
1706/* Divide the number by 2 mod the modulus (prime). (r = a / 2 % m)
1707 *
1708 * r  Result of division by 2.
1709 * a  Number to divide.
1710 * m  Modulus (prime).
1711 */
1712static void sp_256_div2_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
1713{
1714    sp_256_cond_add_10(r, a, m, 0 - (a[0] & 1));
1715    sp_256_norm_10(r);
1716    sp_256_rshift1_10(r, r);
1717}
1718
1719
1720/* Double the Montgomery form projective point p.
1721 *
1722 * r  Result of doubling point.
1723 * p  Point to double.
1724 * t  Temporary ordinate data.
1725 */
1726static void sp_256_proj_point_dbl_10(sp_point* r, const sp_point* p, sp_digit* t)
1727{
1728    sp_point* rp[2];
1729    sp_digit* t1 = t;
1730    sp_digit* t2 = t + 2*10;
1731    sp_digit* x;
1732    sp_digit* y;
1733    sp_digit* z;
1734    int i;
1735
1736    /* When infinity don't double point passed in - constant time. */
1737    rp[0] = r;
1738
1739    /*lint allow cast to different type of pointer*/
1740    rp[1] = (sp_point*)t; /*lint !e9087 !e740*/
1741    XMEMSET(rp[1], 0, sizeof(sp_point));
1742    x = rp[p->infinity]->x;
1743    y = rp[p->infinity]->y;
1744    z = rp[p->infinity]->z;
1745    /* Put point to double into result - good for infinity. */
1746    if (r != p) {
1747        for (i=0; i<10; i++) {
1748            r->x[i] = p->x[i];
1749        }
1750        for (i=0; i<10; i++) {
1751            r->y[i] = p->y[i];
1752        }
1753        for (i=0; i<10; i++) {
1754            r->z[i] = p->z[i];
1755        }
1756        r->infinity = p->infinity;
1757    }
1758
1759    /* T1 = Z * Z */
1760    sp_256_mont_sqr_10(t1, z, p256_mod, p256_mp_mod);
1761    /* Z = Y * Z */
1762    sp_256_mont_mul_10(z, y, z, p256_mod, p256_mp_mod);
1763    /* Z = 2Z */
1764    sp_256_mont_dbl_10(z, z, p256_mod);
1765    /* T2 = X - T1 */
1766    sp_256_mont_sub_10(t2, x, t1, p256_mod);
1767    /* T1 = X + T1 */
1768    sp_256_mont_add_10(t1, x, t1, p256_mod);
1769    /* T2 = T1 * T2 */
1770    sp_256_mont_mul_10(t2, t1, t2, p256_mod, p256_mp_mod);
1771    /* T1 = 3T2 */
1772    sp_256_mont_tpl_10(t1, t2, p256_mod);
1773    /* Y = 2Y */
1774    sp_256_mont_dbl_10(y, y, p256_mod);
1775    /* Y = Y * Y */
1776    sp_256_mont_sqr_10(y, y, p256_mod, p256_mp_mod);
1777    /* T2 = Y * Y */
1778    sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
1779    /* T2 = T2/2 */
1780    sp_256_div2_10(t2, t2, p256_mod);
1781    /* Y = Y * X */
1782    sp_256_mont_mul_10(y, y, x, p256_mod, p256_mp_mod);
1783    /* X = T1 * T1 */
1784    sp_256_mont_mul_10(x, t1, t1, p256_mod, p256_mp_mod);
1785    /* X = X - Y */
1786    sp_256_mont_sub_10(x, x, y, p256_mod);
1787    /* X = X - Y */
1788    sp_256_mont_sub_10(x, x, y, p256_mod);
1789    /* Y = Y - X */
1790    sp_256_mont_sub_10(y, y, x, p256_mod);
1791    /* Y = Y * T1 */
1792    sp_256_mont_mul_10(y, y, t1, p256_mod, p256_mp_mod);
1793    /* Y = Y - T2 */
1794    sp_256_mont_sub_10(y, y, t2, p256_mod);
1795
1796}
1797
1798
1799/* Compare two numbers to determine if they are equal.
1800 * Constant time implementation.
1801 *
1802 * a  First number to compare.
1803 * b  Second number to compare.
1804 * returns 1 when equal and 0 otherwise.
1805 */
1806static int sp_256_cmp_equal_10(const sp_digit* a, const sp_digit* b)
1807{
1808    return ((a[0] ^ b[0]) | (a[1] ^ b[1]) | (a[2] ^ b[2]) | (a[3] ^ b[3]) |
1809            (a[4] ^ b[4]) | (a[5] ^ b[5]) | (a[6] ^ b[6]) | (a[7] ^ b[7]) |
1810            (a[8] ^ b[8]) | (a[9] ^ b[9])) == 0;
1811}
1812
1813/* Add two Montgomery form projective points.
1814 *
1815 * r  Result of addition.
1816 * p  First point to add.
1817 * q  Second point to add.
1818 * t  Temporary ordinate data.
1819 */
1820static void sp_256_proj_point_add_10(sp_point* r, const sp_point* p, const sp_point* q,
1821        sp_digit* t)
1822{
1823    const sp_point* ap[2];
1824    sp_point* rp[2];
1825    sp_digit* t1 = t;
1826    sp_digit* t2 = t + 2*10;
1827    sp_digit* t3 = t + 4*10;
1828    sp_digit* t4 = t + 6*10;
1829    sp_digit* t5 = t + 8*10;
1830    sp_digit* x;
1831    sp_digit* y;
1832    sp_digit* z;
1833    int i;
1834
1835    /* Ensure only the first point is the same as the result. */
1836    if (q == r) {
1837        const sp_point* a = p;
1838        p = q;
1839        q = a;
1840    }
1841
1842    /* Check double */
1843    (void)sp_256_sub_10(t1, p256_mod, q->y);
1844    sp_256_norm_10(t1);
1845    if ((sp_256_cmp_equal_10(p->x, q->x) & sp_256_cmp_equal_10(p->z, q->z) &
1846        (sp_256_cmp_equal_10(p->y, q->y) | sp_256_cmp_equal_10(p->y, t1))) != 0) {
1847        sp_256_proj_point_dbl_10(r, p, t);
1848    }
1849    else {
1850        rp[0] = r;
1851
1852        /*lint allow cast to different type of pointer*/
1853        rp[1] = (sp_point*)t; /*lint !e9087 !e740*/
1854        XMEMSET(rp[1], 0, sizeof(sp_point));
1855        x = rp[p->infinity | q->infinity]->x;
1856        y = rp[p->infinity | q->infinity]->y;
1857        z = rp[p->infinity | q->infinity]->z;
1858
1859        ap[0] = p;
1860        ap[1] = q;
1861        for (i=0; i<10; i++) {
1862            r->x[i] = ap[p->infinity]->x[i];
1863        }
1864        for (i=0; i<10; i++) {
1865            r->y[i] = ap[p->infinity]->y[i];
1866        }
1867        for (i=0; i<10; i++) {
1868            r->z[i] = ap[p->infinity]->z[i];
1869        }
1870        r->infinity = ap[p->infinity]->infinity;
1871
1872        /* U1 = X1*Z2^2 */
1873        sp_256_mont_sqr_10(t1, q->z, p256_mod, p256_mp_mod);
1874        sp_256_mont_mul_10(t3, t1, q->z, p256_mod, p256_mp_mod);
1875        sp_256_mont_mul_10(t1, t1, x, p256_mod, p256_mp_mod);
1876        /* U2 = X2*Z1^2 */
1877        sp_256_mont_sqr_10(t2, z, p256_mod, p256_mp_mod);
1878        sp_256_mont_mul_10(t4, t2, z, p256_mod, p256_mp_mod);
1879        sp_256_mont_mul_10(t2, t2, q->x, p256_mod, p256_mp_mod);
1880        /* S1 = Y1*Z2^3 */
1881        sp_256_mont_mul_10(t3, t3, y, p256_mod, p256_mp_mod);
1882        /* S2 = Y2*Z1^3 */
1883        sp_256_mont_mul_10(t4, t4, q->y, p256_mod, p256_mp_mod);
1884        /* H = U2 - U1 */
1885        sp_256_mont_sub_10(t2, t2, t1, p256_mod);
1886        /* R = S2 - S1 */
1887        sp_256_mont_sub_10(t4, t4, t3, p256_mod);
1888        /* Z3 = H*Z1*Z2 */
1889        sp_256_mont_mul_10(z, z, q->z, p256_mod, p256_mp_mod);
1890        sp_256_mont_mul_10(z, z, t2, p256_mod, p256_mp_mod);
1891        /* X3 = R^2 - H^3 - 2*U1*H^2 */
1892        sp_256_mont_sqr_10(x, t4, p256_mod, p256_mp_mod);
1893        sp_256_mont_sqr_10(t5, t2, p256_mod, p256_mp_mod);
1894        sp_256_mont_mul_10(y, t1, t5, p256_mod, p256_mp_mod);
1895        sp_256_mont_mul_10(t5, t5, t2, p256_mod, p256_mp_mod);
1896        sp_256_mont_sub_10(x, x, t5, p256_mod);
1897        sp_256_mont_dbl_10(t1, y, p256_mod);
1898        sp_256_mont_sub_10(x, x, t1, p256_mod);
1899        /* Y3 = R*(U1*H^2 - X3) - S1*H^3 */
1900        sp_256_mont_sub_10(y, y, x, p256_mod);
1901        sp_256_mont_mul_10(y, y, t4, p256_mod, p256_mp_mod);
1902        sp_256_mont_mul_10(t5, t5, t3, p256_mod, p256_mp_mod);
1903        sp_256_mont_sub_10(y, y, t5, p256_mod);
1904    }
1905}
1906
1907#ifdef WOLFSSL_SP_SMALL
1908/* Multiply the point by the scalar and return the result.
1909 * If map is true then convert result to affine coordinates.
1910 *
1911 * r     Resulting point.
1912 * g     Point to multiply.
1913 * k     Scalar to multiply by.
1914 * map   Indicates whether to convert result to affine.
1915 * heap  Heap to use for allocation.
1916 * returns MEMORY_E when memory allocation fails and MP_OKAY on success.
1917 */
1918static int sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k,
1919        int map, void* heap)
1920{
1921    sp_point* td;
1922    sp_point* t[3];
1923    sp_digit* tmp;
1924    sp_digit n;
1925    int i;
1926    int c, y;
1927    int err = MP_OKAY;
1928
1929    (void)heap;
1930
1931    td = (sp_point*)XMALLOC(sizeof(sp_point) * 3, heap, DYNAMIC_TYPE_ECC);
1932    if (td == NULL)
1933        err = MEMORY_E;
1934    tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
1935                                                              DYNAMIC_TYPE_ECC);
1936    if (tmp == NULL)
1937        err = MEMORY_E;
1938
1939    if (err == MP_OKAY) {
1940        XMEMSET(td, 0, sizeof(*td) * 3);
1941
1942        t[0] = &td[0];
1943        t[1] = &td[1];
1944        t[2] = &td[2];
1945
1946        /* t[0] = {0, 0, 1} * norm */
1947        t[0]->infinity = 1;
1948        /* t[1] = {g->x, g->y, g->z} * norm */
1949        err = sp_256_mod_mul_norm_10(t[1]->x, g->x, p256_mod);
1950    }
1951    if (err == MP_OKAY)
1952        err = sp_256_mod_mul_norm_10(t[1]->y, g->y, p256_mod);
1953    if (err == MP_OKAY)
1954        err = sp_256_mod_mul_norm_10(t[1]->z, g->z, p256_mod);
1955
1956    if (err == MP_OKAY) {
1957        i = 9;
1958        c = 22;
1959        n = k[i--] << (26 - c);
1960        for (; ; c--) {
1961            if (c == 0) {
1962                if (i == -1)
1963                    break;
1964
1965                n = k[i--];
1966                c = 26;
1967            }
1968
1969            y = (n >> 25) & 1;
1970            n <<= 1;
1971
1972            sp_256_proj_point_add_10(t[y^1], t[0], t[1], tmp);
1973
1974            XMEMCPY(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
1975                                  ((size_t)t[1] & addr_mask[y])),
1976                    sizeof(sp_point));
1977            sp_256_proj_point_dbl_10(t[2], t[2], tmp);
1978            XMEMCPY((void*)(((size_t)t[0] & addr_mask[y^1]) +
1979                            ((size_t)t[1] & addr_mask[y])), t[2],
1980                    sizeof(sp_point));
1981        }
1982
1983        if (map != 0) {
1984            sp_256_map_10(r, t[0], tmp);
1985        }
1986        else {
1987            XMEMCPY(r, t[0], sizeof(sp_point));
1988        }
1989    }
1990
1991    if (tmp != NULL) {
1992        XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
1993        XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
1994    }
1995    if (td != NULL) {
1996        XMEMSET(td, 0, sizeof(sp_point) * 3);
1997        XFREE(td, NULL, DYNAMIC_TYPE_ECC);
1998    }
1999
2000    return err;
2001}
2002
2003#elif !defined(WC_NO_CACHE_RESISTANT)
2004/* Multiply the point by the scalar and return the result.
2005 * If map is true then convert result to affine coordinates.
2006 *
2007 * r     Resulting point.
2008 * g     Point to multiply.
2009 * k     Scalar to multiply by.
2010 * map   Indicates whether to convert result to affine.
2011 * heap  Heap to use for allocation.
2012 * returns MEMORY_E when memory allocation fails and MP_OKAY on success.
2013 */
2014static int sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k,
2015        int map, void* heap)
2016{
2017#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
2018    sp_point td[3];
2019    sp_digit tmpd[2 * 10 * 5];
2020#endif
2021    sp_point* t;
2022    sp_digit* tmp;
2023    sp_digit n;
2024    int i;
2025    int c, y;
2026    int err = MP_OKAY;
2027
2028    (void)heap;
2029
2030#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
2031    sp_point td[3];
2032    t = (sp_point*)XMALLOC(sizeof(*td) * 3, heap, DYNAMIC_TYPE_ECC);
2033    if (t == NULL)
2034        err = MEMORY_E;
2035    tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
2036                             DYNAMIC_TYPE_ECC);
2037    if (tmp == NULL)
2038        err = MEMORY_E;
2039#else
2040    t = td;
2041    tmp = tmpd;
2042#endif
2043
2044    if (err == MP_OKAY) {
2045        t[0] = &td[0];
2046        t[1] = &td[1];
2047        t[2] = &td[2];
2048
2049        /* t[0] = {0, 0, 1} * norm */
2050        XMEMSET(&t[0], 0, sizeof(t[0]));
2051        t[0].infinity = 1;
2052        /* t[1] = {g->x, g->y, g->z} * norm */
2053        err = sp_256_mod_mul_norm_10(t[1].x, g->x, p256_mod);
2054    }
2055    if (err == MP_OKAY)
2056        err = sp_256_mod_mul_norm_10(t[1].y, g->y, p256_mod);
2057    if (err == MP_OKAY)
2058        err = sp_256_mod_mul_norm_10(t[1].z, g->z, p256_mod);
2059
2060    if (err == MP_OKAY) {
2061        i = 9;
2062        c = 22;
2063        n = k[i--] << (26 - c);
2064        for (; ; c--) {
2065            if (c == 0) {
2066                if (i == -1)
2067                    break;
2068
2069                n = k[i--];
2070                c = 26;
2071            }
2072
2073            y = (n >> 25) & 1;
2074            n <<= 1;
2075
2076            sp_256_proj_point_add_10(&t[y^1], &t[0], &t[1], tmp);
2077
2078            XMEMCPY(&t[2], (void*)(((size_t)&t[0] & addr_mask[y^1]) +
2079                                 ((size_t)&t[1] & addr_mask[y])), sizeof(t[2]));
2080            sp_256_proj_point_dbl_10(&t[2], &t[2], tmp);
2081            XMEMCPY((void*)(((size_t)&t[0] & addr_mask[y^1]) +
2082                          ((size_t)&t[1] & addr_mask[y])), &t[2], sizeof(t[2]));
2083        }
2084
2085        if (map != 0) {
2086            sp_256_map_10(r, &t[0], tmp);
2087        }
2088        else {
2089            XMEMCPY(r, &t[0], sizeof(sp_point));
2090        }
2091    }
2092
2093#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
2094    if (tmp != NULL) {
2095        XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
2096        XFREE(tmp, heap, DYNAMIC_TYPE_ECC);
2097    }
2098    if (t != NULL) {
2099        XMEMSET(t, 0, sizeof(sp_point) * 3);
2100        XFREE(t, heap, DYNAMIC_TYPE_ECC);
2101    }
2102#else
2103    ForceZero(tmpd, sizeof(tmpd));
2104    ForceZero(td, sizeof(td));
2105#endif
2106
2107    return err;
2108}
2109
2110#else
2111/* A table entry for pre-computed points. */
2112typedef struct sp_table_entry {
2113    sp_digit x[10] __attribute__((aligned(128)));
2114    sp_digit y[10] __attribute__((aligned(128)));
2115} sp_table_entry;
2116
2117/* Multiply the point by the scalar and return the result.
2118 * If map is true then convert result to affine coordinates.
2119 *
2120 * r     Resulting point.
2121 * g     Point to multiply.
2122 * k     Scalar to multiply by.
2123 * map   Indicates whether to convert result to affine.
2124 * heap  Heap to use for allocation.
2125 * returns MEMORY_E when memory allocation fails and MP_OKAY on success.
2126 */
2127static int sp_256_ecc_mulmod_fast_10(sp_point* r, const sp_point* g, const sp_digit* k,
2128        int map, void* heap)
2129{
2130#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
2131    sp_point td[16];
2132    sp_point rtd;
2133    sp_digit tmpd[2 * 10 * 5];
2134#endif
2135    sp_point* t;
2136    sp_point* rt;
2137    sp_digit* tmp;
2138    sp_digit n;
2139    int i;
2140    int c, y;
2141    int err;
2142
2143    (void)heap;
2144
2145    err = sp_ecc_point_new(heap, rtd, rt);
2146#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
2147    t = (sp_point*)XMALLOC(sizeof(sp_point) * 16, heap, DYNAMIC_TYPE_ECC);
2148    if (t == NULL)
2149        err = MEMORY_E;
2150    tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
2151                             DYNAMIC_TYPE_ECC);
2152    if (tmp == NULL)
2153        err = MEMORY_E;
2154#else
2155    t = td;
2156    tmp = tmpd;
2157#endif
2158
2159    if (err == MP_OKAY) {
2160        /* t[0] = {0, 0, 1} * norm */
2161        XMEMSET(&t[0], 0, sizeof(t[0]));
2162        t[0].infinity = 1;
2163        /* t[1] = {g->x, g->y, g->z} * norm */
2164        (void)sp_256_mod_mul_norm_10(t[1].x, g->x, p256_mod);
2165        (void)sp_256_mod_mul_norm_10(t[1].y, g->y, p256_mod);
2166        (void)sp_256_mod_mul_norm_10(t[1].z, g->z, p256_mod);
2167        t[1].infinity = 0;
2168        sp_256_proj_point_dbl_10(&t[ 2], &t[ 1], tmp);
2169        t[ 2].infinity = 0;
2170        sp_256_proj_point_add_10(&t[ 3], &t[ 2], &t[ 1], tmp);
2171        t[ 3].infinity = 0;
2172        sp_256_proj_point_dbl_10(&t[ 4], &t[ 2], tmp);
2173        t[ 4].infinity = 0;
2174        sp_256_proj_point_add_10(&t[ 5], &t[ 3], &t[ 2], tmp);
2175        t[ 5].infinity = 0;
2176        sp_256_proj_point_dbl_10(&t[ 6], &t[ 3], tmp);
2177        t[ 6].infinity = 0;
2178        sp_256_proj_point_add_10(&t[ 7], &t[ 4], &t[ 3], tmp);
2179        t[ 7].infinity = 0;
2180        sp_256_proj_point_dbl_10(&t[ 8], &t[ 4], tmp);
2181        t[ 8].infinity = 0;
2182        sp_256_proj_point_add_10(&t[ 9], &t[ 5], &t[ 4], tmp);
2183        t[ 9].infinity = 0;
2184        sp_256_proj_point_dbl_10(&t[10], &t[ 5], tmp);
2185        t[10].infinity = 0;
2186        sp_256_proj_point_add_10(&t[11], &t[ 6], &t[ 5], tmp);
2187        t[11].infinity = 0;
2188        sp_256_proj_point_dbl_10(&t[12], &t[ 6], tmp);
2189        t[12].infinity = 0;
2190        sp_256_proj_point_add_10(&t[13], &t[ 7], &t[ 6], tmp);
2191        t[13].infinity = 0;
2192        sp_256_proj_point_dbl_10(&t[14], &t[ 7], tmp);
2193        t[14].infinity = 0;
2194        sp_256_proj_point_add_10(&t[15], &t[ 8], &t[ 7], tmp);
2195        t[15].infinity = 0;
2196
2197        i = 8;
2198        n = k[i+1] << 6;
2199        c = 18;
2200        y = n >> 24;
2201        XMEMCPY(rt, &t[y], sizeof(sp_point));
2202        n <<= 8;
2203        for (; i>=0 || c>=4; ) {
2204            if (c < 4) {
2205                n |= k[i--] << (6 - c);
2206                c += 26;
2207            }
2208            y = (n >> 28) & 0xf;
2209            n <<= 4;
2210            c -= 4;
2211
2212            sp_256_proj_point_dbl_10(rt, rt, tmp);
2213            sp_256_proj_point_dbl_10(rt, rt, tmp);
2214            sp_256_proj_point_dbl_10(rt, rt, tmp);
2215            sp_256_proj_point_dbl_10(rt, rt, tmp);
2216
2217            sp_256_proj_point_add_10(rt, rt, &t[y], tmp);
2218        }
2219
2220        if (map != 0) {
2221            sp_256_map_10(r, rt, tmp);
2222        }
2223        else {
2224            XMEMCPY(r, rt, sizeof(sp_point));
2225        }
2226    }
2227
2228#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
2229    if (tmp != NULL) {
2230        XMEMSET(tmp, 0, sizeof(sp_digit) * 2 * 10 * 5);
2231        XFREE(tmp, heap, DYNAMIC_TYPE_ECC);
2232    }
2233    if (t != NULL) {
2234        XMEMSET(t, 0, sizeof(sp_point) * 16);
2235        XFREE(t, heap, DYNAMIC_TYPE_ECC);
2236    }
2237#else
2238    ForceZero(tmpd, sizeof(tmpd));
2239    ForceZero(td, sizeof(td));
2240#endif
2241    sp_ecc_point_free(rt, 1, heap);
2242
2243    return err;
2244}
2245
2246#ifdef FP_ECC
2247/* Double the Montgomery form projective point p a number of times.
2248 *
2249 * r  Result of repeated doubling of point.
2250 * p  Point to double.
2251 * n  Number of times to double
2252 * t  Temporary ordinate data.
2253 */
2254static void sp_256_proj_point_dbl_n_10(sp_point* r, const sp_point* p, int n,
2255        sp_digit* t)
2256{
2257    sp_point* rp[2];
2258    sp_digit* w = t;
2259    sp_digit* a = t + 2*10;
2260    sp_digit* b = t + 4*10;
2261    sp_digit* t1 = t + 6*10;
2262    sp_digit* t2 = t + 8*10;
2263    sp_digit* x;
2264    sp_digit* y;
2265    sp_digit* z;
2266    int i;
2267
2268    rp[0] = r;
2269
2270    /*lint allow cast to different type of pointer*/
2271    rp[1] = (sp_point*)t; /*lint !e9087 !e740*/
2272    XMEMSET(rp[1], 0, sizeof(sp_point));
2273    x = rp[p->infinity]->x;
2274    y = rp[p->infinity]->y;
2275    z = rp[p->infinity]->z;
2276    if (r != p) {
2277        for (i=0; i<10; i++) {
2278            r->x[i] = p->x[i];
2279        }
2280        for (i=0; i<10; i++) {
2281            r->y[i] = p->y[i];
2282        }
2283        for (i=0; i<10; i++) {
2284            r->z[i] = p->z[i];
2285        }
2286        r->infinity = p->infinity;
2287    }
2288
2289    /* Y = 2*Y */
2290    sp_256_mont_dbl_10(y, y, p256_mod);
2291    /* W = Z^4 */
2292    sp_256_mont_sqr_10(w, z, p256_mod, p256_mp_mod);
2293    sp_256_mont_sqr_10(w, w, p256_mod, p256_mp_mod);
2294    while (n-- > 0) {
2295        /* A = 3*(X^2 - W) */
2296        sp_256_mont_sqr_10(t1, x, p256_mod, p256_mp_mod);
2297        sp_256_mont_sub_10(t1, t1, w, p256_mod);
2298        sp_256_mont_tpl_10(a, t1, p256_mod);
2299        /* B = X*Y^2 */
2300        sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
2301        sp_256_mont_mul_10(b, t2, x, p256_mod, p256_mp_mod);
2302        /* X = A^2 - 2B */
2303        sp_256_mont_sqr_10(x, a, p256_mod, p256_mp_mod);
2304        sp_256_mont_dbl_10(t1, b, p256_mod);
2305        sp_256_mont_sub_10(x, x, t1, p256_mod);
2306        /* Z = Z*Y */
2307        sp_256_mont_mul_10(z, z, y, p256_mod, p256_mp_mod);
2308        /* t2 = Y^4 */
2309        sp_256_mont_sqr_10(t2, t2, p256_mod, p256_mp_mod);
2310        if (n != 0) {
2311            /* W = W*Y^4 */
2312            sp_256_mont_mul_10(w, w, t2, p256_mod, p256_mp_mod);
2313        }
2314        /* y = 2*A*(B - X) - Y^4 */
2315        sp_256_mont_sub_10(y, b, x, p256_mod);
2316        sp_256_mont_mul_10(y, y, a, p256_mod, p256_mp_mod);
2317        sp_256_mont_dbl_10(y, y, p256_mod);
2318        sp_256_mont_sub_10(y, y, t2, p256_mod);
2319    }
2320    /* Y = Y/2 */
2321    sp_256_div2_10(y, y, p256_mod);
2322}
2323
2324#endif /* FP_ECC */
2325
2326
2327/* Add two Montgomery form projective points. The second point has a q value of
2328 * one.
2329 * Only the first point can be the same pointer as the result point.
2330 *
2331 * r  Result of addition.
2332 * p  First point to add.
2333 * q  Second point to add.
2334 * t  Temporary ordinate data.
2335 */
2336static void sp_256_proj_point_add_qz1_10(sp_point* r, const sp_point* p,
2337        const sp_point* q, sp_digit* t)
2338{
2339    const sp_point* ap[2];
2340    sp_point* rp[2];
2341    sp_digit* t1 = t;
2342    sp_digit* t2 = t + 2*10;
2343    sp_digit* t3 = t + 4*10;
2344    sp_digit* t4 = t + 6*10;
2345    sp_digit* t5 = t + 8*10;
2346    sp_digit* x;
2347    sp_digit* y;
2348    sp_digit* z;
2349    int i;
2350
2351    /* Check double */
2352    (void)sp_256_sub_10(t1, p256_mod, q->y);
2353    sp_256_norm_10(t1);
2354    if ((sp_256_cmp_equal_10(p->x, q->x) & sp_256_cmp_equal_10(p->z, q->z) &
2355        (sp_256_cmp_equal_10(p->y, q->y) | sp_256_cmp_equal_10(p->y, t1))) != 0) {
2356        sp_256_proj_point_dbl_10(r, p, t);
2357    }
2358    else {
2359        rp[0] = r;
2360
2361        /*lint allow cast to different type of pointer*/
2362        rp[1] = (sp_point*)t; /*lint !e9087 !e740*/
2363        XMEMSET(rp[1], 0, sizeof(sp_point));
2364        x = rp[p->infinity | q->infinity]->x;
2365        y = rp[p->infinity | q->infinity]->y;
2366        z = rp[p->infinity | q->infinity]->z;
2367
2368        ap[0] = p;
2369        ap[1] = q;
2370        for (i=0; i<10; i++) {
2371            r->x[i] = ap[p->infinity]->x[i];
2372        }
2373        for (i=0; i<10; i++) {
2374            r->y[i] = ap[p->infinity]->y[i];
2375        }
2376        for (i=0; i<10; i++) {
2377            r->z[i] = ap[p->infinity]->z[i];
2378        }
2379        r->infinity = ap[p->infinity]->infinity;
2380
2381        /* U2 = X2*Z1^2 */
2382        sp_256_mont_sqr_10(t2, z, p256_mod, p256_mp_mod);
2383        sp_256_mont_mul_10(t4, t2, z, p256_mod, p256_mp_mod);
2384        sp_256_mont_mul_10(t2, t2, q->x, p256_mod, p256_mp_mod);
2385        /* S2 = Y2*Z1^3 */
2386        sp_256_mont_mul_10(t4, t4, q->y, p256_mod, p256_mp_mod);
2387        /* H = U2 - X1 */
2388        sp_256_mont_sub_10(t2, t2, x, p256_mod);
2389        /* R = S2 - Y1 */
2390        sp_256_mont_sub_10(t4, t4, y, p256_mod);
2391        /* Z3 = H*Z1 */
2392        sp_256_mont_mul_10(z, z, t2, p256_mod, p256_mp_mod);
2393        /* X3 = R^2 - H^3 - 2*X1*H^2 */
2394        sp_256_mont_sqr_10(t1, t4, p256_mod, p256_mp_mod);
2395        sp_256_mont_sqr_10(t5, t2, p256_mod, p256_mp_mod);
2396        sp_256_mont_mul_10(t3, x, t5, p256_mod, p256_mp_mod);
2397        sp_256_mont_mul_10(t5, t5, t2, p256_mod, p256_mp_mod);
2398        sp_256_mont_sub_10(x, t1, t5, p256_mod);
2399        sp_256_mont_dbl_10(t1, t3, p256_mod);
2400        sp_256_mont_sub_10(x, x, t1, p256_mod);
2401        /* Y3 = R*(X1*H^2 - X3) - Y1*H^3 */
2402        sp_256_mont_sub_10(t3, t3, x, p256_mod);
2403        sp_256_mont_mul_10(t3, t3, t4, p256_mod, p256_mp_mod);
2404        sp_256_mont_mul_10(t5, t5, y, p256_mod, p256_mp_mod);
2405        sp_256_mont_sub_10(y, t3, t5, p256_mod);
2406    }
2407}
2408
2409#ifdef FP_ECC
2410/* Convert the projective point to affine.
2411 * Ordinates are in Montgomery form.
2412 *
2413 * a  Point to convert.
2414 * t  Temporary data.
2415 */
2416static void sp_256_proj_to_affine_10(sp_point* a, sp_digit* t)
2417{
2418    sp_digit* t1 = t;
2419    sp_digit* t2 = t + 2 * 10;
2420    sp_digit* tmp = t + 4 * 10;
2421
2422    sp_256_mont_inv_10(t1, a->z, tmp);
2423
2424    sp_256_mont_sqr_10(t2, t1, p256_mod, p256_mp_mod);
2425    sp_256_mont_mul_10(t1, t2, t1, p256_mod, p256_mp_mod);
2426
2427    sp_256_mont_mul_10(a->x, a->x, t2, p256_mod, p256_mp_mod);
2428    sp_256_mont_mul_10(a->y, a->y, t1, p256_mod, p256_mp_mod);
2429    XMEMCPY(a->z, p256_norm_mod, sizeof(p256_norm_mod));
2430}
2431
2432
2433/* Generate the pre-computed table of points for the base point.
2434 *
2435 * a      The base point.
2436 * table  Place to store generated point data.
2437 * tmp    Temporary data.
2438 * heap  Heap to use for allocation.
2439 */
2440static int sp_256_gen_stripe_table_10(const sp_point* a,
2441        sp_table_entry* table, sp_digit* tmp, void* heap)
2442{
2443#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
2444    sp_point td, s1d, s2d;
2445#endif
2446    sp_point* t;
2447    sp_point* s1 = NULL;
2448    sp_point* s2 = NULL;
2449    int i, j;
2450    int err;
2451
2452    (void)heap;
2453
2454    err = sp_ecc_point_new(heap, td, t);
2455    if (err == MP_OKAY) {
2456        err = sp_ecc_point_new(heap, s1d, s1);
2457    }
2458    if (err == MP_OKAY) {
2459        err = sp_ecc_point_new(heap, s2d, s2);
2460    }
2461
2462    if (err == MP_OKAY) {
2463        err = sp_256_mod_mul_norm_10(t->x, a->x, p256_mod);
2464    }
2465    if (err == MP_OKAY) {
2466        err = sp_256_mod_mul_norm_10(t->y, a->y, p256_mod);
2467    }
2468    if (err == MP_OKAY) {
2469        err = sp_256_mod_mul_norm_10(t->z, a->z, p256_mod);
2470    }
2471    if (err == MP_OKAY) {
2472        t->infinity = 0;
2473        sp_256_proj_to_affine_10(t, tmp);
2474
2475        XMEMCPY(s1->z, p256_norm_mod, sizeof(p256_norm_mod));
2476        s1->infinity = 0;
2477        XMEMCPY(s2->z, p256_norm_mod, sizeof(p256_norm_mod));
2478        s2->infinity = 0;
2479
2480        /* table[0] = {0, 0, infinity} */
2481        XMEMSET(&table[0], 0, sizeof(sp_table_entry));
2482        /* table[1] = Affine version of 'a' in Montgomery form */
2483        XMEMCPY(table[1].x, t->x, sizeof(table->x));
2484        XMEMCPY(table[1].y, t->y, sizeof(table->y));
2485
2486        for (i=1; i<8; i++) {
2487            sp_256_proj_point_dbl_n_10(t, t, 32, tmp);
2488            sp_256_proj_to_affine_10(t, tmp);
2489            XMEMCPY(table[1<<i].x, t->x, sizeof(table->x));
2490            XMEMCPY(table[1<<i].y, t->y, sizeof(table->y));
2491        }
2492
2493        for (i=1; i<8; i++) {
2494            XMEMCPY(s1->x, table[1<<i].x, sizeof(table->x));
2495            XMEMCPY(s1->y, table[1<<i].y, sizeof(table->y));
2496            for (j=(1<<i)+1; j<(1<<(i+1)); j++) {
2497                XMEMCPY(s2->x, table[j-(1<<i)].x, sizeof(table->x));
2498                XMEMCPY(s2->y, table[j-(1<<i)].y, sizeof(table->y));
2499                sp_256_proj_point_add_qz1_10(t, s1, s2, tmp);
2500                sp_256_proj_to_affine_10(t, tmp);
2501                XMEMCPY(table[j].x, t->x, sizeof(table->x));
2502                XMEMCPY(table[j].y, t->y, sizeof(table->y));
2503            }
2504        }
2505    }
2506
2507    sp_ecc_point_free(s2, 0, heap);
2508    sp_ecc_point_free(s1, 0, heap);
2509    sp_ecc_point_free( t, 0, heap);
2510
2511    return err;
2512}
2513
2514#endif /* FP_ECC */
2515/* Multiply the point by the scalar and return the result.
2516 * If map is true then convert result to affine coordinates.
2517 *
2518 * r     Resulting point.
2519 * k     Scalar to multiply by.
2520 * map   Indicates whether to convert result to affine.
2521 * heap  Heap to use for allocation.
2522 * returns MEMORY_E when memory allocation fails and MP_OKAY on success.
2523 */
2524static int sp_256_ecc_mulmod_stripe_10(sp_point* r, const sp_point* g,
2525        const sp_table_entry* table, const sp_digit* k, int map, void* heap)
2526{
2527#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
2528    sp_point rtd;
2529    sp_point pd;
2530    sp_digit td[2 * 10 * 5];
2531#endif
2532    sp_point* rt;
2533    sp_point* p = NULL;
2534    sp_digit* t;
2535    int i, j;
2536    int y, x;
2537    int err;
2538
2539    (void)g;
2540    (void)heap;
2541
2542    err = sp_ecc_point_new(heap, rtd, rt);
2543    if (err == MP_OKAY) {
2544        err = sp_ecc_point_new(heap, pd, p);
2545    }
2546#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
2547    t = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, heap,
2548                           DYNAMIC_TYPE_ECC);
2549    if (t == NULL) {
2550        err = MEMORY_E;
2551    }
2552#else
2553    t = td;
2554#endif
2555
2556    if (err == MP_OKAY) {
2557        XMEMCPY(p->z, p256_norm_mod, sizeof(p256_norm_mod));
2558        XMEMCPY(rt->z, p256_norm_mod, sizeof(p256_norm_mod));
2559
2560        y = 0;
2561        for (j=0,x=31; j<8; j++,x+=32) {
2562            y |= ((k[x / 26] >> (x % 26)) & 1) << j;
2563        }
2564        XMEMCPY(rt->x, table[y].x, sizeof(table[y].x));
2565        XMEMCPY(rt->y, table[y].y, sizeof(table[y].y));
2566        rt->infinity = !y;
2567        for (i=30; i>=0; i--) {
2568            y = 0;
2569            for (j=0,x=i; j<8; j++,x+=32) {
2570                y |= ((k[x / 26] >> (x % 26)) & 1) << j;
2571            }
2572
2573            sp_256_proj_point_dbl_10(rt, rt, t);
2574            XMEMCPY(p->x, table[y].x, sizeof(table[y].x));
2575            XMEMCPY(p->y, table[y].y, sizeof(table[y].y));
2576            p->infinity = !y;
2577            sp_256_proj_point_add_qz1_10(rt, rt, p, t);
2578        }
2579
2580        if (map != 0) {
2581            sp_256_map_10(r, rt, t);
2582        }
2583        else {
2584            XMEMCPY(r, rt, sizeof(sp_point));
2585        }
2586    }
2587
2588#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
2589    XFREE(t, heap, DYNAMIC_TYPE_ECC);
2590#endif
2591    sp_ecc_point_free(p, 0, heap);
2592    sp_ecc_point_free(rt, 0, heap);
2593
2594    return err;
2595}
2596
2597#ifdef FP_ECC
2598#ifndef FP_ENTRIES
2599    #define FP_ENTRIES 16
2600#endif
2601
2602typedef struct sp_cache_t {
2603    sp_digit x[10] __attribute__((aligned(128)));
2604    sp_digit y[10] __attribute__((aligned(128)));
2605    sp_table_entry table[256] __attribute__((aligned(128)));
2606    word32 cnt;
2607    int set;
2608} sp_cache_t;
2609
2610static THREAD_LS_T sp_cache_t sp_cache[FP_ENTRIES];
2611static THREAD_LS_T int sp_cache_last = -1;
2612static THREAD_LS_T int sp_cache_inited = 0;
2613
2614#ifndef HAVE_THREAD_LS
2615    static wolfSSL_Mutex sp_cache_lock WOLFSSL_MUTEX_INITIALIZER_CLAUSE(sp_cache_lock);
2616#ifdef WOLFSSL_MUTEX_INITIALIZER
2617    static volatile int initCacheMutex = 0;
2618#endif
2619#endif
2620
2621static void sp_ecc_get_cache(const sp_point* g, sp_cache_t** cache)
2622{
2623    int i, j;
2624    word32 least;
2625
2626    if (sp_cache_inited == 0) {
2627        for (i=0; i<FP_ENTRIES; i++) {
2628            sp_cache[i].set = 0;
2629        }
2630        sp_cache_inited = 1;
2631    }
2632
2633    /* Compare point with those in cache. */
2634    for (i=0; i<FP_ENTRIES; i++) {
2635        if (!sp_cache[i].set)
2636            continue;
2637
2638        if (sp_256_cmp_equal_10(g->x, sp_cache[i].x) &
2639                           sp_256_cmp_equal_10(g->y, sp_cache[i].y)) {
2640            sp_cache[i].cnt++;
2641            break;
2642        }
2643    }
2644
2645    /* No match. */
2646    if (i == FP_ENTRIES) {
2647        /* Find empty entry. */
2648        i = (sp_cache_last + 1) % FP_ENTRIES;
2649        for (; i != sp_cache_last; i=(i+1)%FP_ENTRIES) {
2650            if (!sp_cache[i].set) {
2651                break;
2652            }
2653        }
2654
2655        /* Evict least used. */
2656        if (i == sp_cache_last) {
2657            least = sp_cache[0].cnt;
2658            for (j=1; j<FP_ENTRIES; j++) {
2659                if (sp_cache[j].cnt < least) {
2660                    i = j;
2661                    least = sp_cache[i].cnt;
2662                }
2663            }
2664        }
2665
2666        XMEMCPY(sp_cache[i].x, g->x, sizeof(sp_cache[i].x));
2667        XMEMCPY(sp_cache[i].y, g->y, sizeof(sp_cache[i].y));
2668        sp_cache[i].set = 1;
2669        sp_cache[i].cnt = 1;
2670    }
2671
2672    *cache = &sp_cache[i];
2673    sp_cache_last = i;
2674}
2675#endif /* FP_ECC */
2676
2677/* Multiply the base point of P256 by the scalar and return the result.
2678 * If map is true then convert result to affine coordinates.
2679 *
2680 * r     Resulting point.
2681 * g     Point to multiply.
2682 * k     Scalar to multiply by.
2683 * map   Indicates whether to convert result to affine.
2684 * heap  Heap to use for allocation.
2685 * returns MEMORY_E when memory allocation fails and MP_OKAY on success.
2686 */
2687static int sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k,
2688        int map, void* heap)
2689{
2690#ifndef FP_ECC
2691    return sp_256_ecc_mulmod_fast_10(r, g, k, map, heap);
2692#else
2693    sp_digit tmp[2 * 10 * 5];
2694    sp_cache_t* cache;
2695    int err = MP_OKAY;
2696
2697#ifndef HAVE_THREAD_LS
2698#ifndef WOLFSSL_MUTEX_INITIALIZER
2699    if (initCacheMutex == 0) {
2700         wc_InitMutex(&sp_cache_lock);
2701         initCacheMutex = 1;
2702    }
2703#endif
2704    if (wc_LockMutex(&sp_cache_lock) != 0)
2705       err = BAD_MUTEX_E;
2706#endif /* HAVE_THREAD_LS */
2707
2708    if (err == MP_OKAY) {
2709        sp_ecc_get_cache(g, &cache);
2710        if (cache->cnt == 2)
2711            sp_256_gen_stripe_table_10(g, cache->table, tmp, heap);
2712
2713        if (cache->cnt < 2) {
2714            err = sp_256_ecc_mulmod_fast_10(r, g, k, map, heap);
2715        }
2716        else {
2717            err = sp_256_ecc_mulmod_stripe_10(r, g, cache->table, k,
2718                    map, heap);
2719        }
2720#ifndef HAVE_THREAD_LS
2721        wc_UnLockMutex(&sp_cache_lock);
2722#endif /* HAVE_THREAD_LS */
2723    }
2724
2725    return err;
2726#endif
2727}
2728
2729#endif
2730
2731#ifdef WOLFSSL_SP_SMALL
2732/* Multiply the base point of P256 by the scalar and return the result.
2733 * If map is true then convert result to affine coordinates.
2734 *
2735 * r     Resulting point.
2736 * k     Scalar to multiply by.
2737 * map   Indicates whether to convert result to affine.
2738 * heap  Heap to use for allocation.
2739 * returns MEMORY_E when memory allocation fails and MP_OKAY on success.
2740 */
2741static int sp_256_ecc_mulmod_base_10(sp_point* r, const sp_digit* k,
2742        int map, void* heap)
2743{
2744    /* No pre-computed values. */
2745    return sp_256_ecc_mulmod_10(r, &p256_base, k, map, heap);
2746}
2747
2748#else
2749static const sp_table_entry p256_table[256] = {
2750    /* 0 */
2751    { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 },
2752      { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
2753    /* 1 */
2754    { { 0x0a9143c,0x1cc3506,0x360179e,0x3f17fb6,0x075ba95,0x1d88944,
2755        0x3b732b7,0x15719e7,0x376a537,0x0062417 },
2756      { 0x295560a,0x094d5f3,0x245cddf,0x392e867,0x18b4ab8,0x3487cc9,
2757        0x288688d,0x176174b,0x3182588,0x0215c7f } },
2758    /* 2 */
2759    { { 0x147519a,0x2218090,0x32f0202,0x2b09acd,0x0d0981e,0x1e17af2,
2760        0x14a7caa,0x163a6a7,0x10ddbdf,0x03654f1 },
2761      { 0x1590f8f,0x0d8733f,0x09179d6,0x1ad139b,0x372e962,0x0bad933,
2762        0x1961102,0x223cdff,0x37e9eb2,0x0218fae } },
2763    /* 3 */
2764    { { 0x0db6485,0x1ad88d7,0x2f97785,0x288bc28,0x3808f0e,0x3df8c02,
2765        0x28d9544,0x20280f9,0x055b5ff,0x00001d8 },
2766      { 0x38d2010,0x13ae6e0,0x308a763,0x2ecc90d,0x254014f,0x10a9981,
2767        0x247d398,0x0fb8383,0x3613437,0x020c21d } },
2768    /* 4 */
2769    { { 0x2a0d2bb,0x08bf145,0x34994f9,0x1b06988,0x30d5cc1,0x1f18b22,
2770        0x01cf3a5,0x199fe49,0x161fd1b,0x00bd79a },
2771      { 0x1a01797,0x171c2fd,0x21925c1,0x1358255,0x23d20b4,0x1c7f6d4,
2772        0x111b370,0x03dec12,0x1168d6f,0x03d923e } },
2773    /* 5 */
2774    { { 0x137bbbc,0x19a11f8,0x0bec9e5,0x27a29a8,0x3e43446,0x275cd18,
2775        0x0427617,0x00056c7,0x285133d,0x016af80 },
2776      { 0x04c7dab,0x2a0df30,0x0c0792a,0x1310c98,0x3573d9f,0x239b30d,
2777        0x1315627,0x1ce0c32,0x25b6b6f,0x0252edc } },
2778    /* 6 */
2779    { { 0x20f141c,0x26d23dc,0x3c74bbf,0x334b7d6,0x06199b3,0x0441171,
2780        0x3f61294,0x313bf70,0x3cb2f7d,0x03375ae },
2781      { 0x2f436fd,0x19c02fa,0x26becca,0x1b6e64c,0x26f647f,0x053c948,
2782        0x0fa7920,0x397d830,0x2bd4bda,0x028d86f } },
2783    /* 7 */
2784    { { 0x17c13c7,0x2895616,0x03e128a,0x17d42df,0x1c38d63,0x0f02747,
2785        0x039aecf,0x0a4b01c,0x209c4b5,0x02e84b2 },
2786      { 0x1f91dfd,0x023e916,0x07fb9e4,0x19b3ba8,0x13af43b,0x35e02ca,
2787        0x0eb0899,0x3bd2c7b,0x19d701f,0x014faee } },
2788    /* 8 */
2789    { { 0x0e63d34,0x1fb8c6c,0x0fab4fe,0x1caa795,0x0f46005,0x179ed69,
2790        0x093334d,0x120c701,0x39206d5,0x021627e },
2791      { 0x183553a,0x03d7319,0x09e5aa7,0x12b8959,0x2087909,0x0011194,
2792        0x1045071,0x0713f32,0x16d0254,0x03aec1a } },
2793    /* 9 */
2794    { { 0x01647c5,0x1b2856b,0x1799461,0x11f133d,0x0b8127d,0x1937eeb,
2795        0x266aa37,0x1f68f71,0x0cbd1b2,0x03aca08 },
2796      { 0x287e008,0x1be361a,0x38f3940,0x276488d,0x2d87dfa,0x0333b2c,
2797        0x2d2e428,0x368755b,0x09b55a7,0x007ca0a } },
2798    /* 10 */
2799    { { 0x389da99,0x2a8300e,0x0022abb,0x27ae0a1,0x0a6f2d7,0x207017a,
2800        0x047862b,0x1358c9e,0x35905e5,0x00cde92 },
2801      { 0x1f7794a,0x1d40348,0x3f613c6,0x2ddf5b5,0x0207005,0x133f5ba,
2802        0x1a37810,0x3ef5829,0x0d5f4c2,0x0035978 } },
2803    /* 11 */
2804    { { 0x1275d38,0x026efad,0x2358d9d,0x1142f82,0x14268a7,0x1cfac99,
2805        0x362ff49,0x288cbc1,0x24252f4,0x0308f68 },
2806      { 0x394520c,0x06e13c2,0x178e5da,0x18ec16f,0x1096667,0x134a7a8,
2807        0x0dcb869,0x33fc4e9,0x38cc790,0x006778e } },
2808    /* 12 */
2809    { { 0x2c5fe04,0x29c5b09,0x1bdb183,0x02ceee8,0x03b28de,0x132dc4b,
2810        0x32c586a,0x32ff5d0,0x3d491fc,0x038d372 },
2811      { 0x2a58403,0x2351aea,0x3a53b40,0x21a0ba5,0x39a6974,0x1aaaa2b,
2812        0x3901273,0x03dfe78,0x3447b4e,0x039d907 } },
2813    /* 13 */
2814    { { 0x364ba59,0x14e5077,0x02fc7d7,0x3b02c09,0x1d33f10,0x0560616,
2815        0x06dfc6a,0x15efd3c,0x357052a,0x01284b7 },
2816      { 0x039dbd0,0x18ce3e5,0x3e1fbfa,0x352f794,0x0d3c24b,0x07c6cc5,
2817        0x1e4ffa2,0x3a91bf5,0x293bb5b,0x01abd6a } },
2818    /* 14 */
2819    { { 0x0c91999,0x02da644,0x0491da1,0x100a960,0x00a24b4,0x2330824,
2820        0x0094b4b,0x1004cf8,0x35a66a4,0x017f8d1 },
2821      { 0x13e7b4b,0x232af7e,0x391ab0f,0x069f08f,0x3292b50,0x3479898,
2822        0x2889aec,0x2a4590b,0x308ecfe,0x02d5138 } },
2823    /* 15 */
2824    { { 0x2ddfdce,0x231ba45,0x39e6647,0x19be245,0x12c3291,0x35399f8,
2825        0x0d6e764,0x3082d3a,0x2bda6b0,0x0382dac },
2826      { 0x37efb57,0x04b7cae,0x00070d3,0x379e431,0x01aac0d,0x1e6f251,
2827        0x0336ad6,0x0ddd3e4,0x3de25a6,0x01c7008 } },
2828    /* 16 */
2829    { { 0x3e20925,0x230912f,0x286762a,0x30e3f73,0x391c19a,0x34e1c18,
2830        0x16a5d5d,0x093d96a,0x3d421d3,0x0187561 },
2831      { 0x37173ea,0x19ce8a8,0x0b65e87,0x0214dde,0x2238480,0x16ead0f,
2832        0x38441e0,0x3bef843,0x2124621,0x03e847f } },
2833    /* 17 */
2834    { { 0x0b19ffd,0x247cacb,0x3c231c8,0x16ec648,0x201ba8d,0x2b172a3,
2835        0x103d678,0x2fb72db,0x04c1f13,0x0161bac },
2836      { 0x3e8ed09,0x171b949,0x2de20c3,0x0f06067,0x21e81a3,0x1b194be,
2837        0x0fd6c05,0x13c449e,0x0087086,0x006756b } },
2838    /* 18 */
2839    { { 0x09a4e1f,0x27d604c,0x00741e9,0x06fa49c,0x0ab7de7,0x3f4a348,
2840        0x25ef0be,0x158fc9a,0x33f7f9c,0x039f001 },
2841      { 0x2f59f76,0x3598e83,0x30501f6,0x15083f2,0x0669b3b,0x29980b5,
2842        0x0c1f7a7,0x0f02b02,0x0fec65b,0x0382141 } },
2843    /* 19 */
2844    { { 0x031b3ca,0x23da368,0x2d66f09,0x27b9b69,0x06d1cab,0x13c91ba,
2845        0x3d81fa9,0x25ad16f,0x0825b09,0x01e3c06 },
2846      { 0x225787f,0x3bf790e,0x2c9bb7e,0x0347732,0x28016f8,0x0d6ff0d,
2847        0x2a4877b,0x1d1e833,0x3b87e94,0x010e9dc } },
2848    /* 20 */
2849    { { 0x2b533d5,0x1ddcd34,0x1dc0625,0x3da86f7,0x3673b8a,0x1e7b0a4,
2850        0x3e7c9aa,0x19ac55d,0x251c3b2,0x02edb79 },
2851      { 0x25259b3,0x24c0ead,0x3480e7e,0x34f40e9,0x3d6a0af,0x2cf3f09,
2852        0x2c83d19,0x2e66f16,0x19a5d18,0x0182d18 } },
2853    /* 21 */
2854    { { 0x2e5aa1c,0x28e3846,0x3658bd6,0x0ad279c,0x1b8b765,0x397e1fb,
2855        0x130014e,0x3ff342c,0x3b2aeeb,0x02743c9 },
2856      { 0x2730a55,0x0918c5e,0x083aca9,0x0bf76ef,0x19c955b,0x300669c,
2857        0x01dfe0a,0x312341f,0x26d356e,0x0091295 } },
2858    /* 22 */
2859    { { 0x2cf1f96,0x00e52ba,0x271c6db,0x2a40930,0x19f2122,0x0b2f4ee,
2860        0x26ac1b8,0x3bda498,0x0873581,0x0117963 },
2861      { 0x38f9dbc,0x3d1e768,0x2040d3f,0x11ba222,0x3a8aaf1,0x1b82fb5,
2862        0x1adfb24,0x2de9251,0x21cc1e4,0x0301038 } },
2863    /* 23 */
2864    { { 0x38117b6,0x2bc001b,0x1433847,0x3fdce8d,0x3651969,0x3651d7a,
2865        0x2b35761,0x1bb1d20,0x097682c,0x00737d7 },
2866      { 0x1f04839,0x1dd6d04,0x16987db,0x3d12378,0x17dbeac,0x1c2cc86,
2867        0x121dd1b,0x3fcf6ca,0x1f8a92d,0x00119d5 } },
2868    /* 24 */
2869    { { 0x0e8ffcd,0x2b174af,0x1a82cc8,0x22cbf98,0x30d53c4,0x080b5b1,
2870        0x3161727,0x297cfdb,0x2113b83,0x0011b97 },
2871      { 0x0007f01,0x23fd936,0x3183e7b,0x0496bd0,0x07fb1ef,0x178680f,
2872        0x1c5ea63,0x0016c11,0x2c3303d,0x01b8041 } },
2873    /* 25 */
2874    { { 0x0dd73b1,0x1cd6122,0x10d948c,0x23e657b,0x3767070,0x15a8aad,
2875        0x385ea8c,0x33c7ce0,0x0ede901,0x0110965 },
2876      { 0x2d4b65b,0x2a8b244,0x0c37f8f,0x0ee5b24,0x394c234,0x3a5e347,
2877        0x26e4a15,0x39a3b4c,0x2514c2e,0x029e5be } },
2878    /* 26 */
2879    { { 0x23addd7,0x3ed8120,0x13b3359,0x20f959a,0x09e2a61,0x32fcf20,
2880        0x05b78e3,0x19ba7e2,0x1a9c697,0x0392b4b },
2881      { 0x2048a61,0x3dfd0a3,0x19a0357,0x233024b,0x3082d19,0x00fb63b,
2882        0x3a1af4c,0x1450ff0,0x046c37b,0x0317a50 } },
2883    /* 27 */
2884    { { 0x3e75f9e,0x294e30a,0x3a78476,0x3a32c48,0x36fd1a9,0x0427012,
2885        0x1e4df0b,0x11d1f61,0x1afdb46,0x018ca0f },
2886      { 0x2f2df15,0x0a33dee,0x27f4ce7,0x1542b66,0x3e592c4,0x20d2f30,
2887        0x3226ade,0x2a4e3ea,0x1ab1981,0x01a2f46 } },
2888    /* 28 */
2889    { { 0x087d659,0x3ab5446,0x305ac08,0x3d2cd64,0x33374d5,0x3f9d3f8,
2890        0x186981c,0x37f5a5a,0x2f53c6f,0x01254a4 },
2891      { 0x2cec896,0x1e32786,0x04844a8,0x043b16d,0x3d964b2,0x1935829,
2892        0x16f7e26,0x1a0dd9a,0x30d2603,0x003b1d4 } },
2893    /* 29 */
2894    { { 0x12687bb,0x04e816b,0x21fa2da,0x1abccb8,0x3a1f83b,0x375181e,
2895        0x0f5ef51,0x0fc2ce4,0x3a66486,0x003d881 },
2896      { 0x3138233,0x1f8eec3,0x2718bd6,0x1b09caa,0x2dd66b9,0x1bb222b,
2897        0x1004072,0x1b73e3b,0x07208ed,0x03fc36c } },
2898    /* 30 */
2899    { { 0x095d553,0x3e84053,0x0a8a749,0x3f575a0,0x3a44052,0x3ced59b,
2900        0x3b4317f,0x03a8c60,0x13c8874,0x00c4ed4 },
2901      { 0x0d11549,0x0b8ab02,0x221cb40,0x02ed37b,0x2071ee1,0x1fc8c83,
2902        0x3987dd4,0x27e049a,0x0f986f1,0x00b4eaf } },
2903    /* 31 */
2904    { { 0x15581a2,0x2214060,0x11af4c2,0x1598c88,0x19a0a6d,0x32acba6,
2905        0x3a7a0f0,0x2337c66,0x210ded9,0x0300dbe },
2906      { 0x1fbd009,0x3822eb0,0x181629a,0x2401b45,0x30b68b1,0x2e78363,
2907        0x2b32779,0x006530b,0x2c4b6d4,0x029aca8 } },
2908    /* 32 */
2909    { { 0x13549cf,0x0f943db,0x265ed43,0x1bfeb35,0x06f3369,0x3847f2d,
2910        0x1bfdacc,0x26181a5,0x252af7c,0x02043b8 },
2911      { 0x159bb2c,0x143f85c,0x357b654,0x2f9d62c,0x2f7dfbe,0x1a7fa9c,
2912        0x057e74d,0x05d14ac,0x17a9273,0x035215c } },
2913    /* 33 */
2914    { { 0x0cb5a98,0x106a2bc,0x10bf117,0x24c7cc4,0x3d3da8f,0x2ce0ab7,
2915        0x14e2cba,0x1813866,0x1a72f9a,0x01a9811 },
2916      { 0x2b2411d,0x3034fe8,0x16e0170,0x0f9443a,0x0be0eb8,0x2196cf3,
2917        0x0c9f738,0x15e40ef,0x0faf9e1,0x034f917 } },
2918    /* 34 */
2919    { { 0x03f7669,0x3da6efa,0x3d6bce1,0x209ca1d,0x109f8ae,0x09109e3,
2920        0x08ae543,0x3067255,0x1dee3c2,0x0081dd5 },
2921      { 0x3ef1945,0x358765b,0x28c387b,0x3bec4b4,0x218813c,0x0b7d92a,
2922        0x3cd1d67,0x2c0367e,0x2e57154,0x0123717 } },
2923    /* 35 */
2924    { { 0x3e5a199,0x1e42ffd,0x0bb7123,0x33e6273,0x1e0efb8,0x294671e,
2925        0x3a2bfe0,0x3d11709,0x2eddff6,0x03cbec2 },
2926      { 0x0b5025f,0x0255d7c,0x1f2241c,0x35d03ea,0x0550543,0x202fef4,
2927        0x23c8ad3,0x354963e,0x015db28,0x0284fa4 } },
2928    /* 36 */
2929    { { 0x2b65cbc,0x1e8d428,0x0226f9f,0x1c8a919,0x10b04b9,0x08fc1e8,
2930        0x1ce241e,0x149bc99,0x2b01497,0x00afc35 },
2931      { 0x3216fb7,0x1374fd2,0x226ad3d,0x19fef76,0x0f7d7b8,0x1c21417,
2932        0x37b83f6,0x3a27eba,0x25a162f,0x010aa52 } },
2933    /* 37 */
2934    { { 0x2adf191,0x1ab42fa,0x28d7584,0x2409689,0x20f8a48,0x253707d,
2935        0x2030504,0x378f7a1,0x169c65e,0x00b0b76 },
2936      { 0x3849c17,0x085c764,0x10dd6d0,0x2e87689,0x1460488,0x30e9521,
2937        0x10c7063,0x1b6f120,0x21f42c5,0x03d0dfe } },
2938    /* 38 */
2939    { { 0x20f7dab,0x035c512,0x29ac6aa,0x24c5ddb,0x20f0497,0x17ce5e1,
2940        0x00a050f,0x1eaa14b,0x3335470,0x02abd16 },
2941      { 0x18d364a,0x0df0cf0,0x316585e,0x018f925,0x0d40b9b,0x17b1511,
2942        0x1716811,0x1caf3d0,0x10df4f2,0x0337d8c } },
2943    /* 39 */
2944    { { 0x2a8b7ef,0x0f188e3,0x2287747,0x06216f0,0x008e935,0x2f6a38d,
2945        0x1567722,0x0bfc906,0x0bada9e,0x03c3402 },
2946      { 0x014d3b1,0x099c749,0x2a76291,0x216c067,0x3b37549,0x14ef2f6,
2947        0x21b96d4,0x1ee2d71,0x2f5ca88,0x016f570 } },
2948    /* 40 */
2949    { { 0x09a3154,0x3d1a7bd,0x2e9aef0,0x255b8ac,0x03e85a5,0x2a492a7,
2950        0x2aec1ea,0x11c6516,0x3c8a09e,0x02a84b7 },
2951      { 0x1f69f1d,0x09c89d3,0x1e7326f,0x0b28bfd,0x0e0e4c8,0x1ea7751,
2952        0x18ce73b,0x2a406e7,0x273e48c,0x01b00db } },
2953    /* 41 */
2954    { { 0x36e3138,0x2b84a83,0x345a5cf,0x00096b4,0x16966ef,0x159caf1,
2955        0x13c64b4,0x2f89226,0x25896af,0x00a4bfd },
2956      { 0x2213402,0x1435117,0x09fed52,0x09d0e4b,0x0f6580e,0x2871cba,
2957        0x3b397fd,0x1c9d825,0x090311b,0x0191383 } },
2958    /* 42 */
2959    { { 0x07153f0,0x1087869,0x18c9e1e,0x1e64810,0x2b86c3b,0x0175d9c,
2960        0x3dce877,0x269de4e,0x393cab7,0x03c96b9 },
2961      { 0x1869d0c,0x06528db,0x02641f3,0x209261b,0x29d55c8,0x25ba517,
2962        0x3b5ea30,0x028f927,0x25313db,0x00e6e39 } },
2963    /* 43 */
2964    { { 0x2fd2e59,0x150802d,0x098f377,0x19a4957,0x135e2c0,0x38a95ce,
2965        0x1ab21a0,0x36c1b67,0x32f0f19,0x00e448b },
2966      { 0x3cad53c,0x3387800,0x17e3cfb,0x03f9970,0x3225b2c,0x2a84e1d,
2967        0x3af1d29,0x3fe35ca,0x2f8ce80,0x0237a02 } },
2968    /* 44 */
2969    { { 0x07bbb76,0x3aa3648,0x2758afb,0x1f085e0,0x1921c7e,0x3010dac,
2970        0x22b74b1,0x230137e,0x1062e36,0x021c652 },
2971      { 0x3993df5,0x24a2ee8,0x126ab5f,0x2d7cecf,0x0639d75,0x16d5414,
2972        0x1aa78a8,0x3f78404,0x26a5b74,0x03f0c57 } },
2973    /* 45 */
2974    { { 0x0d6ecfa,0x3f506ba,0x3f86561,0x3d86bb1,0x15f8c44,0x2491d07,
2975        0x052a7b4,0x2422261,0x3adee38,0x039b529 },
2976      { 0x193c75d,0x14bb451,0x1162605,0x293749c,0x370a70d,0x2e8b1f6,
2977        0x2ede937,0x2b95f4a,0x39a9be2,0x00d77eb } },
2978    /* 46 */
2979    { { 0x2736636,0x15bf36a,0x2b7e6b9,0x25eb8b2,0x209f51d,0x3cd2659,
2980        0x10bf410,0x034afec,0x3d71c83,0x0076971 },
2981      { 0x0ce6825,0x07920cf,0x3c3b5c4,0x23fe55c,0x015ad11,0x08c0dae,
2982        0x0552c7f,0x2e75a8a,0x0fddbf4,0x01c1df0 } },
2983    /* 47 */
2984    { { 0x2b9661c,0x0ffe351,0x3d71bf6,0x1ac34b3,0x3a1dfd3,0x211fe3d,
2985        0x33e140a,0x3f9100d,0x32ee50e,0x014ea18 },
2986      { 0x16d8051,0x1bfda1a,0x068a097,0x2571d3d,0x1daec0c,0x39389af,
2987        0x194dc35,0x3f3058a,0x36d34e1,0x000a329 } },
2988    /* 48 */
2989    { { 0x09877ee,0x351f73f,0x0002d11,0x0420074,0x2c8b362,0x130982d,
2990        0x02c1175,0x3c11b40,0x0d86962,0x001305f },
2991      { 0x0daddf5,0x2f4252c,0x15c06d9,0x1d49339,0x1bea235,0x0b680ed,
2992        0x3356e67,0x1d1d198,0x1e9fed9,0x03dee93 } },
2993    /* 49 */
2994    { { 0x3e1263f,0x2fe8d3a,0x3ce6d0d,0x0d5c6b9,0x3557637,0x0a9bd48,
2995        0x0405538,0x0710749,0x2005213,0x038c7e5 },
2996      { 0x26b6ec6,0x2e485ba,0x3c44d1b,0x0b9cf0b,0x037a1d1,0x27428a5,
2997        0x0e7eac8,0x351ef04,0x259ce34,0x02a8e98 } },
2998    /* 50 */
2999    { { 0x2f3dcd3,0x3e77d4d,0x3360fbc,0x1434afd,0x36ceded,0x3d413d6,
3000        0x1710fad,0x36bb924,0x1627e79,0x008e637 },
3001      { 0x109569e,0x1c168db,0x3769cf4,0x2ed4527,0x0ea0619,0x17d80d3,
3002        0x1c03773,0x18843fe,0x1b21c04,0x015c5fd } },
3003    /* 51 */
3004    { { 0x1dd895e,0x08a7248,0x04519fe,0x001030a,0x18e5185,0x358dfb3,
3005        0x13d2391,0x0a37be8,0x0560e3c,0x019828b },
3006      { 0x27fcbd0,0x2a22bb5,0x30969cc,0x1e03aa7,0x1c84724,0x0ba4ad3,
3007        0x32f4817,0x0914cca,0x14c4f52,0x01893b9 } },
3008    /* 52 */
3009    { { 0x097eccc,0x1273936,0x00aa095,0x364fe62,0x04d49d1,0x10e9f08,
3010        0x3c24230,0x3ef01c8,0x2fb92bd,0x013ce4a },
3011      { 0x1e44fd9,0x27e3e9f,0x2156696,0x3915ecc,0x0b66cfb,0x1a3af0f,
3012        0x2fa8033,0x0e6736c,0x177ccdb,0x0228f9e } },
3013    /* 53 */
3014    { { 0x2c4b125,0x06207c1,0x0a8cdde,0x003db8f,0x1ae34e3,0x31e84fa,
3015        0x2999de5,0x11013bd,0x02370c2,0x00e2234 },
3016      { 0x0f91081,0x200d591,0x1504762,0x1857c05,0x23d9fcf,0x0cb34db,
3017        0x27edc86,0x08cd860,0x2471810,0x029798b } },
3018    /* 54 */
3019    { { 0x3acd6c8,0x097b8cb,0x3c661a8,0x15152f2,0x1699c63,0x237e64c,
3020        0x23edf79,0x16b7033,0x0e6466a,0x00b11da },
3021      { 0x0a64bc9,0x1bfe324,0x1f5cb34,0x08391de,0x0630a60,0x3017a21,
3022        0x09d064b,0x14a8365,0x041f9e6,0x01ed799 } },
3023    /* 55 */
3024    { { 0x128444a,0x2508b07,0x2a39216,0x362f84d,0x2e996c5,0x2c31ff3,
3025        0x07afe5f,0x1d1288e,0x3cb0c8d,0x02e2bdc },
3026      { 0x38b86fd,0x3a0ea8c,0x1cff5fd,0x1629629,0x3fee3f1,0x02b250c,
3027        0x2e8f6f2,0x0225727,0x15f7f3f,0x0280d8e } },
3028    /* 56 */
3029    { { 0x10f7770,0x0f1aee8,0x0e248c7,0x20684a8,0x3a6f16d,0x06f0ae7,
3030        0x0df6825,0x2d4cc40,0x301875f,0x012f8da },
3031      { 0x3b56dbb,0x1821ba7,0x24f8922,0x22c1f9e,0x0306fef,0x1b54bc8,
3032        0x2ccc056,0x00303ba,0x2871bdc,0x0232f26 } },
3033    /* 57 */
3034    { { 0x0dac4ab,0x0625730,0x3112e13,0x101c4bf,0x3a874a4,0x2873b95,
3035        0x32ae7c6,0x0d7e18c,0x13e0c08,0x01139d5 },
3036      { 0x334002d,0x00fffdd,0x025c6d5,0x22c2cd1,0x19d35cb,0x3a1ce2d,
3037        0x3702760,0x3f06257,0x03a5eb8,0x011c29a } },
3038    /* 58 */
3039    { { 0x0513482,0x1d87724,0x276a81b,0x0a807a4,0x3028720,0x339cc20,
3040        0x2441ee0,0x31bbf36,0x290c63d,0x0059041 },
3041      { 0x106a2ed,0x0d2819b,0x100bf50,0x114626c,0x1dd4d77,0x2e08632,
3042        0x14ae72a,0x2ed3f64,0x1fd7abc,0x035cd1e } },
3043    /* 59 */
3044    { { 0x2d4c6e5,0x3bec596,0x104d7ed,0x23d6c1b,0x0262cf0,0x15d72c5,
3045        0x2d5bb18,0x199ac4b,0x1e30771,0x020591a },
3046      { 0x21e291e,0x2e75e55,0x1661d7a,0x08b0778,0x3eb9daf,0x0d78144,
3047        0x1827eb1,0x0fe73d2,0x123f0dd,0x0028db7 } },
3048    /* 60 */
3049    { { 0x1d5533c,0x34cb1d0,0x228f098,0x27a1a11,0x17c5f5a,0x0d26f44,
3050        0x2228ade,0x2c460e6,0x3d6fdba,0x038cc77 },
3051      { 0x3cc6ed8,0x02ada1a,0x260e510,0x2f7bde8,0x37160c3,0x33a1435,
3052        0x23d9a7b,0x0ce2641,0x02a492e,0x034ed1e } },
3053    /* 61 */
3054    { { 0x3821f90,0x26dba3c,0x3aada14,0x3b59bad,0x292edd9,0x2804c45,
3055        0x3669531,0x296f42e,0x35a4c86,0x01ca049 },
3056      { 0x3ff47e5,0x2163df4,0x2441503,0x2f18405,0x15e1616,0x37f66ec,
3057        0x30f11a7,0x141658a,0x27ece14,0x00b018b } },
3058    /* 62 */
3059    { { 0x159ac2e,0x3e65bc0,0x2713a76,0x0db2f6c,0x3281e77,0x2391811,
3060        0x16d2880,0x1fbc4ab,0x1f92c4e,0x00a0a8d },
3061      { 0x0ce5cd2,0x152c7b0,0x02299c3,0x3244de7,0x2cf99ef,0x3a0b047,
3062        0x2caf383,0x0aaf664,0x113554d,0x031c735 } },
3063    /* 63 */
3064    { { 0x1b578f4,0x177a702,0x3a7a488,0x1638ebf,0x31884e2,0x2460bc7,
3065        0x36b1b75,0x3ce8e3d,0x340cf47,0x03143d9 },
3066      { 0x34b68ea,0x12b7ccd,0x1fe2a9c,0x08da659,0x0a406f3,0x1694c14,
3067        0x06a2228,0x16370be,0x3a72129,0x02e7b2c } },
3068    /* 64 */
3069    { { 0x0f8b16a,0x21043bd,0x266a56f,0x3fb11ec,0x197241a,0x36721f0,
3070        0x006b8e6,0x2ac6c29,0x202cd42,0x0200fcf },
3071      { 0x0dbec69,0x0c26a01,0x105f7f0,0x3dceeeb,0x3a83b85,0x363865f,
3072        0x097273a,0x2b70718,0x00e5067,0x03025d1 } },
3073    /* 65 */
3074    { { 0x379ab34,0x295bcb0,0x38d1846,0x22e1077,0x3a8ee06,0x1db1a3b,
3075        0x3144591,0x07cc080,0x2d5915f,0x03c6bcc },
3076      { 0x175bd50,0x0dd4c57,0x27bc99c,0x2ebdcbd,0x3837cff,0x235dc8f,
3077        0x13a4184,0x0722c18,0x130e2d4,0x008f43c } },
3078    /* 66 */
3079    { { 0x01500d9,0x2adbb7d,0x2da8857,0x397f2fa,0x10d890a,0x25c9654,
3080        0x3e86488,0x3eb754b,0x1d6c0a3,0x02c0a23 },
3081      { 0x10bcb08,0x083cc19,0x2e16853,0x04da575,0x271af63,0x2626a9d,
3082        0x3520a7b,0x32348c7,0x24ff408,0x03ff4dc } },
3083    /* 67 */
3084    { { 0x058e6cb,0x1a3992d,0x1d28539,0x080c5e9,0x2992dad,0x2a9d7d5,
3085        0x14ae0b7,0x09b7ce0,0x34ad78c,0x03d5643 },
3086      { 0x30ba55a,0x092f4f3,0x0bae0fc,0x12831de,0x20fc472,0x20ed9d2,
3087        0x29864f6,0x1288073,0x254f6f7,0x00635b6 } },
3088    /* 68 */
3089    { { 0x1be5a2b,0x0f88975,0x33c6ed9,0x20d64d3,0x06fe799,0x0989bff,
3090        0x1409262,0x085a90c,0x0d97990,0x0142eed },
3091      { 0x17ec63e,0x06471b9,0x0db2378,0x1006077,0x265422c,0x08db83d,
3092        0x28099b0,0x1270d06,0x11801fe,0x00ac400 } },
3093    /* 69 */
3094    { { 0x3391593,0x22d7166,0x30fcfc6,0x2896609,0x3c385f5,0x066b72e,
3095        0x04f3aad,0x2b831c5,0x19983fb,0x0375562 },
3096      { 0x0b82ff4,0x222e39d,0x34c993b,0x101c79c,0x2d2e03c,0x0f00c8a,
3097        0x3a9eaf4,0x1810669,0x151149d,0x039b931 } },
3098    /* 70 */
3099    { { 0x29af288,0x1956ec7,0x293155f,0x193deb6,0x1647e1a,0x2ca0839,
3100        0x297e4bc,0x15bfd0d,0x1b107ed,0x0147803 },
3101      { 0x31c327e,0x05a6e1d,0x02ad43d,0x02d2a5b,0x129cdb2,0x37ad1de,
3102        0x3d51f53,0x245df01,0x2414982,0x0388bd0 } },
3103    /* 71 */
3104    { { 0x35f1abb,0x17a3d18,0x0874cd4,0x2d5a14e,0x17edc0c,0x16a00d3,
3105        0x072c1fb,0x1232725,0x33d52dc,0x03dc24d },
3106      { 0x0af30d6,0x259aeea,0x369c401,0x12bc4de,0x295bf5f,0x0d8711f,
3107        0x26162a9,0x16c44e5,0x288e727,0x02f54b4 } },
3108    /* 72 */
3109    { { 0x05fa877,0x1571ea7,0x3d48ab1,0x1c9f4e8,0x017dad6,0x0f46276,
3110        0x343f9e7,0x1de990f,0x0e4c8aa,0x028343e },
3111      { 0x094f92d,0x3abf633,0x1b3a0bb,0x2f83137,0x0d818c8,0x20bae85,
3112        0x0c65f8b,0x1a8008b,0x0c7946d,0x0295b1e } },
3113    /* 73 */
3114    { { 0x1d09529,0x08e46c3,0x1fcf296,0x298f6b7,0x1803e0e,0x2d6fd20,
3115        0x37351f5,0x0d9e8b1,0x1f8731a,0x0362fbf },
3116      { 0x00157f4,0x06750bf,0x2650ab9,0x35ffb23,0x2f51cae,0x0b522c2,
3117        0x39cb400,0x191e337,0x0a5ce9f,0x021529a } },
3118    /* 74 */
3119    { { 0x3506ea5,0x17d9ed8,0x0d66dc3,0x22693f8,0x19286c4,0x3a57353,
3120        0x101d3bf,0x1aa54fc,0x20b9884,0x0172b3a },
3121      { 0x0eac44d,0x37d8327,0x1c3aa90,0x3d0d534,0x23db29a,0x3576eaf,
3122        0x1d3de8a,0x3bea423,0x11235e4,0x039260b } },
3123    /* 75 */
3124    { { 0x34cd55e,0x01288b0,0x1132231,0x2cc9a03,0x358695b,0x3e87650,
3125        0x345afa1,0x01267ec,0x3f616b2,0x02011ad },
3126      { 0x0e7d098,0x0d6078e,0x0b70b53,0x237d1bc,0x0d7f61e,0x132de31,
3127        0x1ea9ea4,0x2bd54c3,0x27b9082,0x03ac5f2 } },
3128    /* 76 */
3129    { { 0x2a145b9,0x06d661d,0x31ec175,0x03f06f1,0x3a5cf6b,0x249c56e,
3130        0x2035653,0x384c74f,0x0bafab5,0x0025ec0 },
3131      { 0x25f69e1,0x1b23a55,0x1199aa6,0x16ad6f9,0x077e8f7,0x293f661,
3132        0x33ba11d,0x3327980,0x07bafdb,0x03e571d } },
3133    /* 77 */
3134    { { 0x2bae45e,0x3c074ef,0x2955558,0x3c312f1,0x2a8ebe9,0x2f193f1,
3135        0x3705b1d,0x360deba,0x01e566e,0x00d4498 },
3136      { 0x21161cd,0x1bc787e,0x2f87933,0x3553197,0x1328ab8,0x093c879,
3137        0x17eee27,0x2adad1d,0x1236068,0x003be5c } },
3138    /* 78 */
3139    { { 0x0ca4226,0x2633dd5,0x2c8e025,0x0e3e190,0x05eede1,0x1a385e4,
3140        0x163f744,0x2f25522,0x1333b4f,0x03f05b6 },
3141      { 0x3c800ca,0x1becc79,0x2daabe9,0x0c499e2,0x1138063,0x3fcfa2d,
3142        0x2244976,0x1e85cf5,0x2f1b95d,0x0053292 } },
3143    /* 79 */
3144    { { 0x12f81d5,0x1dc6eaf,0x11967a4,0x1a407df,0x31a5f9d,0x2b67241,
3145        0x18bef7c,0x08c7762,0x063f59c,0x01015ec },
3146      { 0x1c05c0a,0x360bfa2,0x1f85bff,0x1bc7703,0x3e4911c,0x0d685b6,
3147        0x2fccaea,0x02c4cef,0x164f133,0x0070ed7 } },
3148    /* 80 */
3149    { { 0x0ec21fe,0x052ffa0,0x3e825fe,0x1ab0956,0x3f6ce11,0x3d29759,
3150        0x3c5a072,0x18ebe62,0x148db7e,0x03eb49c },
3151      { 0x1ab05b3,0x02dab0a,0x1ae690c,0x0f13894,0x137a9a8,0x0aab79f,
3152        0x3dc875c,0x06a1029,0x1e39f0e,0x01dce1f } },
3153    /* 81 */
3154    { { 0x16c0dd7,0x3b31269,0x2c741e9,0x3611821,0x2a5cffc,0x1416bb3,
3155        0x3a1408f,0x311fa3d,0x1c0bef0,0x02cdee1 },
3156      { 0x00e6a8f,0x1adb933,0x0f23359,0x2fdace2,0x2fd6d4b,0x0e73bd3,
3157        0x2453fac,0x0a356ae,0x2c8f9f6,0x02704d6 } },
3158    /* 82 */
3159    { { 0x0e35743,0x28c80a1,0x0def32a,0x2c6168f,0x1320d6a,0x37c6606,
3160        0x21b1761,0x2147ee0,0x21fc433,0x015c84d },
3161      { 0x1fc9168,0x36cda9c,0x003c1f0,0x1cd7971,0x15f98ba,0x1ef363d,
3162        0x0ca87e3,0x046f7d9,0x3c9e6bb,0x0372eb0 } },
3163    /* 83 */
3164    { { 0x118cbe2,0x3665a11,0x304ef01,0x062727a,0x3d242fc,0x11ffbaf,
3165        0x3663c7e,0x1a189c9,0x09e2d62,0x02e3072 },
3166      { 0x0e1d569,0x162f772,0x0cd051a,0x322df62,0x3563809,0x047cc7a,
3167        0x027fd9f,0x08b509b,0x3da2f94,0x01748ee } },
3168    /* 84 */
3169    { { 0x1c8f8be,0x31ca525,0x22bf0a1,0x200efcd,0x02961c4,0x3d8f52b,
3170        0x018403d,0x3a40279,0x1cb91ec,0x030427e },
3171      { 0x0945705,0x0257416,0x05c0c2d,0x25b77ae,0x3b9083d,0x2901126,
3172        0x292b8d7,0x07b8611,0x04f2eee,0x026f0cd } },
3173    /* 85 */
3174    { { 0x2913074,0x2b8d590,0x02b10d5,0x09d2295,0x255491b,0x0c41cca,
3175        0x1ca665b,0x133051a,0x1525f1a,0x00a5647 },
3176      { 0x04f983f,0x3d6daee,0x04e1e76,0x1067d7e,0x1be7eef,0x02ea862,
3177        0x00d4968,0x0ccb048,0x11f18ef,0x018dd95 } },
3178    /* 86 */
3179    { { 0x22976cc,0x17c5395,0x2c38bda,0x3983bc4,0x222bca3,0x332a614,
3180        0x3a30646,0x261eaef,0x1c808e2,0x02f6de7 },
3181      { 0x306a772,0x32d7272,0x2dcefd2,0x2abf94d,0x038f475,0x30ad76e,
3182        0x23e0227,0x3052b0a,0x001add3,0x023ba18 } },
3183    /* 87 */
3184    { { 0x0ade873,0x25a6069,0x248ccbe,0x13713ee,0x17ee9aa,0x28152e9,
3185        0x2e28995,0x2a92cb3,0x17a6f77,0x024b947 },
3186      { 0x190a34d,0x2ebea1c,0x1ed1948,0x16fdaf4,0x0d698f7,0x32bc451,
3187        0x0ee6e30,0x2aaab40,0x06f0a56,0x01460be } },
3188    /* 88 */
3189    { { 0x24cc99c,0x1884b1e,0x1ca1fba,0x1a0f9b6,0x2ff609b,0x2b26316,
3190        0x3b27cb5,0x29bc976,0x35d4073,0x024772a },
3191      { 0x3575a70,0x1b30f57,0x07fa01b,0x0e5be36,0x20cb361,0x26605cd,
3192        0x1d4e8c8,0x13cac59,0x2db9797,0x005e833 } },
3193    /* 89 */
3194    { { 0x36c8d3a,0x1878a81,0x124b388,0x0e4843e,0x1701aad,0x0ea0d76,
3195        0x10eae41,0x37d0653,0x36c7f4c,0x00ba338 },
3196      { 0x37a862b,0x1cf6ac0,0x08fa912,0x2dd8393,0x101ba9b,0x0eebcb7,
3197        0x2453883,0x1a3cfe5,0x2cb34f6,0x03d3331 } },
3198    /* 90 */
3199    { { 0x1f79687,0x3d4973c,0x281544e,0x2564bbe,0x17c5954,0x171e34a,
3200        0x231741a,0x3cf2784,0x0889a0d,0x02b036d },
3201      { 0x301747f,0x3f1c477,0x1f1386b,0x163bc5f,0x1592b93,0x332daed,
3202        0x080e4f5,0x1d28b96,0x26194c9,0x0256992 } },
3203    /* 91 */
3204    { { 0x15a4c93,0x07bf6b0,0x114172c,0x1ce0961,0x140269b,0x1b2c2eb,
3205        0x0dfb1c1,0x019ddaa,0x0ba2921,0x008c795 },
3206      { 0x2e6d2dc,0x37e45e2,0x2918a70,0x0fce444,0x34d6aa6,0x396dc88,
3207        0x27726b5,0x0c787d8,0x032d8a7,0x02ac2f8 } },
3208    /* 92 */
3209    { { 0x1131f2d,0x2b43a63,0x3101097,0x38cec13,0x0637f09,0x17a69d2,
3210        0x086196d,0x299e46b,0x0802cf6,0x03c6f32 },
3211      { 0x0daacb4,0x1a4503a,0x100925c,0x15583d9,0x23c4e40,0x1de4de9,
3212        0x1cc8fc4,0x2c9c564,0x0695aeb,0x02145a5 } },
3213    /* 93 */
3214    { { 0x1dcf593,0x17050fc,0x3e3bde3,0x0a6c062,0x178202b,0x2f7674f,
3215        0x0dadc29,0x15763a7,0x1d2daad,0x023d9f6 },
3216      { 0x081ea5f,0x045959d,0x190c841,0x3a78d31,0x0e7d2dd,0x1414fea,
3217        0x1d43f40,0x22d77ff,0x2b9c072,0x03e115c } },
3218    /* 94 */
3219    { { 0x3af71c9,0x29e9c65,0x25655e1,0x111e9cd,0x3a14494,0x3875418,
3220        0x34ae070,0x0b06686,0x310616b,0x03b7b89 },
3221      { 0x1734121,0x00d3d44,0x29f0b2f,0x1552897,0x31cac6e,0x1030bb3,
3222        0x0148f3a,0x35fd237,0x29b44eb,0x027f49f } },
3223    /* 95 */
3224    { { 0x2e2cb16,0x1d962bd,0x19b63cc,0x0b3f964,0x3e3eb7d,0x1a35560,
3225        0x0c58161,0x3ce1d6a,0x3b6958f,0x029030b },
3226      { 0x2dcc158,0x3b1583f,0x30568c9,0x31957c8,0x27ad804,0x28c1f84,
3227        0x3967049,0x37b3f64,0x3b87dc6,0x0266f26 } },
3228    /* 96 */
3229    { { 0x27dafc6,0x2548764,0x0d1984a,0x1a57027,0x252c1fb,0x24d9b77,
3230        0x1581a0f,0x1f99276,0x10ba16d,0x026af88 },
3231      { 0x0915220,0x2be1292,0x16c6480,0x1a93760,0x2fa7317,0x1a07296,
3232        0x1539871,0x112c31f,0x25787f3,0x01e2070 } },
3233    /* 97 */
3234    { { 0x0bcf3ff,0x266d478,0x34f6933,0x31449fd,0x00d02cb,0x340765a,
3235        0x3465a2d,0x225023e,0x319a30e,0x00579b8 },
3236      { 0x20e05f4,0x35b834f,0x0404646,0x3710d62,0x3fad7bd,0x13e1434,
3237        0x21c7d1c,0x1cb3af9,0x2cf1911,0x003957e } },
3238    /* 98 */
3239    { { 0x0787564,0x36601be,0x1ce67e9,0x084c7a1,0x21a3317,0x2067a35,
3240        0x0158cab,0x195ddac,0x1766fe9,0x035cf42 },
3241      { 0x2b7206e,0x20d0947,0x3b42424,0x03f1862,0x0a51929,0x38c2948,
3242        0x0bb8595,0x2942d77,0x3748f15,0x0249428 } },
3243    /* 99 */
3244    { { 0x2577410,0x3c23e2f,0x28c6caf,0x00d41de,0x0fd408a,0x30298e9,
3245        0x363289e,0x2302fc7,0x082c1cc,0x01dd050 },
3246      { 0x30991cd,0x103e9ba,0x029605a,0x19927f7,0x0c1ca08,0x0c93f50,
3247        0x28a3c7b,0x082e4e9,0x34d12eb,0x0232c13 } },
3248    /* 100 */
3249    { { 0x106171c,0x0b4155a,0x0c3fb1c,0x336c090,0x19073e9,0x2241a10,
3250        0x0e6b4fd,0x0ed476e,0x1ef4712,0x039390a },
3251      { 0x0ec36f4,0x3754f0e,0x2a270b8,0x007fd2d,0x0f9d2dc,0x1e6a692,
3252        0x066e078,0x1954974,0x2ff3c6e,0x00def28 } },
3253    /* 101 */
3254    { { 0x3562470,0x0b8f1f7,0x0ac94cd,0x28b0259,0x244f272,0x031e4ef,
3255        0x2d5df98,0x2c8a9f1,0x2dc3002,0x016644f },
3256      { 0x350592a,0x0e6a0d5,0x1e027a1,0x2039e0f,0x399e01d,0x2817593,
3257        0x0c0375e,0x3889b3e,0x24ab013,0x010de1b } },
3258    /* 102 */
3259    { { 0x256b5a6,0x0ac3b67,0x28f9ff3,0x29b67f1,0x30750d9,0x25e11a9,
3260        0x15e8455,0x279ebb0,0x298b7e7,0x0218e32 },
3261      { 0x2fc24b2,0x2b82582,0x28f22f5,0x2bd36b3,0x305398e,0x3b2e9e3,
3262        0x365dd0a,0x29bc0ed,0x36a7b3a,0x007b374 } },
3263    /* 103 */
3264    { { 0x05ff2f3,0x2b3589b,0x29785d3,0x300a1ce,0x0a2d516,0x0844355,
3265        0x14c9fad,0x3ccb6b6,0x385d459,0x0361743 },
3266      { 0x0b11da3,0x002e344,0x18c49f7,0x0c29e0c,0x1d2c22c,0x08237b3,
3267        0x2988f49,0x0f18955,0x1c3b4ed,0x02813c6 } },
3268    /* 104 */
3269    { { 0x17f93bd,0x249323b,0x11f6087,0x174e4bd,0x3cb64ac,0x086dc6b,
3270        0x2e330a8,0x142c1f2,0x2ea5c09,0x024acbb },
3271      { 0x1b6e235,0x3132521,0x00f085a,0x2a4a4db,0x1ab2ca4,0x0142224,
3272        0x3aa6b3e,0x09db203,0x2215834,0x007b9e0 } },
3273    /* 105 */
3274    { { 0x23e79f7,0x28b8039,0x1906a60,0x2cbce67,0x1f590e7,0x181f027,
3275        0x21054a6,0x3854240,0x2d857a6,0x03cfcb3 },
3276      { 0x10d9b55,0x1443cfc,0x2648200,0x2b36190,0x09d2fcf,0x22f439f,
3277        0x231aa7e,0x3884395,0x0543da3,0x003d5a9 } },
3278    /* 106 */
3279    { { 0x043e0df,0x06ffe84,0x3e6d5b2,0x3327001,0x26c74b6,0x12a145e,
3280        0x256ec0d,0x3898c69,0x3411969,0x02f63c5 },
3281      { 0x2b7494a,0x2eee1af,0x38388a9,0x1bd17ce,0x21567d4,0x13969e6,
3282        0x3a12a7a,0x3e8277d,0x03530cc,0x00b4687 } },
3283    /* 107 */
3284    { { 0x06508da,0x38e04d4,0x15a7192,0x312875e,0x3336180,0x2a6512c,
3285        0x1b59497,0x2e91b37,0x25eb91f,0x02841e9 },
3286      { 0x394d639,0x0747143,0x37d7e6d,0x1d62962,0x08b4af3,0x34df287,
3287        0x3c5584b,0x26bc869,0x20af87a,0x0060f5d } },
3288    /* 108 */
3289    { { 0x1de59a4,0x1a5c443,0x2f8729d,0x01c3a2f,0x0f1ad8d,0x3cbaf9e,
3290        0x1b49634,0x35d508a,0x39dc269,0x0075105 },
3291      { 0x390d30e,0x37033e0,0x110cb32,0x14c37a0,0x20a3b27,0x2f00ce6,
3292        0x2f1dc52,0x34988c6,0x0c29606,0x01dc7e7 } },
3293    /* 109 */
3294    { { 0x1040739,0x24f9de1,0x2939999,0x2e6009a,0x244539d,0x17e3f09,
3295        0x00f6f2f,0x1c63b3d,0x2310362,0x019109e },
3296      { 0x1428aa8,0x3cb61e1,0x09a84f4,0x0ffafed,0x07b7adc,0x08f406b,
3297        0x1b2c6df,0x035b480,0x3496ae9,0x012766d } },
3298    /* 110 */
3299    { { 0x35d1099,0x2362f10,0x1a08cc7,0x13a3a34,0x12adbcd,0x32da290,
3300        0x02e2a02,0x151140b,0x01b3f60,0x0240df6 },
3301      { 0x34c7b61,0x2eb09c1,0x172e7cd,0x2ad5eff,0x2fe2031,0x25b54d4,
3302        0x0cec965,0x18e7187,0x26a7cc0,0x00230f7 } },
3303    /* 111 */
3304    { { 0x2d552ab,0x374083d,0x01f120f,0x2601736,0x156baff,0x04d44a4,
3305        0x3b7c3e9,0x1acbc1b,0x0424579,0x031a425 },
3306      { 0x1231bd1,0x0eba710,0x020517b,0x21d7316,0x21eac6e,0x275a848,
3307        0x0837abf,0x0eb0082,0x302cafe,0x00fe8f6 } },
3308    /* 112 */
3309    { { 0x1058880,0x28f9941,0x03f2d75,0x3bd90e5,0x17da365,0x2ac9249,
3310        0x07861cf,0x023fd05,0x1b0fdb8,0x031712f },
3311      { 0x272b56b,0x04f8d2c,0x043a735,0x25446e4,0x1c8327e,0x221125a,
3312        0x0ce37df,0x2dad7f6,0x39446c2,0x00b55b6 } },
3313    /* 113 */
3314    { { 0x346ac6b,0x05e0bff,0x2425246,0x0981e8b,0x1d19f79,0x2692378,
3315        0x3ea3c40,0x2e90beb,0x19de503,0x003d5af },
3316      { 0x05cda49,0x353b44d,0x299d137,0x3f205bc,0x2821158,0x3ad0d00,
3317        0x06a54aa,0x2d7c79f,0x39d1173,0x01000ee } },
3318    /* 114 */
3319    { { 0x0803387,0x3a06268,0x14043b8,0x3d4e72f,0x1ece115,0x0a1dfc8,
3320        0x17208dd,0x0be790a,0x122a07f,0x014dd95 },
3321      { 0x0a4182d,0x202886a,0x1f79a49,0x1e8c867,0x0a2bbd0,0x28668b5,
3322        0x0d0a2e1,0x115259d,0x3586c5d,0x01e815b } },
3323    /* 115 */
3324    { { 0x18a2a47,0x2c95627,0x2773646,0x1230f7c,0x15b5829,0x2fc354e,
3325        0x2c000ea,0x099d547,0x2f17a1a,0x01df520 },
3326      { 0x3853948,0x06f6561,0x3feeb8a,0x2f5b3ef,0x3a6f817,0x01a0791,
3327        0x2ec0578,0x2c392ad,0x12b2b38,0x0104540 } },
3328    /* 116 */
3329    { { 0x1e28ced,0x0fc3d1b,0x2c473c7,0x1826c4f,0x21d5da7,0x39718e4,
3330        0x38ce9e6,0x0251986,0x172fbea,0x0337c11 },
3331      { 0x053c3b0,0x0f162db,0x043c1cb,0x04111ee,0x297fe3c,0x32e5e03,
3332        0x2b8ae12,0x0c427ec,0x1da9738,0x03b9c0f } },
3333    /* 117 */
3334    { { 0x357e43a,0x054503f,0x11b8345,0x34ec6e0,0x2d44660,0x3d0ae61,
3335        0x3b5dff8,0x33884ac,0x09da162,0x00a82b6 },
3336      { 0x3c277ba,0x129a51a,0x027664e,0x1530507,0x0c788c9,0x2afd89d,
3337        0x1aa64cc,0x1196450,0x367ac2b,0x0358b42 } },
3338    /* 118 */
3339    { { 0x0054ac4,0x1761ecb,0x378839c,0x167c9f7,0x2570058,0x0604a35,
3340        0x37cbf3b,0x0909bb7,0x3f2991c,0x02ce688 },
3341      { 0x0b16ae5,0x212857c,0x351b952,0x2c684db,0x30c6a05,0x09c01e0,
3342        0x23c137f,0x1331475,0x092c067,0x0013b40 } },
3343    /* 119 */
3344    { { 0x2e90393,0x0617466,0x24e61f4,0x0a528f5,0x03047b4,0x2153f05,
3345        0x0001a69,0x30e1eb8,0x3c10177,0x0282a47 },
3346      { 0x22c831e,0x28fc06b,0x3e16ff0,0x208adc9,0x0bb76ae,0x28c1d6d,
3347        0x12c8a15,0x031063c,0x1889ed2,0x002133e } },
3348    /* 120 */
3349    { { 0x0a6becf,0x14277bf,0x3328d98,0x201f7fe,0x12fceae,0x1de3a2e,
3350        0x0a15c44,0x3ddf976,0x1b273ab,0x0355e55 },
3351      { 0x1b5d4f1,0x369e78c,0x3a1c210,0x12cf3e9,0x3aa52f0,0x309f082,
3352        0x112089d,0x107c753,0x24202d1,0x023853a } },
3353    /* 121 */
3354    { { 0x2897042,0x140d17c,0x2c4aeed,0x07d0d00,0x18d0533,0x22f7ec8,
3355        0x19c194c,0x3456323,0x2372aa4,0x0165f86 },
3356      { 0x30bd68c,0x1fb06b3,0x0945032,0x372ac09,0x06d4be0,0x27f8fa1,
3357        0x1c8d7ac,0x137a96e,0x236199b,0x0328fc0 } },
3358    /* 122 */
3359    { { 0x170bd20,0x2842d58,0x1de7592,0x3c5b4fd,0x20ea897,0x12cab78,
3360        0x363ff14,0x01f928c,0x17e309c,0x02f79ff },
3361      { 0x0f5432c,0x2edb4ae,0x044b516,0x32f810d,0x2210dc1,0x23e56d6,
3362        0x301e6ff,0x34660f6,0x10e0a7d,0x02d88eb } },
3363    /* 123 */
3364    { { 0x0c7b65b,0x2f59d58,0x2289a75,0x2408e92,0x1ab8c55,0x1ec99e5,
3365        0x220fd0d,0x04defe0,0x24658ec,0x035aa8b },
3366      { 0x138bb85,0x2f002d4,0x295c10a,0x08760ce,0x28c31d1,0x1c0a8cb,
3367        0x0ff00b1,0x144eac9,0x2e02dcc,0x0044598 } },
3368    /* 124 */
3369    { { 0x3b42b87,0x050057b,0x0dff781,0x1c06db1,0x1bd9f5d,0x1f5f04a,
3370        0x2cccd7a,0x143e19b,0x1cb94b7,0x036cfb8 },
3371      { 0x34837cf,0x3cf6c3c,0x0d4fb26,0x22ee55e,0x1e7eed1,0x315995f,
3372        0x2cdf937,0x1a96574,0x0425220,0x0221a99 } },
3373    /* 125 */
3374    { { 0x1b569ea,0x0d33ed9,0x19c13c2,0x107dc84,0x2200111,0x0569867,
3375        0x2dc85da,0x05ef22e,0x0eb018a,0x029c33d },
3376      { 0x04a6a65,0x3e5eba3,0x378f224,0x09c04d0,0x036e5cf,0x3df8258,
3377        0x3a609e4,0x1eddef8,0x2abd174,0x02a91dc } },
3378    /* 126 */
3379    { { 0x2a60cc0,0x1d84c5e,0x115f676,0x1840da0,0x2c79163,0x2f06ed6,
3380        0x198bb4b,0x3e5d37b,0x1dc30fa,0x018469b },
3381      { 0x15ee47a,0x1e32f30,0x16a530e,0x2093836,0x02e8962,0x3767b62,
3382        0x335adf3,0x27220db,0x2f81642,0x0173ffe } },
3383    /* 127 */
3384    { { 0x37a99cd,0x1533fe6,0x05a1c0d,0x27610f1,0x17bf3b9,0x0b1ce78,
3385        0x0a908f6,0x265300e,0x3237dc1,0x01b969a },
3386      { 0x3a5db77,0x2d15382,0x0d63ef8,0x1feb3d8,0x0b7b880,0x19820de,
3387        0x11c0c67,0x2af3396,0x38d242d,0x0120688 } },
3388    /* 128 */
3389    { { 0x1d0b34a,0x05ef00d,0x00a7e34,0x1ae0c9f,0x1440b38,0x300d8b4,
3390        0x37262da,0x3e50e3e,0x14ce0cd,0x00b1044 },
3391      { 0x195a0b1,0x173bc6b,0x03622ba,0x2a19f55,0x1c09b37,0x07921b2,
3392        0x16cdd20,0x24a5c9b,0x2bf42ff,0x00811de } },
3393    /* 129 */
3394    { { 0x0d65dbf,0x145cf06,0x1ad82f7,0x038ce7b,0x077bf94,0x33c4007,
3395        0x22d26bd,0x25ad9c0,0x09ac773,0x02b1990 },
3396      { 0x2261cc3,0x2ecdbf1,0x3e908b0,0x3246439,0x0213f7b,0x1179b04,
3397        0x01cebaa,0x0be1595,0x175cc12,0x033a39a } },
3398    /* 130 */
3399    { { 0x00a67d2,0x086d06f,0x248a0f1,0x0291134,0x362d476,0x166d1cd,
3400        0x044f1d6,0x2d2a038,0x365250b,0x0023f78 },
3401      { 0x08bf287,0x3b0f6a1,0x1d6eace,0x20b4cda,0x2c2a621,0x0912520,
3402        0x02dfdc9,0x1b35cd6,0x3d2565d,0x00bdf8b } },
3403    /* 131 */
3404    { { 0x3770fa7,0x2e4b6f0,0x03f9ae4,0x170de41,0x1095e8d,0x1dd845c,
3405        0x334e9d1,0x00ab953,0x12e9077,0x03196fa },
3406      { 0x2fd0a40,0x228c0fd,0x384b275,0x38ef339,0x3e7d822,0x3e5d9ef,
3407        0x24f5854,0x0ece9eb,0x247d119,0x012ffe3 } },
3408    /* 132 */
3409    { { 0x0ff1480,0x07487c0,0x1b16cd4,0x1f41d53,0x22ab8fb,0x2f83cfa,
3410        0x01d2efb,0x259f6b2,0x2e65772,0x00f9392 },
3411      { 0x05303e6,0x23cdb4f,0x23977e1,0x12e4898,0x03bd999,0x0c930f0,
3412        0x170e261,0x180a27b,0x2fd58ec,0x014e22b } },
3413    /* 133 */
3414    { { 0x25d7713,0x0c5fad7,0x09daad1,0x3b9d779,0x109b985,0x1d3ec98,
3415        0x35bc4fc,0x2f838cb,0x0d14f75,0x0173e42 },
3416      { 0x2657b12,0x10d4423,0x19e6760,0x296e5bb,0x2bfd421,0x25c3330,
3417        0x29f51f8,0x0338838,0x24060f0,0x029a62e } },
3418    /* 134 */
3419    { { 0x3748fec,0x2c5a1bb,0x2cf973d,0x289fa74,0x3e6e755,0x38997bf,
3420        0x0b6544c,0x2b6358c,0x38a7aeb,0x02c50bb },
3421      { 0x3d5770a,0x06be7c5,0x012fad3,0x19cb2cd,0x266af3b,0x3ccd677,
3422        0x160d1bd,0x141d5af,0x2965851,0x034625a } },
3423    /* 135 */
3424    { { 0x3c41c08,0x255eacc,0x22e1ec5,0x2b151a3,0x087de94,0x311cbdb,
3425        0x016b73a,0x368e462,0x20b7981,0x0099ec3 },
3426      { 0x262b988,0x1539763,0x21e76e5,0x15445b4,0x1d8ddc7,0x34a9be6,
3427        0x10faf03,0x24e4d18,0x07aa111,0x02d538a } },
3428    /* 136 */
3429    { { 0x38a876b,0x048ad45,0x04b40a0,0x3fc2144,0x251ff96,0x13ca7dd,
3430        0x0b31ab1,0x3539814,0x28b5f87,0x0212aec },
3431      { 0x270790a,0x350e7e0,0x346bd5e,0x276178f,0x22d6cb5,0x3078884,
3432        0x355c1b6,0x15901d7,0x3671765,0x03950db } },
3433    /* 137 */
3434    { { 0x286e8d5,0x2409788,0x13be53f,0x2d21911,0x0353c95,0x10238e8,
3435        0x32f5bde,0x3a67b60,0x28b5b9c,0x001013d },
3436      { 0x381e8e5,0x0cef7a9,0x2f5bcad,0x06058f0,0x33cdf50,0x04672a8,
3437        0x1769600,0x31c055d,0x3df0ac1,0x00e9098 } },
3438    /* 138 */
3439    { { 0x2eb596d,0x197b326,0x12b4c29,0x39c08f2,0x101ea03,0x3804e58,
3440        0x04b4b62,0x28d9d1c,0x13f905e,0x0032a3f },
3441      { 0x11b2b61,0x08e9095,0x0d06925,0x270e43f,0x21eb7a8,0x0e4a98f,
3442        0x31d2be0,0x030cf9f,0x2644ddb,0x025b728 } },
3443    /* 139 */
3444    { { 0x07510af,0x2ed0e8e,0x2a01203,0x2a2a68d,0x0846fea,0x3e540de,
3445        0x3a57702,0x1677348,0x2123aad,0x010d8f8 },
3446      { 0x0246a47,0x0e871d0,0x124dca4,0x34b9577,0x2b362b8,0x363ebe5,
3447        0x3086045,0x26313e6,0x15cd8bb,0x0210384 } },
3448    /* 140 */
3449    { { 0x023e8a7,0x0817884,0x3a0bf12,0x3376371,0x3c808a8,0x18e9777,
3450        0x12a2721,0x35b538a,0x2bd30de,0x017835a },
3451      { 0x0fc0f64,0x1c8709f,0x2d8807a,0x0743957,0x242eec0,0x347e76c,
3452        0x27bef91,0x289689a,0x0f42945,0x01f7a92 } },
3453    /* 141 */
3454    { { 0x1060a81,0x3dbc739,0x1615abd,0x1cbe3e5,0x3e79f9c,0x1ab09a2,
3455        0x136c540,0x05b473f,0x2beebfd,0x02af0a8 },
3456      { 0x3e2eac7,0x19be474,0x04668ac,0x18f4b74,0x36f10ba,0x0a0b4c6,
3457        0x10e3770,0x3bf059e,0x3946c7e,0x013a8d4 } },
3458    /* 142 */
3459    { { 0x266309d,0x28be354,0x1a3eed8,0x3020651,0x10a51c6,0x1e31770,
3460        0x0af45a5,0x3ff0f3b,0x2891c94,0x00e9db9 },
3461      { 0x17b0d0f,0x33a291f,0x0a5f9aa,0x25a3d61,0x2963ace,0x39a5fef,
3462        0x230c724,0x1919146,0x10a465e,0x02084a8 } },
3463    /* 143 */
3464    { { 0x3ab8caa,0x31870f3,0x2390ef7,0x2103850,0x218eb8e,0x3a5ccf2,
3465        0x1dff677,0x2c59334,0x371599c,0x02a9f2a },
3466      { 0x0837bd1,0x3249cef,0x35d702f,0x3430dab,0x1c06407,0x108f692,
3467        0x221292f,0x05f0c5d,0x073fe06,0x01038e0 } },
3468    /* 144 */
3469    { { 0x3bf9b7c,0x2020929,0x30d0f4f,0x080fef8,0x3365d23,0x1f3e738,
3470        0x3e53209,0x1549afe,0x300b305,0x038d811 },
3471      { 0x0c6c2c7,0x2e6445b,0x3ee64dc,0x022e932,0x0726837,0x0deb67b,
3472        0x1ed4346,0x3857f73,0x277a3de,0x01950b5 } },
3473    /* 145 */
3474    { { 0x36c377a,0x0adb41e,0x08be3f3,0x11e40d1,0x36cb038,0x036a2bd,
3475        0x3dd3a82,0x1bc875b,0x2ee09bb,0x02994d2 },
3476      { 0x035facf,0x05e0344,0x07e630a,0x0ce772d,0x335e55a,0x111fce4,
3477        0x250fe1c,0x3bc89ba,0x32fdc9a,0x03cf2d9 } },
3478    /* 146 */
3479    { { 0x355fd83,0x1c67f8e,0x1d10eb3,0x1b21d77,0x0e0d7a4,0x173a9e1,
3480        0x2c9fa90,0x1c39cce,0x22eaae8,0x01f2bea },
3481      { 0x153b338,0x0534107,0x26c69b8,0x283be1f,0x3e0acc0,0x059cac3,
3482        0x13d1081,0x148bbee,0x3c1b9bd,0x002aac4 } },
3483    /* 147 */
3484    { { 0x2681297,0x3389e34,0x146addc,0x2c6d425,0x2cb350e,0x1986abc,
3485        0x0431737,0x04ba4b7,0x2028470,0x012e469 },
3486      { 0x2f8ddcf,0x3c4255c,0x1af4dcf,0x07a6a44,0x208ebf6,0x0dc90c3,
3487        0x34360ac,0x072ad23,0x0537232,0x01254d3 } },
3488    /* 148 */
3489    { { 0x07b7e9d,0x3df5c7c,0x116f83d,0x28c4f35,0x3a478ef,0x3011fb8,
3490        0x2f264b6,0x317b9e3,0x04fd65a,0x032bd1b },
3491      { 0x2aa8266,0x3431de4,0x04bba04,0x19a44da,0x0edf454,0x392c5ac,
3492        0x265168a,0x1dc3d5b,0x25704c6,0x00533a7 } },
3493    /* 149 */
3494    { { 0x25e8f91,0x1178fa5,0x2492994,0x2eb2c3c,0x0d3aca1,0x0322828,
3495        0x1cc70f9,0x269c74c,0x0a53e4c,0x006edc2 },
3496      { 0x18bdd7a,0x2a79a55,0x26b1d5c,0x0200628,0x0734a05,0x3273c7b,
3497        0x13aa714,0x0040ac2,0x2f2da30,0x03e7449 } },
3498    /* 150 */
3499    { { 0x3f9563e,0x2f29eab,0x14a0749,0x3fad264,0x1dd077a,0x3d7c59c,
3500        0x3a0311b,0x331a789,0x0b9729e,0x0201ebf },
3501      { 0x1b08b77,0x2a4cdf2,0x3e387f8,0x21510f1,0x286c3a7,0x1dbf62e,
3502        0x3afa594,0x3363217,0x0d16568,0x01d46b7 } },
3503    /* 151 */
3504    { { 0x0715c0d,0x28e2d04,0x17f78ae,0x1c63dda,0x1d113ea,0x0fefc1b,
3505        0x1eab149,0x1d0fd99,0x0682537,0x00a7b11 },
3506      { 0x10bebbc,0x11c672d,0x14223d9,0x2ff9141,0x1399ee5,0x34b7b6c,
3507        0x0d5b3a8,0x01df643,0x0e392a4,0x03fe4dc } },
3508    /* 152 */
3509    { { 0x2b75b65,0x0b5a6f1,0x11c559a,0x3549999,0x24188f8,0x37a75f4,
3510        0x29f33e3,0x34068a2,0x38ba2a9,0x025dd91 },
3511      { 0x29af2c7,0x0988b64,0x0923885,0x1b539a4,0x1334f5d,0x226947a,
3512        0x2cc7e5a,0x20beb39,0x13fac2f,0x01d298c } },
3513    /* 153 */
3514    { { 0x35f079c,0x137f76d,0x2fbbb2f,0x254638d,0x185b07c,0x1f34db7,
3515        0x2cfcf0e,0x218f46d,0x2150ff4,0x02add6f },
3516      { 0x33fc9b7,0x0d9f005,0x0fd081b,0x0834965,0x2b90a74,0x102448d,
3517        0x3dbf03c,0x167d857,0x02e0b44,0x013afab } },
3518    /* 154 */
3519    { { 0x09f2c53,0x317f9d7,0x1411eb6,0x0463aba,0x0d25220,0x256b176,
3520        0x087633f,0x2bff322,0x07b2c1b,0x037e662 },
3521      { 0x10aaecb,0x23bb4a1,0x2272bb7,0x06c075a,0x09d4918,0x0736f2b,
3522        0x0dd511b,0x101625e,0x0a7779f,0x009ec10 } },
3523    /* 155 */
3524    { { 0x33b2eb2,0x0176dfd,0x2118904,0x022386c,0x2e0df85,0x2588c9f,
3525        0x1b71525,0x28fd540,0x137e4cf,0x02ce4f7 },
3526      { 0x3d75165,0x0c39ecf,0x3554a12,0x30af34c,0x2d66344,0x3ded408,
3527        0x36f1be0,0x0d065b0,0x012d046,0x0025623 } },
3528    /* 156 */
3529    { { 0x2601c3b,0x1824fc0,0x335fe08,0x3e33d70,0x0fb0252,0x252bfca,
3530        0x1cf2808,0x1922e55,0x1a9db9f,0x020721e },
3531      { 0x2f56c51,0x39a1f31,0x218c040,0x1a4fc5d,0x3fed471,0x0164d4e,
3532        0x388a419,0x06f1113,0x0f55fc1,0x03e8352 } },
3533    /* 157 */
3534    { { 0x1608e4d,0x3872778,0x022cbc6,0x044d60a,0x3010dda,0x15fb0b5,
3535        0x37ddc11,0x19f5bda,0x156b6a3,0x023a838 },
3536      { 0x383b3b4,0x1380bc8,0x353ca35,0x250fc07,0x169966b,0x3780f29,
3537        0x36632b2,0x2d6b13f,0x124fa00,0x00fd6ae } },
3538    /* 158 */
3539    { { 0x1739efb,0x2ec3656,0x2c0d337,0x3d39faf,0x1c751b0,0x04699f4,
3540        0x252dd64,0x095b8b6,0x0872b74,0x022f1da },
3541      { 0x2d3d253,0x38edca0,0x379fa5b,0x287d635,0x3a9f679,0x059d9ee,
3542        0x0ac168e,0x3cd3e87,0x19060fc,0x02ce1bc } },
3543    /* 159 */
3544    { { 0x3edcfc2,0x0f04d4b,0x2f0d31f,0x1898be2,0x25396bf,0x15ca230,
3545        0x02b4eae,0x2713668,0x0f71b06,0x0132d18 },
3546      { 0x38095ea,0x1ed34d6,0x3603ae6,0x165bf01,0x192bbf8,0x1852859,
3547        0x075f66b,0x1488f85,0x10895ef,0x014b035 } },
3548    /* 160 */
3549    { { 0x1339848,0x3084385,0x0c8d231,0x3a1c1de,0x0e87a28,0x255b85c,
3550        0x1de6616,0x2702e74,0x1382bb0,0x012b0f2 },
3551      { 0x198987d,0x381545a,0x34d619b,0x312b827,0x18b2376,0x28fe4cf,
3552        0x20b7651,0x017d077,0x0c7e397,0x00e0365 } },
3553    /* 161 */
3554    { { 0x1542e75,0x0d56aa0,0x39b701a,0x287b806,0x396c724,0x0935c21,
3555        0x3a29776,0x0debdac,0x171de26,0x00b38f8 },
3556      { 0x1d5bc1a,0x3fad27d,0x22b5cfe,0x1f89ddf,0x0a65560,0x144dd5b,
3557        0x2aac2f9,0x139353f,0x0520b62,0x00b9b36 } },
3558    /* 162 */
3559    { { 0x031c31d,0x16552e3,0x1a0c368,0x0016fc8,0x168533d,0x171e7b2,
3560        0x17626e7,0x275502f,0x14742c6,0x03285dd },
3561      { 0x2d2dbb2,0x3b6bffd,0x1d18cc6,0x2f45d2a,0x0fd0d8c,0x2915e3a,
3562        0x1e8793a,0x0b39a1d,0x3139cab,0x02a5da9 } },
3563    /* 163 */
3564    { { 0x3fb353d,0x147c6e4,0x3a720a6,0x22d5ff3,0x1d75cab,0x06c54a0,
3565        0x08cfa73,0x12666aa,0x3170a1f,0x021c829 },
3566      { 0x13e1b90,0x3a34dda,0x1fc38c3,0x02c5bdb,0x2d345dc,0x14aa1d0,
3567        0x28d00ab,0x224f23a,0x329c769,0x025c67b } },
3568    /* 164 */
3569    { { 0x0e35909,0x3bb6356,0x0116820,0x370cf77,0x29366d8,0x3881409,
3570        0x3999d06,0x013075f,0x176e157,0x02941ca },
3571      { 0x0e70b2e,0x28dfab1,0x2a8a002,0x15da242,0x084dcf6,0x116ca97,
3572        0x31bf186,0x1dc9735,0x09df7b7,0x0264e27 } },
3573    /* 165 */
3574    { { 0x2da7a4b,0x3023c9e,0x1366238,0x00ff4e2,0x03abe9d,0x19bd44b,
3575        0x272e897,0x20b91ad,0x2aa202c,0x02a2201 },
3576      { 0x380184e,0x08112b4,0x0b85660,0x31049aa,0x3a8cb78,0x36113c5,
3577        0x1670c0a,0x373f9e7,0x3fb4738,0x00010ef } },
3578    /* 166 */
3579    { { 0x2d5192e,0x26d770d,0x32af8d5,0x34d1642,0x1acf885,0x05805e0,
3580        0x166d0a1,0x1219a0d,0x301ba6c,0x014bcfb },
3581      { 0x2dcb64d,0x19cca83,0x379f398,0x08e01a0,0x10a482c,0x0103cc2,
3582        0x0be5fa7,0x1f9d45b,0x1899ef2,0x00ca5af } },
3583    /* 167 */
3584    { { 0x14d81d7,0x2aea251,0x1b3c476,0x3bd47ae,0x29eade7,0x0715e61,
3585        0x1a21cd8,0x1c7a586,0x2bfaee5,0x00ee43f },
3586      { 0x096f7cb,0x0c08f95,0x1bc4939,0x361fed4,0x255be41,0x26fad73,
3587        0x31dd489,0x02c600f,0x29d9f81,0x01ba201 } },
3588    /* 168 */
3589    { { 0x03ea1db,0x1eac46d,0x1292ce3,0x2a54967,0x20a7ff1,0x3e13c61,
3590        0x1b02218,0x2b44e14,0x3eadefa,0x029c88a },
3591      { 0x30a9144,0x31e3b0a,0x19c5a2a,0x147cbe9,0x05a0240,0x051f38e,
3592        0x11eca56,0x31a4247,0x123bc2a,0x02fa535 } },
3593    /* 169 */
3594    { { 0x3226ce7,0x1251782,0x0b7072f,0x11e59fa,0x2b8afd7,0x169b18f,
3595        0x2a46f18,0x31d9bb7,0x2fe9be8,0x01de0b7 },
3596      { 0x1b38626,0x34aa90f,0x3ad1760,0x21ddbd9,0x3460ae7,0x1126736,
3597        0x1b86fc5,0x0b92cd0,0x167a289,0x000e0e1 } },
3598    /* 170 */
3599    { { 0x1ec1a0f,0x36bbf5e,0x1c972d8,0x3f73ace,0x13bbcd6,0x23d86a5,
3600        0x175ffc5,0x2d083d5,0x2c4adf7,0x036f661 },
3601      { 0x1f39eb7,0x2a20505,0x176c81a,0x3d6e636,0x16ee2fc,0x3cbdc5f,
3602        0x25475dc,0x2ef4151,0x3c46860,0x0238934 } },
3603    /* 171 */
3604    { { 0x2587390,0x3639526,0x0588749,0x13c32fb,0x212bb19,0x09660f1,
3605        0x207da4b,0x2bf211b,0x1c4407b,0x01506a6 },
3606      { 0x24c8842,0x105a498,0x05ffdb2,0x0ab61b0,0x26044c1,0x3dff3d8,
3607        0x1d14b44,0x0d74716,0x049f57d,0x030024b } },
3608    /* 172 */
3609    { { 0x32e61ef,0x31d70f7,0x35cad3c,0x320b86c,0x07e8841,0x027ca7d,
3610        0x2d30d19,0x2513718,0x2347286,0x01d7901 },
3611      { 0x3c237d0,0x107f16e,0x01c9e7d,0x3c3b13c,0x0c9537b,0x20af54d,
3612        0x051a162,0x2161a47,0x258c784,0x016df2d } },
3613    /* 173 */
3614    { { 0x228ead1,0x29c2122,0x07f6964,0x023f4ed,0x1802dc5,0x19f96ce,
3615        0x24bfd17,0x25e866b,0x2ba8df0,0x01eb84f },
3616      { 0x2dd384e,0x05bbe3a,0x3f06fd2,0x366dacb,0x30361a2,0x2f36d7c,
3617        0x0b98784,0x38ff481,0x074e2a8,0x01e1f60 } },
3618    /* 174 */
3619    { { 0x17fbb1c,0x0975add,0x1debc5e,0x2cb2880,0x3e47bdd,0x3488cff,
3620        0x15e9a36,0x2121129,0x0199ef2,0x017088a },
3621      { 0x0315250,0x352a162,0x17c1773,0x0ae09c2,0x321b21a,0x3bd74cf,
3622        0x3c4ea1d,0x3cac2ad,0x3abbaf0,0x039174d } },
3623    /* 175 */
3624    { { 0x0511c8a,0x3c78d0a,0x2cd3d2d,0x322f729,0x3ebb229,0x09f0e69,
3625        0x0a71a76,0x2e74d5e,0x12284df,0x03b5ef0 },
3626      { 0x3dea561,0x0a9b7e4,0x0ed1cf2,0x237523c,0x05443f1,0x2eb48fa,
3627        0x3861405,0x1b49f62,0x0c945ca,0x02ab25f } },
3628    /* 176 */
3629    { { 0x16bd00a,0x13a9d28,0x3cc1eb5,0x2b7d702,0x2d839e9,0x3e6ff01,
3630        0x2bb7f11,0x3713824,0x3b31163,0x00c63e5 },
3631      { 0x30d7138,0x0316fb0,0x0220ecc,0x08eaf0c,0x244e8df,0x0088d81,
3632        0x37972fb,0x3fd34ae,0x2a19a84,0x03e907e } },
3633    /* 177 */
3634    { { 0x2642269,0x0b65d29,0x03bd440,0x33a6ede,0x3c81814,0x2507982,
3635        0x0d38e47,0x3a788e6,0x32c1d26,0x00e2eda },
3636      { 0x2577f87,0x392895a,0x3e1cc64,0x14f7047,0x08b52d2,0x08a01ca,
3637        0x336abf6,0x00697fc,0x105ce76,0x0253742 } },
3638    /* 178 */
3639    { { 0x293f92a,0x33df737,0x3315156,0x32e26d7,0x0a01333,0x26579d4,
3640        0x004df9c,0x0aba409,0x067d25c,0x02481de },
3641      { 0x3f39d44,0x1c78042,0x13d7e24,0x0825aed,0x35f2c90,0x3270f63,
3642        0x04b7b35,0x3ad4531,0x28bd29b,0x0207a10 } },
3643    /* 179 */
3644    { { 0x077199f,0x270aeb1,0x0dd96dd,0x3b9ad7b,0x28cb8ee,0x3903f43,
3645        0x37db3fe,0x292c62b,0x362dbbf,0x006e52a },
3646      { 0x247f143,0x0362cf3,0x216344f,0x3f18fd1,0x351e623,0x31664e0,
3647        0x0f270fc,0x243bbc6,0x2280555,0x001a8e3 } },
3648    /* 180 */
3649    { { 0x3355b49,0x2c04e6c,0x399b2e5,0x182d3af,0x020e265,0x09a7cf7,
3650        0x0ffa6bd,0x353e302,0x02083d9,0x029ecdb },
3651      { 0x33e8830,0x0570e86,0x1c0b64d,0x386a27e,0x0d5fcea,0x0b45a4c,
3652        0x2ee4a2e,0x0a8833f,0x2b4a282,0x02f9531 } },
3653    /* 181 */
3654    { { 0x191167c,0x36cf7e3,0x225ed6c,0x1e79e99,0x0517c3f,0x11ab1fd,
3655        0x05648f3,0x08aedc4,0x1abeae0,0x02fcc29 },
3656      { 0x3828a68,0x1e16fa4,0x30368e7,0x0c9fcfb,0x25161c3,0x24851ac,
3657        0x1b5feb5,0x344eb84,0x0de2732,0x0347208 } },
3658    /* 182 */
3659    { { 0x038b363,0x384d1e4,0x2519043,0x151ac17,0x158c11f,0x009b2b4,
3660        0x257abe6,0x2368d3f,0x3ed68a1,0x02df45e },
3661      { 0x29c2559,0x2962478,0x3d8444c,0x1d96fff,0x04f7a03,0x1391a52,
3662        0x0de4af7,0x3319126,0x15e6412,0x00e65ff } },
3663    /* 183 */
3664    { { 0x3d61507,0x1d1a0a2,0x0d2af20,0x354d299,0x329e132,0x2a28578,
3665        0x2ddfb08,0x04fa3ff,0x1293c6c,0x003bae2 },
3666      { 0x3e259f8,0x1a68fa9,0x3e67e9b,0x39b44f9,0x1ce1db7,0x347e9a1,
3667        0x3318f6a,0x2dbbc9d,0x2f8c922,0x008a245 } },
3668    /* 184 */
3669    { { 0x212ab5b,0x2b896c2,0x0136959,0x07e55ef,0x0cc1117,0x05b8ac3,
3670        0x18429ed,0x025fa01,0x11d6e93,0x03b016b },
3671      { 0x03f3708,0x2e96fab,0x1d77157,0x0d4c2d6,0x131baf9,0x0608d39,
3672        0x3552371,0x06cdd1e,0x1567ff1,0x01f4c50 } },
3673    /* 185 */
3674    { { 0x2dfefab,0x270173d,0x37077bd,0x1a372cd,0x1be2f22,0x28e2ee5,
3675        0x3ead973,0x35e8f94,0x2fc9bc1,0x03a7399 },
3676      { 0x36a02a1,0x2855d9b,0x00ed75a,0x37d8398,0x138c087,0x233706e,
3677        0x147f346,0x01947e2,0x3017228,0x0365942 } },
3678    /* 186 */
3679    { { 0x2057e60,0x2d31296,0x25e4504,0x2fa37bc,0x1cbccc3,0x1f0732f,
3680        0x3532081,0x2de8a98,0x19a804e,0x005359a },
3681      { 0x31f411a,0x2a10576,0x369c2c8,0x02fe035,0x109fbaf,0x30bddeb,
3682        0x1eef901,0x1662ad3,0x0410d43,0x01bd31a } },
3683    /* 187 */
3684    { { 0x2c24a96,0x1b7d3a5,0x19a3872,0x217f2f6,0x2534dbc,0x2cab8c2,
3685        0x066ef28,0x26aecf1,0x0fd6118,0x01310d4 },
3686      { 0x055b8da,0x1fdc5be,0x38a1296,0x25118f0,0x341a423,0x2ba4cd0,
3687        0x3e1413e,0x062d70d,0x2425a31,0x029c9b4 } },
3688    /* 188 */
3689    { { 0x08c1086,0x1acfba5,0x22e1dae,0x0f72f4e,0x3f1de50,0x0f408bc,
3690        0x35ed3f0,0x3ce48fc,0x282cc6c,0x004d8e7 },
3691      { 0x1afaa86,0x24e3ef3,0x22589ac,0x3ec9952,0x1f45bc5,0x14144ca,
3692        0x23b26e4,0x0d68c65,0x1e1c1a3,0x032a4d9 } },
3693    /* 189 */
3694    { { 0x03b2d20,0x16b1d53,0x241b361,0x05e4138,0x1742a54,0x32741c7,
3695        0x0521c4c,0x1ca96c2,0x034970b,0x02738a7 },
3696      { 0x13e0ad6,0x207dcdb,0x034c8cc,0x27bcbe1,0x18060da,0x33a18b6,
3697        0x2d1d1a6,0x2be60d7,0x3d7ab42,0x012312a } },
3698    /* 190 */
3699    { { 0x0c7485a,0x06c3310,0x0dbfd22,0x2ef949d,0x0ead455,0x098f4ba,
3700        0x3c76989,0x0cf2d24,0x032f67b,0x01e005f },
3701      { 0x30cb5ee,0x0d5da64,0x0ed2b9d,0x2503102,0x1c0d14e,0x1cbc693,
3702        0x37bf552,0x07013e2,0x054de5c,0x014f341 } },
3703    /* 191 */
3704    { { 0x128ccac,0x1617e97,0x346ebcd,0x158016d,0x25f823e,0x34048ea,
3705        0x39f0a1c,0x3ea3df1,0x1c1d3d7,0x03ba919 },
3706      { 0x151803b,0x01967c1,0x2f70781,0x27df39a,0x06c0b59,0x24a239c,
3707        0x15a7702,0x2464d06,0x2a47ae6,0x006db90 } },
3708    /* 192 */
3709    { { 0x27d04c3,0x024df3d,0x38112e8,0x38a27ba,0x01e312b,0x0965358,
3710        0x35d8879,0x2f4f55a,0x214187f,0x0008936 },
3711      { 0x05fe36f,0x2ee18c3,0x1f5f87a,0x1813bd4,0x0580f3c,0x0ed0a7b,
3712        0x0fb1bfb,0x3fcce59,0x2f042bf,0x01820e3 } },
3713    /* 193 */
3714    { { 0x20bbe99,0x32cbc9f,0x39ee432,0x3cc12a8,0x37bda44,0x3ea4e40,
3715        0x097c7a9,0x0590d7d,0x2022d33,0x018dbac },
3716      { 0x3ae00aa,0x3439864,0x2d2ffcf,0x3f8c6b9,0x0875a00,0x3e4e407,
3717        0x3658a29,0x22eb3d0,0x2b63921,0x022113b } },
3718    /* 194 */
3719    { { 0x33bae58,0x05c749a,0x1f3e114,0x1c45f8e,0x27db3df,0x06a3ab6,
3720        0x37bc7f8,0x1e27b34,0x3dc51fb,0x009eea0 },
3721      { 0x3f54de5,0x3d0e7fe,0x1a71a7d,0x02ed7f8,0x0727703,0x2ca5e92,
3722        0x2e8e35d,0x292ad0b,0x13487f3,0x02b6d8b } },
3723    /* 195 */
3724    { { 0x175df2a,0x05a28a8,0x32e99b1,0x13d8630,0x2082aa0,0x11ac245,
3725        0x24f2e71,0x322cb27,0x17675e7,0x02e643f },
3726      { 0x1f37313,0x2765ad3,0x0789082,0x1e742d0,0x11c2055,0x2021dc4,
3727        0x09ae4a7,0x346359b,0x2f94d10,0x0205c1f } },
3728    /* 196 */
3729    { { 0x3d6ff96,0x1f2ac80,0x336097d,0x3f03610,0x35b851b,0x010b6d2,
3730        0x0823c4d,0x2a9709a,0x2ead5a8,0x00de4b6 },
3731      { 0x01afa0b,0x0621965,0x3671528,0x1050b60,0x3f3e9e7,0x2f93829,
3732        0x0825275,0x006e85f,0x35e94b0,0x016af58 } },
3733    /* 197 */
3734    { { 0x2c4927c,0x3ea1382,0x0f23727,0x0d69f23,0x3e38860,0x2b72837,
3735        0x3cd5ea4,0x2d84292,0x321846a,0x016656f },
3736      { 0x29dfa33,0x3e182e0,0x018be90,0x2ba563f,0x2caafe2,0x218c0d9,
3737        0x3baf447,0x1047a6c,0x0a2d483,0x01130cb } },
3738    /* 198 */
3739    { { 0x00ed80c,0x2a5fc79,0x0a82a74,0x2c4c74b,0x15f938c,0x30b5ab6,
3740        0x32124b7,0x295314f,0x2fb8082,0x007c858 },
3741      { 0x20b173e,0x19f315c,0x12f97e4,0x198217c,0x040e8a6,0x3275977,
3742        0x2bc20e4,0x01f2633,0x02bc3e9,0x023c750 } },
3743    /* 199 */
3744    { { 0x3c4058a,0x24be73e,0x16704f5,0x2d8a4bd,0x3b15e14,0x3076315,
3745        0x1cfe37b,0x36fe715,0x343926e,0x02c6603 },
3746      { 0x2c76b09,0x0cf824c,0x3f7898c,0x274cec1,0x11df527,0x18eed18,
3747        0x08ead48,0x23915bc,0x19b3744,0x00a0a2b } },
3748    /* 200 */
3749    { { 0x0cf4ac5,0x1c8b131,0x0afb696,0x0ff7799,0x2f5ac1a,0x022420c,
3750        0x11baa2e,0x2ce4015,0x1275a14,0x0125cfc },
3751      { 0x22eac5d,0x360cd4c,0x3568e59,0x3d42f66,0x35e07ee,0x09620e4,
3752        0x36720fa,0x22b1eac,0x2d0db16,0x01b6b23 } },
3753    /* 201 */
3754    { { 0x1a835ef,0x1516bbb,0x2d51f7b,0x3487443,0x14aa113,0x0dd06c2,
3755        0x1a65e01,0x379300d,0x35920b9,0x012c8fb },
3756      { 0x04c7341,0x2eda00f,0x3c37e82,0x1b4fd62,0x0d45770,0x1478fba,
3757        0x127863a,0x26939cd,0x134ddf4,0x01375c5 } },
3758    /* 202 */
3759    { { 0x1476cd9,0x1119ca5,0x325bbf9,0x0bf8c69,0x0648d07,0x312d9f8,
3760        0x01c8b8f,0x136ec51,0x0002f4a,0x03f4c5c },
3761      { 0x195d0e1,0x10ffd22,0x29aa1cb,0x3443bdc,0x276e695,0x05e6260,
3762        0x15f9764,0x3cd9783,0x18c9569,0x0053eb1 } },
3763    /* 203 */
3764    { { 0x312ae18,0x280197c,0x3fc9ad9,0x303f324,0x251958d,0x29f4a11,
3765        0x2142408,0x3694366,0x25136ab,0x03b5f1d },
3766      { 0x1d4abbc,0x1c3c689,0x13ea462,0x3cfc684,0x39b5dd8,0x2d4654b,
3767        0x09b0755,0x27d4f18,0x3f74d2e,0x03fbf2d } },
3768    /* 204 */
3769    { { 0x2119185,0x2525eae,0x1ba4bd0,0x0c2ab11,0x1d54e8c,0x294845e,
3770        0x2479dea,0x3602d24,0x17e87e0,0x0060069 },
3771      { 0x0afffb0,0x34fe37f,0x1240073,0x02eb895,0x06cf33c,0x2d7f7ef,
3772        0x1d763b5,0x04191e0,0x11e1ead,0x027e3f0 } },
3773    /* 205 */
3774    { { 0x269544c,0x0e85c57,0x3813158,0x19fc12d,0x20eaf85,0x1e2930c,
3775        0x22a8fd2,0x1a6a478,0x09d3d3a,0x02a74e0 },
3776      { 0x1a2da3b,0x30b0b16,0x0847936,0x3d86257,0x138ccbc,0x0f5421a,
3777        0x25244e6,0x23bdd79,0x1aee117,0x00c01ae } },
3778    /* 206 */
3779    { { 0x1eead28,0x07cac32,0x1fbc0bb,0x17627d3,0x17eef63,0x0b3a24e,
3780        0x0757fdb,0x3dd841d,0x3d745f8,0x002ae17 },
3781      { 0x25b4549,0x29f24cf,0x2f21ecd,0x1725e48,0x04be2bb,0x10ee010,
3782        0x1a1274b,0x10b0898,0x27511e9,0x02c48b5 } },
3783    /* 207 */
3784    { { 0x2a5ae7a,0x181ef99,0x0be33be,0x3e9dab7,0x101e703,0x3adb971,
3785        0x1043014,0x2ebb2be,0x1c1097d,0x027d667 },
3786      { 0x3f250ed,0x16dc603,0x20dc6d7,0x1d0d268,0x38eb915,0x02c89e8,
3787        0x1605a41,0x12de109,0x0e08a29,0x01f554a } },
3788    /* 208 */
3789    { { 0x0c26def,0x163d988,0x2d1ef0f,0x3a960ac,0x1025585,0x0738e20,
3790        0x27d79b0,0x05cc3ef,0x201303f,0x00a333a },
3791      { 0x1644ba5,0x2af345e,0x30b8d1d,0x3a01bff,0x31fc643,0x1acf85e,
3792        0x0a76fc6,0x04efe98,0x348a1d0,0x03062eb } },
3793    /* 209 */
3794    { { 0x1c4216d,0x18e3217,0x02ac34e,0x19c8185,0x200c010,0x17d4192,
3795        0x13a1719,0x165af51,0x09db7a9,0x0277be0 },
3796      { 0x3ab8d2c,0x2190b99,0x22b641e,0x0cd88de,0x3b42404,0x1310862,
3797        0x106a6d6,0x23395f5,0x0b06880,0x000d5fe } },
3798    /* 210 */
3799    { { 0x0d2cc88,0x36f9913,0x339d8e9,0x237c2e3,0x0cc61c2,0x34c2832,
3800        0x309874c,0x2621d28,0x2dd1b48,0x0392806 },
3801      { 0x17cd8f9,0x07bab3d,0x0c482ed,0x0faf565,0x31b767d,0x2f4bde1,
3802        0x295c717,0x330c29c,0x179ce10,0x0119b5f } },
3803    /* 211 */
3804    { { 0x1ada2c7,0x0c624a7,0x227d47d,0x30e3e6a,0x14fa0a6,0x0829678,
3805        0x24fd288,0x2b46a43,0x122451e,0x0319ca9 },
3806      { 0x186b655,0x01f3217,0x0af1306,0x0efe6b5,0x2f0235d,0x1c45ca9,
3807        0x2086805,0x1d44e66,0x0faf2a6,0x0178f59 } },
3808    /* 212 */
3809    { { 0x33b4416,0x10431e6,0x2d99aa6,0x217aac9,0x0cd8fcf,0x2d95a9d,
3810        0x3ff74ad,0x10bf17a,0x295eb8e,0x01b229e },
3811      { 0x02a63bd,0x182e9ec,0x004710c,0x00e2e3c,0x06b2f23,0x04b642c,
3812        0x2c37383,0x32a4631,0x022ad82,0x00d22b9 } },
3813    /* 213 */
3814    { { 0x0cda2fb,0x1d198d7,0x26d27f4,0x286381c,0x022acca,0x24ac7c8,
3815        0x2df7824,0x0b4ba16,0x1e0d9ef,0x03041d3 },
3816      { 0x29a65b3,0x0f3912b,0x151bfcf,0x2b0175c,0x0fd71e4,0x39aa5e2,
3817        0x311f50c,0x13ff351,0x3dbc9e5,0x03eeb7e } },
3818    /* 214 */
3819    { { 0x0a99363,0x0fc7348,0x2775171,0x23db3c8,0x2b91565,0x134d66c,
3820        0x0175cd2,0x1bf365a,0x2b48371,0x02dfe5d },
3821      { 0x16dbf74,0x2389357,0x2f36575,0x3f5c70e,0x38d23ba,0x090f7f8,
3822        0x3477600,0x3201523,0x32ecafc,0x03d3506 } },
3823    /* 215 */
3824    { { 0x1abd48d,0x073ca3f,0x38a451f,0x0d8cb01,0x1ce81be,0x05c51ba,
3825        0x0e29741,0x03c41ab,0x0eae016,0x0060209 },
3826      { 0x2e58358,0x1da62d9,0x2358038,0x14b39b2,0x1635687,0x39079b1,
3827        0x380e345,0x1b49608,0x23983cf,0x019f97d } },
3828    /* 216 */
3829    { { 0x34899ef,0x332e373,0x04c0f89,0x3c27aed,0x1949015,0x09663b2,
3830        0x2f9276b,0x07f1951,0x09a04c1,0x027fbde },
3831      { 0x3d2a071,0x19fb3d4,0x1b096d3,0x1fe9146,0x3b10e1a,0x0478bbb,
3832        0x2b3fb06,0x1388329,0x181a99c,0x02f2030 } },
3833    /* 217 */
3834    { { 0x1eb82e6,0x14dbe39,0x3920972,0x31fd5b2,0x21a484f,0x02d7697,
3835        0x0e21715,0x37c431e,0x2629f8c,0x01249c3 },
3836      { 0x26b50ad,0x26deefa,0x0ffc1a3,0x30688e2,0x39a0284,0x041c65e,
3837        0x03eb178,0x0bdfd50,0x2f96137,0x034bb94 } },
3838    /* 218 */
3839    { { 0x0e0362a,0x334a162,0x194dd37,0x29e3e97,0x2442fa8,0x10d2949,
3840        0x3836e5a,0x2dccebf,0x0bee5ab,0x037ed1e },
3841      { 0x33eede6,0x3c739d9,0x2f04a91,0x350ad6c,0x3a5390a,0x14c368b,
3842        0x26f7bf5,0x11ce979,0x0b408df,0x0366850 } },
3843    /* 219 */
3844    { { 0x28ea498,0x0886d5b,0x2e090e0,0x0a4d58f,0x2623478,0x0d74ab7,
3845        0x2b83913,0x12c6b81,0x18d623f,0x01d8301 },
3846      { 0x198aa79,0x26d6330,0x3a7f0b8,0x34bc1ea,0x2f74890,0x378955a,
3847        0x204110f,0x0102538,0x02d8f19,0x01c5066 } },
3848    /* 220 */
3849    { { 0x14b0f45,0x2838cd3,0x14e16f0,0x0e0e4aa,0x2d9280b,0x0f18757,
3850        0x3324c6b,0x1391ceb,0x1ce89d5,0x00ebe74 },
3851      { 0x0930371,0x3de6048,0x3097fd8,0x1308705,0x3eda266,0x3108c26,
3852        0x1545dcd,0x1f7583a,0x1c37395,0x02c7e05 } },
3853    /* 221 */
3854    { { 0x1fec44a,0x2a9e3a2,0x0caf84f,0x11cf2a9,0x0c8c2ae,0x06da989,
3855        0x1c807dc,0x3c149a4,0x1141543,0x02906bb },
3856      { 0x15ffe04,0x0d4e65f,0x2e20424,0x37d896d,0x18bacb2,0x1e05ddd,
3857        0x1660be8,0x183be17,0x1dd86fb,0x035ba70 } },
3858    /* 222 */
3859    { { 0x2853264,0x0ba5fb1,0x0a0b3aa,0x2df88c1,0x2771533,0x23aba6f,
3860        0x112bb7b,0x3e3086e,0x210ae9b,0x027271b },
3861      { 0x030b74c,0x0269678,0x1e90a23,0x135a98c,0x24ed749,0x126de7c,
3862        0x344b23a,0x186da27,0x19640fa,0x0159af5 } },
3863    /* 223 */
3864    { { 0x18061f3,0x3004630,0x3c70066,0x34df20f,0x1190b25,0x1c9cc91,
3865        0x1fc8e02,0x0d17bc1,0x390f525,0x033cb1c },
3866      { 0x0eb30cf,0x2f3ad04,0x303aa09,0x2e835dd,0x1cfd2eb,0x143fc95,
3867        0x02c43a1,0x025e7a1,0x3558aa2,0x000bd45 } },
3868    /* 224 */
3869    { { 0x1db7d07,0x3bde52b,0x1500396,0x1089115,0x20b4fc7,0x1e2a8f3,
3870        0x3f8eacc,0x365f7eb,0x1a5e8d4,0x0053a6b },
3871      { 0x37079e2,0x120284b,0x000edaa,0x33792c2,0x145baa3,0x20e055f,
3872        0x365e2d7,0x26ba005,0x3ab8e9d,0x0282b53 } },
3873    /* 225 */
3874    { { 0x2653618,0x2dd8852,0x2a5f0bf,0x0f0c7aa,0x2187281,0x1252757,
3875        0x13e7374,0x3b47855,0x0b86e56,0x02f354c },
3876      { 0x2e9c47b,0x2fa14cc,0x19ab169,0x3fad401,0x0dc2776,0x24afeed,
3877        0x3a97611,0x0d07736,0x3cf6979,0x02424a0 } },
3878    /* 226 */
3879    { { 0x2e81a13,0x000c91d,0x123967b,0x265885c,0x29bee1a,0x0cb8675,
3880        0x2d361bd,0x1526823,0x3c9ace1,0x00d7bad },
3881      { 0x24e5bdc,0x02b969f,0x2c6e128,0x34edb3b,0x12dcd2c,0x3899af0,
3882        0x24224c6,0x3a1914b,0x0f4448a,0x026a2cb } },
3883    /* 227 */
3884    { { 0x1d03b59,0x1c6fc82,0x32abf64,0x28ed96b,0x1c90e62,0x2f57bb2,
3885        0x3ff168e,0x04de7fd,0x0f4d449,0x01af6d8 },
3886      { 0x255bc30,0x2bfaf22,0x3fe0dad,0x0584025,0x1c79ead,0x3078ef7,
3887        0x2197414,0x022a50b,0x0fd94ba,0x0007b0f } },
3888    /* 228 */
3889    { { 0x09485c2,0x09dfaf7,0x10c7ba6,0x1e48bec,0x248cc9a,0x028a362,
3890        0x21d60f7,0x193d93d,0x1c04754,0x0346b2c },
3891      { 0x2f36612,0x240ac49,0x0d8bd26,0x13b8186,0x259c3a4,0x020d5fb,
3892        0x38a8133,0x09b0937,0x39d4056,0x01f7341 } },
3893    /* 229 */
3894    { { 0x05a4b48,0x1f534fc,0x07725ce,0x148dc8c,0x2adcd29,0x04aa456,
3895        0x0f79718,0x066e346,0x189377d,0x002fd4d },
3896      { 0x068ea73,0x336569b,0x184d35e,0x32a08e9,0x3c7f3bb,0x11ce9c8,
3897        0x3674c6f,0x21bf27e,0x0d9e166,0x034a2f9 } },
3898    /* 230 */
3899    { { 0x0fa8e4b,0x2e6418e,0x18fc5d2,0x1ba24ff,0x0559f18,0x0dbedbf,
3900        0x2de2aa4,0x22338e9,0x3aa510f,0x035d801 },
3901      { 0x23a4988,0x02aad94,0x02732d1,0x111d374,0x0b455cf,0x0d01c9e,
3902        0x067082a,0x2ec05fd,0x368b303,0x03cad4b } },
3903    /* 231 */
3904    { { 0x035b4ca,0x1fabea6,0x1cbc0d5,0x3f2ed9a,0x02d2232,0x1990c66,
3905        0x2eb680c,0x3b4ea3b,0x18ecc5a,0x03636fa },
3906      { 0x1a02709,0x26f8ff1,0x1fa8cba,0x397d6e8,0x230be68,0x043aa14,
3907        0x3d43cdf,0x25c17fa,0x3a3ee55,0x0380564 } },
3908    /* 232 */
3909    { { 0x275a0a6,0x16bd43a,0x0033d3e,0x2b15e16,0x2512226,0x005d901,
3910        0x26d50fd,0x3bc19bf,0x3b1aeb8,0x02bfb01 },
3911      { 0x0bb0a31,0x26559e0,0x1aae7fb,0x330dcc2,0x16f1af3,0x06afce2,
3912        0x13a15a0,0x2ff7645,0x3546e2d,0x029c6e4 } },
3913    /* 233 */
3914    { { 0x0f593d2,0x384b806,0x122bbf8,0x0a281e0,0x1d1a904,0x2e93cab,
3915        0x0505db0,0x08f6454,0x05c6285,0x014e880 },
3916      { 0x3f2b935,0x22d8e79,0x161a07c,0x16b060a,0x02bff97,0x146328b,
3917        0x3ceea77,0x238f61a,0x19b3d58,0x02fd1f4 } },
3918    /* 234 */
3919    { { 0x17665d5,0x259e9f7,0x0de5672,0x15cbcbd,0x34e3030,0x035240f,
3920        0x0005ae8,0x286d851,0x07f39c9,0x000070b },
3921      { 0x1efc6d6,0x2a0051a,0x2724143,0x2a9ef1e,0x0c810bd,0x1e05429,
3922        0x25670ba,0x2e66d7d,0x0e786ff,0x03f6b7e } },
3923    /* 235 */
3924    { { 0x3c00785,0x232e23f,0x2b67fd3,0x244ed23,0x077fa75,0x3cda3ef,
3925        0x14d055b,0x0f25011,0x24d5aa4,0x00ea0e3 },
3926      { 0x297bb9a,0x198ca4f,0x14d9561,0x18d1076,0x39eb933,0x2b6caa0,
3927        0x1591a60,0x0768d45,0x257873e,0x00f36e0 } },
3928    /* 236 */
3929    { { 0x1e77eab,0x0502a5f,0x0109137,0x0350592,0x3f7e1c5,0x3ac7437,
3930        0x2dcad2c,0x1fee9d8,0x089f1f5,0x0169833 },
3931      { 0x0d45673,0x0d8e090,0x065580b,0x065644f,0x11b82be,0x3592dd0,
3932        0x3284b8d,0x23f0015,0x16fdbfd,0x0248bfd } },
3933    /* 237 */
3934    { { 0x1a129a1,0x1977bb2,0x0e041b2,0x15f30a1,0x0a5b1ce,0x3afef8f,
3935        0x380c46c,0x3358810,0x27df6c5,0x01ca466 },
3936      { 0x3b90f9a,0x3d14ea3,0x031b298,0x02e2390,0x2d719c0,0x25bc615,
3937        0x2c0e777,0x0226b8c,0x3803624,0x0179e45 } },
3938    /* 238 */
3939    { { 0x363cdfb,0x1bb155f,0x24fd5c1,0x1c7c72b,0x28e6a35,0x18165f2,
3940        0x226bea5,0x0beaff3,0x371e24c,0x0138294 },
3941      { 0x1765357,0x29034e9,0x22b4276,0x11035ce,0x23c89af,0x074468c,
3942        0x3370ae4,0x013bae3,0x018d566,0x03d7fde } },
3943    /* 239 */
3944    { { 0x209df21,0x0f8ff86,0x0e47fbf,0x23b99ba,0x126d5d2,0x2722405,
3945        0x16bd0a2,0x1799082,0x0e9533f,0x039077c },
3946      { 0x3ba9e3f,0x3f6902c,0x1895305,0x3ac9813,0x3f2340c,0x3c0d9f1,
3947        0x26e1927,0x0557c21,0x16eac4f,0x023b75f } },
3948    /* 240 */
3949    { { 0x3fc8ff3,0x0770382,0x342fc9a,0x0afa4db,0x314efd8,0x328e07b,
3950        0x016f7cc,0x3ba599c,0x1caed8a,0x0050cb0 },
3951      { 0x0b23c26,0x2120a5c,0x3273ec6,0x1cc1cd6,0x2a64fe8,0x2bbc3d6,
3952        0x09f6e5e,0x34b1b8e,0x00b5ac8,0x032bbd2 } },
3953    /* 241 */
3954    { { 0x1315922,0x1725e1d,0x0ca5524,0x1c4c18f,0x3d82951,0x193bcb2,
3955        0x0e60d0b,0x388dbcf,0x37e8efa,0x0342e85 },
3956      { 0x1b3af60,0x26ba3ec,0x220e53a,0x394f4b6,0x01a796a,0x3e7bbca,
3957        0x163605d,0x2b85807,0x17c1c54,0x03cc725 } },
3958    /* 242 */
3959    { { 0x1cc4597,0x1635492,0x2028c0f,0x2c2eb82,0x2dc5015,0x0d2a052,
3960        0x05fc557,0x1f0ebbf,0x0cb96e1,0x0004d01 },
3961      { 0x1a824bf,0x3896172,0x2ed7b29,0x178007a,0x0d59318,0x07bda2b,
3962        0x2ee6826,0x0f9b235,0x04b9193,0x01bcddf } },
3963    /* 243 */
3964    { { 0x0333fd2,0x0eeb46a,0x15b89f9,0x00968aa,0x2a89302,0x2bdd6b3,
3965        0x1e5037e,0x2541884,0x24ed2d0,0x01b6e8f },
3966      { 0x04399cd,0x3be6334,0x3adea48,0x1bb9adc,0x31811c6,0x05fb2bc,
3967        0x360752c,0x3d29dcb,0x3423bec,0x03c4f3c } },
3968    /* 244 */
3969    { { 0x119e2eb,0x2e7b02a,0x0f68cee,0x257d8b0,0x183a9a1,0x2ae88a6,
3970        0x3a3bb67,0x2eb4f3e,0x1a9274b,0x0320fea },
3971      { 0x2fa1ce0,0x346c2d8,0x2fbf0d7,0x3d4d063,0x0e58b60,0x09c1bc1,
3972        0x28ef9e5,0x09a0efe,0x0f45d70,0x02d275c } },
3973    /* 245 */
3974    { { 0x2d5513b,0x31d443e,0x1e2d914,0x3b2c5d4,0x105f32e,0x27ee756,
3975        0x050418d,0x3c73db6,0x1bb0c30,0x01673eb },
3976      { 0x1cb7fd6,0x1eb08d5,0x26a3e16,0x2e20810,0x0249367,0x029e219,
3977        0x2ec58c9,0x12d9fab,0x362354a,0x016eafc } },
3978    /* 246 */
3979    { { 0x2424865,0x260747b,0x177f37c,0x1e3cb95,0x08b0028,0x2783016,
3980        0x2970f1b,0x323c1c0,0x2a79026,0x0186231 },
3981      { 0x0f244da,0x26866f4,0x087306f,0x173ec20,0x31ecced,0x3c84d8d,
3982        0x070f9b9,0x2e764d5,0x075df50,0x0264ff9 } },
3983    /* 247 */
3984    { { 0x32c3609,0x0c737e6,0x14ea68e,0x300b11b,0x184eb19,0x29dd440,
3985        0x09ec1a9,0x185adeb,0x0664c80,0x0207dd9 },
3986      { 0x1fbe978,0x30a969d,0x33561d7,0x34fc60e,0x36743fe,0x00774af,
3987        0x0d1f045,0x018360e,0x12a5fe9,0x01592a0 } },
3988    /* 248 */
3989    { { 0x2817d1d,0x2993d3e,0x2e0f7a5,0x112faa0,0x255f968,0x355fe6a,
3990        0x3f5a0fc,0x075b2d7,0x3cf00e5,0x0089afc },
3991      { 0x32833cf,0x06a7e4b,0x09a8d6d,0x1693d3e,0x320a0a3,0x3cfdfdd,
3992        0x136c498,0x1e0d845,0x347ff25,0x01a1de7 } },
3993    /* 249 */
3994    { { 0x3043d08,0x030705c,0x20fa79b,0x1d07f00,0x0a54467,0x29b49b4,
3995        0x367e289,0x0b82f4d,0x0d1eb09,0x025ef2c },
3996      { 0x32ed3c3,0x1baaa3c,0x3c482ab,0x146ca06,0x3c8a4f1,0x3e85e3c,
3997        0x1bf4f3b,0x1195534,0x3e80a78,0x02a1cbf } },
3998    /* 250 */
3999    { { 0x32b2086,0x2de4d68,0x3486b1a,0x03a0583,0x2e1eb71,0x2dab9af,
4000        0x10cd913,0x28daa6f,0x3fcb732,0x000a04a },
4001      { 0x3605318,0x3f5f2b3,0x2d1da63,0x143f7f5,0x1646e5d,0x040b586,
4002        0x1683982,0x25abe87,0x0c9fe53,0x001ce47 } },
4003    /* 251 */
4004    { { 0x380d02b,0x055fc22,0x3f7fc50,0x3458a1d,0x26b8333,0x23550ab,
4005        0x0a1af87,0x0a821eb,0x2dc7e6d,0x00d574a },
4006      { 0x07386e1,0x3ccd68a,0x3275b41,0x253e390,0x2fd272a,0x1e6627a,
4007        0x2ca2cde,0x0e9e4a1,0x1e37c2a,0x00f70ac } },
4008    /* 252 */
4009    { { 0x0581352,0x2748701,0x02bed68,0x094dd9e,0x30a00c8,0x3fb5c07,
4010        0x3bd5909,0x211ac80,0x1103ccd,0x0311e1a },
4011      { 0x0c768ed,0x29dc209,0x36575db,0x009a107,0x272feea,0x2b33383,
4012        0x313ed56,0x134c9cc,0x168d5bb,0x033310a } },
4013    /* 253 */
4014    { { 0x17620b9,0x143784f,0x256a94e,0x229664a,0x1d89a5c,0x1d521f2,
4015        0x0076406,0x1c73f70,0x342aa48,0x03851fa },
4016      { 0x0f3ae46,0x2ad3bab,0x0fbe274,0x3ed40d4,0x2fd4936,0x232103a,
4017        0x2afe474,0x25b8f7c,0x047080e,0x008e6b0 } },
4018    /* 254 */
4019    { { 0x3fee8d4,0x347cd4a,0x0fec481,0x33fe9ec,0x0ce80b5,0x33a6bcf,
4020        0x1c4c9e2,0x3967441,0x1a3f5f7,0x03157e8 },
4021      { 0x257c227,0x1bc53a0,0x200b318,0x0fcd0af,0x2c5b165,0x2a413ec,
4022        0x2fc998a,0x2da6426,0x19cd4f4,0x0025336 } },
4023    /* 255 */
4024    { { 0x303beba,0x2072135,0x32918a9,0x140cb3a,0x08631d1,0x0ef527b,
4025        0x05f2c9e,0x2b4ce91,0x0b642ab,0x02e428c },
4026      { 0x0a5abf9,0x15013ed,0x3603b46,0x30dd76d,0x3004750,0x28d7627,
4027        0x1a42ccc,0x093ddbe,0x39a1b79,0x00067e2 } },
4028};
4029
4030/* Multiply the base point of P256 by the scalar and return the result.
4031 * If map is true then convert result to affine coordinates.
4032 *
4033 * r     Resulting point.
4034 * k     Scalar to multiply by.
4035 * map   Indicates whether to convert result to affine.
4036 * heap  Heap to use for allocation.
4037 * returns MEMORY_E when memory allocation fails and MP_OKAY on success.
4038 */
4039static int sp_256_ecc_mulmod_base_10(sp_point* r, const sp_digit* k,
4040        int map, void* heap)
4041{
4042    return sp_256_ecc_mulmod_stripe_10(r, &p256_base, p256_table,
4043                                      k, map, heap);
4044}
4045
4046#endif
4047
4048
4049#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
4050#endif
4051#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
4052/* Multiply a by scalar b into r. (r = a * b)
4053 *
4054 * r  A single precision integer.
4055 * a  A single precision integer.
4056 * b  A scalar.
4057 */
4058SP_NOINLINE static void sp_256_mul_d_10(sp_digit* r, const sp_digit* a,
4059    sp_digit b)
4060{
4061#ifdef WOLFSSL_SP_SMALL
4062    int64_t tb = b;
4063    int64_t t = 0;
4064    int i;
4065
4066    for (i = 0; i < 10; i++) {
4067        t += tb * a[i];
4068        r[i] = t & 0x3ffffff;
4069        t >>= 26;
4070    }
4071    r[10] = (sp_digit)t;
4072#else
4073    int64_t tb = b;
4074    int64_t t[10];
4075
4076    t[ 0] = Q6_P_mpy_RR(tb, a[0]);
4077    t[ 1] = Q6_P_mpy_RR(tb, a[1]);
4078    t[ 2] = Q6_P_mpy_RR(tb, a[2]);
4079    t[ 3] = Q6_P_mpy_RR(tb, a[3]);
4080    t[ 4] = Q6_P_mpy_RR(tb, a[4]);
4081    t[ 5] = Q6_P_mpy_RR(tb, a[5]);
4082    t[ 6] = Q6_P_mpy_RR(tb, a[6]);
4083    t[ 7] = Q6_P_mpy_RR(tb, a[7]);
4084    t[ 8] = Q6_P_mpy_RR(tb, a[8]);
4085    t[ 9] = Q6_P_mpy_RR(tb, a[9]);
4086    r[ 0] =                           Q6_R_and_RR(t[ 0], 0x3ffffff);
4087    r[ 1] = (sp_digit)(t[ 0] >> 26) + Q6_R_and_RR(t[ 1], 0x3ffffff);
4088    r[ 2] = (sp_digit)(t[ 1] >> 26) + Q6_R_and_RR(t[ 2], 0x3ffffff);
4089    r[ 3] = (sp_digit)(t[ 2] >> 26) + Q6_R_and_RR(t[ 3], 0x3ffffff);
4090    r[ 4] = (sp_digit)(t[ 3] >> 26) + Q6_R_and_RR(t[ 4], 0x3ffffff);
4091    r[ 5] = (sp_digit)(t[ 4] >> 26) + Q6_R_and_RR(t[ 5], 0x3ffffff);
4092    r[ 6] = (sp_digit)(t[ 5] >> 26) + Q6_R_and_RR(t[ 6], 0x3ffffff);
4093    r[ 7] = (sp_digit)(t[ 6] >> 26) + Q6_R_and_RR(t[ 7], 0x3ffffff);
4094    r[ 8] = (sp_digit)(t[ 7] >> 26) + Q6_R_and_RR(t[ 8], 0x3ffffff);
4095    r[ 9] = (sp_digit)(t[ 8] >> 26) + Q6_R_and_RR(t[ 9], 0x3ffffff);
4096    r[10] = (sp_digit)(t[ 9] >> 26);
4097#endif /* WOLFSSL_SP_SMALL */
4098}
4099
4100#ifdef WOLFSSL_SP_DIV_32
4101static WC_INLINE sp_digit sp_256_div_word_10(sp_digit d1, sp_digit d0,
4102    sp_digit dv)
4103{
4104    sp_digit d, r, t, dv;
4105    int64_t t0, t1;
4106
4107    /* dv has 14 bits. */
4108    dv = (div >> 12) + 1;
4109    /* All 26 bits from d1 and top 5 bits from d0. */
4110    d = (d1 << 5) | (d0 >> 21);
4111    r = d / dv;
4112    d -= r * dv;
4113    /* Up to 17 bits in r */
4114    /* Next 9 bits from d0. */
4115    d <<= 9;
4116    r <<= 9;
4117    d |= (d0 >> 12) & ((1 << 9) - 1);
4118    t = d / dv;
4119    d -= t * dv;
4120    r += t;
4121    /* Up to 26 bits in r */
4122
4123    /* Handle rounding error with dv - top part */
4124    t0 = ((int64_t)d1 << 26) + d0;
4125    t1 = (int64_t)r * dv;
4126    t1 = t0 - t1;
4127    t = (sp_digit)(t1 >> 12) / dv;
4128    r += t;
4129
4130    /* Handle rounding error with dv - bottom 32 bits */
4131    t1 = (sp_digit)t0 - (r * dv);
4132    t = (sp_digit)t1 / dv;
4133    r += t;
4134
4135    return r;
4136}
4137#endif /* WOLFSSL_SP_DIV_32 */
4138
4139/* Divide d in a and put remainder into r (m*d + r = a)
4140 * m is not calculated as it is not needed at this time.
4141 *
4142 * a  Number to be divided.
4143 * d  Number to divide with.
4144 * m  Multiplier result.
4145 * r  Remainder from the division.
4146 * returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
4147 */
4148static int sp_256_div_10(const sp_digit* a, const sp_digit* d, sp_digit* m,
4149        sp_digit* r)
4150{
4151    int i;
4152#ifndef WOLFSSL_SP_DIV_32
4153    int64_t d1;
4154#endif
4155    sp_digit dv, r1;
4156#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4157    sp_digit* td;
4158#else
4159    sp_digit t1d[20], t2d[10 + 1];
4160#endif
4161    sp_digit* t1;
4162    sp_digit* t2;
4163    int err = MP_OKAY;
4164
4165    (void)m;
4166
4167#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4168    td = (sp_digit*)XMALLOC(sizeof(sp_digit) * (3 * 10 + 1), NULL,
4169                                                       DYNAMIC_TYPE_TMP_BUFFER);
4170    if (td == NULL) {
4171        err = MEMORY_E;
4172    }
4173#endif
4174
4175    if (err == MP_OKAY) {
4176#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4177        t1 = td;
4178        t2 = td + 2 * 10;
4179#else
4180        t1 = t1d;
4181        t2 = t2d;
4182#endif
4183
4184        dv = d[9];
4185        XMEMCPY(t1, a, sizeof(*t1) * 2U * 10U);
4186        for (i=9; i>=0; i--) {
4187            t1[10 + i] += t1[10 + i - 1] >> 26;
4188            t1[10 + i - 1] = Q6_R_and_RR(t1[10 + i - 1], 0x3ffffff);
4189#ifndef WOLFSSL_SP_DIV_32
4190            d1 = t1[10 + i];
4191            d1 <<= 26;
4192            d1 += t1[10 + i - 1];
4193            r1 = (sp_digit)(d1 / dv);
4194#else
4195            r1 = sp_256_div_word_10(t1[10 + i], t1[10 + i - 1], dv);
4196#endif
4197
4198            sp_256_mul_d_10(t2, d, r1);
4199            (void)sp_256_sub_10(&t1[i], &t1[i], t2);
4200            t1[10 + i] -= t2[10];
4201            t1[10 + i] += t1[10 + i - 1] >> 26;
4202            t1[10 + i - 1] = Q6_R_and_RR(t1[10 + i - 1], 0x3ffffff);
4203            r1 = (((-t1[10 + i]) << 26) - t1[10 + i - 1]) / dv;
4204            r1++;
4205            sp_256_mul_d_10(t2, d, r1);
4206            (void)sp_256_add_10(&t1[i], &t1[i], t2);
4207            t1[10 + i] += t1[10 + i - 1] >> 26;
4208            t1[10 + i - 1] = Q6_R_and_RR(t1[10 + i - 1], 0x3ffffff);
4209        }
4210        t1[10 - 1] += t1[10 - 2] >> 26;
4211        t1[10 - 2] &= 0x3ffffff;
4212        d1 = t1[10 - 1];
4213        r1 = (sp_digit)(d1 / dv);
4214
4215        sp_256_mul_d_10(t2, d, r1);
4216        (void)sp_256_sub_10(t1, t1, t2);
4217        XMEMCPY(r, t1, sizeof(*r) * 2U * 10U);
4218        for (i=0; i<8; i++) {
4219            r[i+1] += r[i] >> 26;
4220            r[i] &= 0x3ffffff;
4221        }
4222        sp_256_cond_add_10(r, r, d, 0 - ((r[9] < 0) ?
4223                    (sp_digit)1 : (sp_digit)0));
4224    }
4225
4226#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4227    XFREE(td, NULL, DYNAMIC_TYPE_TMP_BUFFER);
4228#endif
4229
4230    return err;
4231}
4232
4233/* Reduce a modulo m into r. (r = a mod m)
4234 *
4235 * r  A single precision number that is the reduced result.
4236 * a  A single precision number that is to be reduced.
4237 * m  A single precision number that is the modulus to reduce with.
4238 * returns MEMORY_E when unable to allocate memory and MP_OKAY otherwise.
4239 */
4240static int sp_256_mod_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
4241{
4242    return sp_256_div_10(a, m, NULL, r);
4243}
4244
4245#endif
4246#if defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)
4247#ifdef WOLFSSL_SP_SMALL
4248/* Order-2 for the P256 curve. */
4249static const word32 p256_order_2[8] = {
4250    0xfc63254fU,0xf3b9cac2U,0xa7179e84U,0xbce6faadU,0xffffffffU,0xffffffffU,
4251    0x00000000U,0xffffffffU
4252};
4253#else
4254/* The low half of the order-2 of the P256 curve. */
4255static const word32 p256_order_low[4] = {
4256    0xfc63254fU,0xf3b9cac2U,0xa7179e84U,0xbce6faadU
4257};
4258#endif /* WOLFSSL_SP_SMALL */
4259
4260/* Multiply two number mod the order of P256 curve. (r = a * b mod order)
4261 *
4262 * r  Result of the multiplication.
4263 * a  First operand of the multiplication.
4264 * b  Second operand of the multiplication.
4265 */
4266static void sp_256_mont_mul_order_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
4267{
4268    sp_256_mul_10(r, a, b);
4269    sp_256_mont_reduce_order_10(r, p256_order, p256_mp_order);
4270}
4271
4272/* Square number mod the order of P256 curve. (r = a * a mod order)
4273 *
4274 * r  Result of the squaring.
4275 * a  Number to square.
4276 */
4277static void sp_256_mont_sqr_order_10(sp_digit* r, const sp_digit* a)
4278{
4279    sp_256_sqr_10(r, a);
4280    sp_256_mont_reduce_order_10(r, p256_order, p256_mp_order);
4281}
4282
4283#ifndef WOLFSSL_SP_SMALL
4284/* Square number mod the order of P256 curve a number of times.
4285 * (r = a ^ n mod order)
4286 *
4287 * r  Result of the squaring.
4288 * a  Number to square.
4289 */
4290static void sp_256_mont_sqr_n_order_10(sp_digit* r, const sp_digit* a, int n)
4291{
4292    int i;
4293
4294    sp_256_mont_sqr_order_10(r, a);
4295    for (i=1; i<n; i++) {
4296        sp_256_mont_sqr_order_10(r, r);
4297    }
4298}
4299#endif /* !WOLFSSL_SP_SMALL */
4300
4301/* Invert the number, in Montgomery form, modulo the order of the P256 curve.
4302 * (r = 1 / a mod order)
4303 *
4304 * r   Inverse result.
4305 * a   Number to invert.
4306 * td  Temporary data.
4307 */
4308static void sp_256_mont_inv_order_10(sp_digit* r, const sp_digit* a,
4309        sp_digit* td)
4310{
4311#ifdef WOLFSSL_SP_SMALL
4312    sp_digit* t = td;
4313    int i;
4314
4315    XMEMCPY(t, a, sizeof(sp_digit) * 10);
4316    for (i=254; i>=0; i--) {
4317        sp_256_mont_sqr_order_10(t, t);
4318        if ((p256_order_2[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
4319            sp_256_mont_mul_order_10(t, t, a);
4320        }
4321    }
4322    XMEMCPY(r, t, sizeof(sp_digit) * 10U);
4323#else
4324    sp_digit* t = td;
4325    sp_digit* t2 = td + 2 * 10;
4326    sp_digit* t3 = td + 4 * 10;
4327    int i;
4328
4329
4330    /* t = a^2 */
4331    sp_256_mont_sqr_order_10(t, a);
4332    /* t = a^3 = t * a */
4333    sp_256_mont_mul_order_10(t, t, a);
4334    /* t2= a^c = t ^ 2 ^ 2 */
4335    sp_256_mont_sqr_n_order_10(t2, t, 2);
4336    /* t3= a^f = t2 * t */
4337    sp_256_mont_mul_order_10(t3, t2, t);
4338    /* t2= a^f0 = t3 ^ 2 ^ 4 */
4339    sp_256_mont_sqr_n_order_10(t2, t3, 4);
4340    /* t = a^ff = t2 * t3 */
4341    sp_256_mont_mul_order_10(t, t2, t3);
4342    /* t3= a^ff00 = t ^ 2 ^ 8 */
4343    sp_256_mont_sqr_n_order_10(t2, t, 8);
4344    /* t = a^ffff = t2 * t */
4345    sp_256_mont_mul_order_10(t, t2, t);
4346    /* t2= a^ffff0000 = t ^ 2 ^ 16 */
4347    sp_256_mont_sqr_n_order_10(t2, t, 16);
4348    /* t = a^ffffffff = t2 * t */
4349    sp_256_mont_mul_order_10(t, t2, t);
4350    /* t2= a^ffffffff0000000000000000 = t ^ 2 ^ 64  */
4351    sp_256_mont_sqr_n_order_10(t2, t, 64);
4352    /* t2= a^ffffffff00000000ffffffff = t2 * t */
4353    sp_256_mont_mul_order_10(t2, t2, t);
4354    /* t2= a^ffffffff00000000ffffffff00000000 = t2 ^ 2 ^ 32  */
4355    sp_256_mont_sqr_n_order_10(t2, t2, 32);
4356    /* t2= a^ffffffff00000000ffffffffffffffff = t2 * t */
4357    sp_256_mont_mul_order_10(t2, t2, t);
4358    /* t2= a^ffffffff00000000ffffffffffffffffbce6 */
4359
4360    for (i=127; i>=112; i--) {
4361        sp_256_mont_sqr_order_10(t2, t2);
4362        if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
4363            sp_256_mont_mul_order_10(t2, t2, a);
4364        }
4365    }
4366    /* t2= a^ffffffff00000000ffffffffffffffffbce6f */
4367    sp_256_mont_sqr_n_order_10(t2, t2, 4);
4368    sp_256_mont_mul_order_10(t2, t2, t3);
4369    /* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84 */
4370    for (i=107; i>=64; i--) {
4371        sp_256_mont_sqr_order_10(t2, t2);
4372        if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
4373            sp_256_mont_mul_order_10(t2, t2, a);
4374        }
4375    }
4376    /* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f */
4377    sp_256_mont_sqr_n_order_10(t2, t2, 4);
4378    sp_256_mont_mul_order_10(t2, t2, t3);
4379    /* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2 */
4380    for (i=59; i>=32; i--) {
4381        sp_256_mont_sqr_order_10(t2, t2);
4382        if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
4383            sp_256_mont_mul_order_10(t2, t2, a);
4384        }
4385    }
4386    /* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2f */
4387    sp_256_mont_sqr_n_order_10(t2, t2, 4);
4388    sp_256_mont_mul_order_10(t2, t2, t3);
4389    /* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254 */
4390    for (i=27; i>=0; i--) {
4391        sp_256_mont_sqr_order_10(t2, t2);
4392        if (((sp_digit)p256_order_low[i / 32] & ((sp_int_digit)1 << (i % 32))) != 0) {
4393            sp_256_mont_mul_order_10(t2, t2, a);
4394        }
4395    }
4396    /* t2= a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632540 */
4397    sp_256_mont_sqr_n_order_10(t2, t2, 4);
4398    /* r = a^ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc63254f */
4399    sp_256_mont_mul_order_10(r, t2, t3);
4400#endif /* WOLFSSL_SP_SMALL */
4401}
4402
4403#endif /* HAVE_ECC_SIGN || HAVE_ECC_VERIFY */
4404
4405#ifdef HAVE_ECC_VERIFY
4406
4407
4408/* Verify the signature values with the hash and public key.
4409 *   e = Truncate(hash, 256)
4410 *   u1 = e/s mod order
4411 *   u2 = r/s mod order
4412 *   r == (u1.G + u2.Q)->x mod order
4413 * Optimization: Leave point in projective form.
4414 *   (x, y, 1) == (x' / z'*z', y' / z'*z'*z', z' / z')
4415 *   (r + n*order).z'.z' mod prime == (u1.G + u2.Q)->x'
4416 * The hash is truncated to the first 256 bits.
4417 *
4418 * hash     Hash to sign.
4419 * hashLen  Length of the hash data.
4420 * rng      Random number generator.
4421 * priv     Private part of key - scalar.
4422 * rm       First part of result as an mp_int.
4423 * sm       Sirst part of result as an mp_int.
4424 * heap     Heap to use for allocation.
4425 * returns RNG failures, MEMORY_E when memory allocation fails and
4426 * MP_OKAY on success.
4427 */
4428int wolfSSL_DSP_ECC_Verify_256(remote_handle64 h, int32 *u1, int hashLen, int32* r, int rSz, int32* s, int sSz,
4429	int32* x, int xSz, int32* y, int ySz, int32* z, int zSz, int* res)
4430{
4431#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4432    sp_digit* d = NULL;
4433#else
4434    sp_digit u2d[2*10] __attribute__((aligned(128)));
4435    sp_digit tmpd[2*10 * 5] __attribute__((aligned(128)));
4436    sp_point p1d;
4437    sp_point p2d;
4438#endif
4439    sp_digit* u2 = NULL;
4440    sp_digit* tmp = NULL;
4441    sp_point* p1;
4442    sp_point* p2 = NULL;
4443    sp_digit carry;
4444    int32_t c;
4445    int err;
4446    void* heap = NULL;
4447
4448    (void)h;
4449    (void)hashLen;
4450
4451    err = sp_ecc_point_new(heap, p1d, p1);
4452    if (err == MP_OKAY) {
4453        err = sp_ecc_point_new(heap, p2d, p2);
4454    }
4455
4456    if (err == MP_OKAY) {
4457        u2 = u2d;
4458        tmp = tmpd;
4459
4460        XMEMCPY(u2, r, 40);
4461        XMEMCPY(p2->x, x, 40);
4462        XMEMCPY(p2->y, y, 40);
4463        XMEMCPY(p2->z, z, 40);
4464
4465            sp_256_mul_10(s, s, p256_norm_order);
4466        err = sp_256_mod_10(s, s, p256_order);
4467    }
4468    if (err == MP_OKAY) {
4469        sp_256_norm_10(s);
4470        {
4471
4472            sp_256_mont_inv_order_10(s, s, tmp);
4473            sp_256_mont_mul_order_10(u1, u1, s);
4474            sp_256_mont_mul_order_10(u2, u2, s);
4475        }
4476
4477            err = sp_256_ecc_mulmod_base_10(p1, u1, 0, heap);
4478    }
4479    if (err == MP_OKAY) {
4480            err = sp_256_ecc_mulmod_10(p2, p2, u2, 0, heap);
4481    }
4482
4483    if (err == MP_OKAY) {
4484            sp_256_proj_point_add_10(p1, p1, p2, tmp);
4485
4486        /* (r + n*order).z'.z' mod prime == (u1.G + u2.Q)->x' */
4487        /* Reload r and convert to Montgomery form. */
4488        XMEMCPY(u2, r, 40);
4489        err = sp_256_mod_mul_norm_10(u2, u2, p256_mod);
4490    }
4491
4492    if (err == MP_OKAY) {
4493        /* u1 = r.z'.z' mod prime */
4494        sp_256_mont_sqr_10(p1->z, p1->z, p256_mod, p256_mp_mod);
4495        sp_256_mont_mul_10(u1, u2, p1->z, p256_mod, p256_mp_mod);
4496        *res = (int)(sp_256_cmp_10(p1->x, u1) == 0);
4497        if (*res == 0) {
4498            /* Reload r and add order. */
4499            XMEMCPY(u2, r, 40);
4500            carry = sp_256_add_10(u2, u2, p256_order);
4501            /* Carry means result is greater than mod and is not valid. */
4502            if (carry == 0) {
4503                sp_256_norm_10(u2);
4504
4505                /* Compare with mod and if greater or equal then not valid. */
4506                c = sp_256_cmp_10(u2, p256_mod);
4507                if (c < 0) {
4508                    /* Convert to Montogomery form */
4509                    err = sp_256_mod_mul_norm_10(u2, u2, p256_mod);
4510                    if (err == MP_OKAY) {
4511                        /* u1 = (r + 1*order).z'.z' mod prime */
4512                        sp_256_mont_mul_10(u1, u2, p1->z, p256_mod,
4513                                                                  p256_mp_mod);
4514                        *res = (int)(sp_256_cmp_10(p1->x, u2) == 0);
4515                    }
4516                }
4517            }
4518        }
4519    }
4520
4521#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4522    XFREE(d, heap, DYNAMIC_TYPE_ECC);
4523#endif
4524    sp_ecc_point_free(p1, 0, heap);
4525    sp_ecc_point_free(p2, 0, heap);
4526
4527    return err;
4528}
4529
4530/** Free the Fixed Point cache */
4531void wc_ecc_fp_free(void)
4532{
4533}
4534
4535
4536AEEResult wolfSSL_open(const char *uri, remote_handle64 *handle)
4537{
4538  /* can be any value or ignored, rpc layer doesn't care
4539   * also ok
4540   * *handle = 0;
4541   * *handle = 0xdeadc0de;
4542   */
4543   *handle = (remote_handle64)XMALLOC(1, NULL, DYNAMIC_TYPE_ECC);
4544   return 0;
4545}
4546
4547AEEResult wolfSSL_close(remote_handle64 handle)
4548{
4549   if (handle)
4550      XFREE((void*)handle, NULL, DYNAMIC_TYPE_ECC);
4551   return 0;
4552}
4553#endif /* HAVE_ECC_VERIFY */
4554
4555#ifdef WOLFSSL_PUBLIC_ECC_ADD_DBL
4556/* Add two projective EC points together.
4557 * (pX, pY, pZ) + (qX, qY, qZ) = (rX, rY, rZ)
4558 *
4559 * pX   First EC point's X ordinate.
4560 * pY   First EC point's Y ordinate.
4561 * pZ   First EC point's Z ordinate.
4562 * qX   Second EC point's X ordinate.
4563 * qY   Second EC point's Y ordinate.
4564 * qZ   Second EC point's Z ordinate.
4565 * rX   Resultant EC point's X ordinate.
4566 * rY   Resultant EC point's Y ordinate.
4567 * rZ   Resultant EC point's Z ordinate.
4568 * returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
4569 */
4570int sp_ecc_proj_add_point_256(mp_int* pX, mp_int* pY, mp_int* pZ,
4571                              mp_int* qX, mp_int* qY, mp_int* qZ,
4572                              mp_int* rX, mp_int* rY, mp_int* rZ)
4573{
4574#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
4575    sp_digit tmpd[2 * 10 * 5];
4576    sp_point pd;
4577    sp_point qd;
4578#endif
4579    sp_digit* tmp;
4580    sp_point* p;
4581    sp_point* q = NULL;
4582    int err;
4583
4584    err = sp_ecc_point_new(NULL, pd, p);
4585    if (err == MP_OKAY) {
4586        err = sp_ecc_point_new(NULL, qd, q);
4587    }
4588#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4589    if (err == MP_OKAY) {
4590        tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 5, NULL,
4591                                                              DYNAMIC_TYPE_ECC);
4592        if (tmp == NULL) {
4593            err = MEMORY_E;
4594        }
4595    }
4596#else
4597    tmp = tmpd;
4598#endif
4599
4600    if (err == MP_OKAY) {
4601        sp_256_from_mp(p->x, 10, pX);
4602        sp_256_from_mp(p->y, 10, pY);
4603        sp_256_from_mp(p->z, 10, pZ);
4604        sp_256_from_mp(q->x, 10, qX);
4605        sp_256_from_mp(q->y, 10, qY);
4606        sp_256_from_mp(q->z, 10, qZ);
4607
4608            sp_256_proj_point_add_10(p, p, q, tmp);
4609    }
4610
4611    if (err == MP_OKAY) {
4612        err = sp_256_to_mp(p->x, rX);
4613    }
4614    if (err == MP_OKAY) {
4615        err = sp_256_to_mp(p->y, rY);
4616    }
4617    if (err == MP_OKAY) {
4618        err = sp_256_to_mp(p->z, rZ);
4619    }
4620
4621#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4622    XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
4623#endif
4624    sp_ecc_point_free(q, 0, NULL);
4625    sp_ecc_point_free(p, 0, NULL);
4626
4627    return err;
4628}
4629
4630
4631/* Double a projective EC point.
4632 * (pX, pY, pZ) + (pX, pY, pZ) = (rX, rY, rZ)
4633 *
4634 * pX   EC point's X ordinate.
4635 * pY   EC point's Y ordinate.
4636 * pZ   EC point's Z ordinate.
4637 * rX   Resultant EC point's X ordinate.
4638 * rY   Resultant EC point's Y ordinate.
4639 * rZ   Resultant EC point's Z ordinate.
4640 * returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
4641 */
4642int sp_ecc_proj_dbl_point_256(mp_int* pX, mp_int* pY, mp_int* pZ,
4643                              mp_int* rX, mp_int* rY, mp_int* rZ)
4644{
4645#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
4646    sp_digit tmpd[2 * 10 * 2];
4647    sp_point pd;
4648#endif
4649    sp_digit* tmp;
4650    sp_point* p;
4651    int err;
4652
4653    err = sp_ecc_point_new(NULL, pd, p);
4654#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4655    if (err == MP_OKAY) {
4656        tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 2, NULL,
4657                                                              DYNAMIC_TYPE_ECC);
4658        if (tmp == NULL) {
4659            err = MEMORY_E;
4660        }
4661    }
4662#else
4663    tmp = tmpd;
4664#endif
4665
4666    if (err == MP_OKAY) {
4667        sp_256_from_mp(p->x, 10, pX);
4668        sp_256_from_mp(p->y, 10, pY);
4669        sp_256_from_mp(p->z, 10, pZ);
4670
4671            sp_256_proj_point_dbl_10(p, p, tmp);
4672    }
4673
4674    if (err == MP_OKAY) {
4675        err = sp_256_to_mp(p->x, rX);
4676    }
4677    if (err == MP_OKAY) {
4678        err = sp_256_to_mp(p->y, rY);
4679    }
4680    if (err == MP_OKAY) {
4681        err = sp_256_to_mp(p->z, rZ);
4682    }
4683
4684#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4685    XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
4686#endif
4687    sp_ecc_point_free(p, 0, NULL);
4688
4689    return err;
4690}
4691
4692/* Map a projective EC point to affine in place.
4693 * pZ will be one.
4694 *
4695 * pX   EC point's X ordinate.
4696 * pY   EC point's Y ordinate.
4697 * pZ   EC point's Z ordinate.
4698 * returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
4699 */
4700int sp_ecc_map_256(mp_int* pX, mp_int* pY, mp_int* pZ)
4701{
4702#if !defined(WOLFSSL_SP_SMALL) && !defined(WOLFSSL_SMALL_STACK)
4703    sp_digit tmpd[2 * 10 * 4];
4704    sp_point pd;
4705#endif
4706    sp_digit* tmp;
4707    sp_point* p;
4708    int err;
4709
4710    err = sp_ecc_point_new(NULL, pd, p);
4711#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4712    if (err == MP_OKAY) {
4713        tmp = (sp_digit*)XMALLOC(sizeof(sp_digit) * 2 * 10 * 4, NULL,
4714                                                              DYNAMIC_TYPE_ECC);
4715        if (tmp == NULL) {
4716            err = MEMORY_E;
4717        }
4718    }
4719#else
4720    tmp = tmpd;
4721#endif
4722    if (err == MP_OKAY) {
4723        sp_256_from_mp(p->x, 10, pX);
4724        sp_256_from_mp(p->y, 10, pY);
4725        sp_256_from_mp(p->z, 10, pZ);
4726
4727        sp_256_map_10(p, p, tmp);
4728    }
4729
4730    if (err == MP_OKAY) {
4731        err = sp_256_to_mp(p->x, pX);
4732    }
4733    if (err == MP_OKAY) {
4734        err = sp_256_to_mp(p->y, pY);
4735    }
4736    if (err == MP_OKAY) {
4737        err = sp_256_to_mp(p->z, pZ);
4738    }
4739
4740#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4741    XFREE(tmp, NULL, DYNAMIC_TYPE_ECC);
4742#endif
4743    sp_ecc_point_free(p, 0, NULL);
4744
4745    return err;
4746}
4747#endif /* WOLFSSL_PUBLIC_ECC_ADD_DBL */
4748#ifdef HAVE_COMP_KEY
4749/* Find the square root of a number mod the prime of the curve.
4750 *
4751 * y  The number to operate on and the result.
4752 * returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
4753 */
4754static int sp_256_mont_sqrt_10(sp_digit* y)
4755{
4756#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4757    sp_digit* d;
4758#else
4759    sp_digit t1d[2 * 10];
4760    sp_digit t2d[2 * 10];
4761#endif
4762    sp_digit* t1;
4763    sp_digit* t2;
4764    int err = MP_OKAY;
4765
4766#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4767    d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 4 * 10, NULL, DYNAMIC_TYPE_ECC);
4768    if (d == NULL) {
4769        err = MEMORY_E;
4770    }
4771#endif
4772
4773    if (err == MP_OKAY) {
4774#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4775        t1 = d + 0 * 10;
4776        t2 = d + 2 * 10;
4777#else
4778        t1 = t1d;
4779        t2 = t2d;
4780#endif
4781
4782        {
4783            /* t2 = y ^ 0x2 */
4784            sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
4785            /* t1 = y ^ 0x3 */
4786            sp_256_mont_mul_10(t1, t2, y, p256_mod, p256_mp_mod);
4787            /* t2 = y ^ 0xc */
4788            sp_256_mont_sqr_n_10(t2, t1, 2, p256_mod, p256_mp_mod);
4789            /* t1 = y ^ 0xf */
4790            sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
4791            /* t2 = y ^ 0xf0 */
4792            sp_256_mont_sqr_n_10(t2, t1, 4, p256_mod, p256_mp_mod);
4793            /* t1 = y ^ 0xff */
4794            sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
4795            /* t2 = y ^ 0xff00 */
4796            sp_256_mont_sqr_n_10(t2, t1, 8, p256_mod, p256_mp_mod);
4797            /* t1 = y ^ 0xffff */
4798            sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
4799            /* t2 = y ^ 0xffff0000 */
4800            sp_256_mont_sqr_n_10(t2, t1, 16, p256_mod, p256_mp_mod);
4801            /* t1 = y ^ 0xffffffff */
4802            sp_256_mont_mul_10(t1, t1, t2, p256_mod, p256_mp_mod);
4803            /* t1 = y ^ 0xffffffff00000000 */
4804            sp_256_mont_sqr_n_10(t1, t1, 32, p256_mod, p256_mp_mod);
4805            /* t1 = y ^ 0xffffffff00000001 */
4806            sp_256_mont_mul_10(t1, t1, y, p256_mod, p256_mp_mod);
4807            /* t1 = y ^ 0xffffffff00000001000000000000000000000000 */
4808            sp_256_mont_sqr_n_10(t1, t1, 96, p256_mod, p256_mp_mod);
4809            /* t1 = y ^ 0xffffffff00000001000000000000000000000001 */
4810            sp_256_mont_mul_10(t1, t1, y, p256_mod, p256_mp_mod);
4811            sp_256_mont_sqr_n_10(y, t1, 94, p256_mod, p256_mp_mod);
4812        }
4813    }
4814
4815#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4816    XFREE(d, NULL, DYNAMIC_TYPE_ECC);
4817#endif
4818
4819    return err;
4820}
4821
4822/* Uncompress the point given the X ordinate.
4823 *
4824 * xm    X ordinate.
4825 * odd   Whether the Y ordinate is odd.
4826 * ym    Calculated Y ordinate.
4827 * returns MEMORY_E if dynamic memory allocation fails and MP_OKAY otherwise.
4828 */
4829int sp_ecc_uncompress_256(mp_int* xm, int odd, mp_int* ym)
4830{
4831#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4832    sp_digit* d;
4833#else
4834    sp_digit xd[2 * 10];
4835    sp_digit yd[2 * 10];
4836#endif
4837    sp_digit* x = NULL;
4838    sp_digit* y = NULL;
4839    int err = MP_OKAY;
4840
4841#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4842    d = (sp_digit*)XMALLOC(sizeof(sp_digit) * 4 * 10, NULL, DYNAMIC_TYPE_ECC);
4843    if (d == NULL) {
4844        err = MEMORY_E;
4845    }
4846#endif
4847
4848    if (err == MP_OKAY) {
4849#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4850        x = d + 0 * 10;
4851        y = d + 2 * 10;
4852#else
4853        x = xd;
4854        y = yd;
4855#endif
4856
4857        sp_256_from_mp(x, 10, xm);
4858        err = sp_256_mod_mul_norm_10(x, x, p256_mod);
4859    }
4860    if (err == MP_OKAY) {
4861        /* y = x^3 */
4862        {
4863            sp_256_mont_sqr_10(y, x, p256_mod, p256_mp_mod);
4864            sp_256_mont_mul_10(y, y, x, p256_mod, p256_mp_mod);
4865        }
4866        /* y = x^3 - 3x */
4867        sp_256_mont_sub_10(y, y, x, p256_mod);
4868        sp_256_mont_sub_10(y, y, x, p256_mod);
4869        sp_256_mont_sub_10(y, y, x, p256_mod);
4870        /* y = x^3 - 3x + b */
4871        err = sp_256_mod_mul_norm_10(x, p256_b, p256_mod);
4872    }
4873    if (err == MP_OKAY) {
4874        sp_256_mont_add_10(y, y, x, p256_mod);
4875        /* y = sqrt(x^3 - 3x + b) */
4876        err = sp_256_mont_sqrt_10(y);
4877    }
4878    if (err == MP_OKAY) {
4879        XMEMSET(y + 10, 0, 10U * sizeof(sp_digit));
4880        sp_256_mont_reduce_10(y, p256_mod, p256_mp_mod);
4881        if ((((word32)y[0] ^ (word32)odd) & 1U) != 0U) {
4882            sp_256_mont_sub_10(y, p256_mod, y, p256_mod);
4883        }
4884
4885        err = sp_256_to_mp(y, ym);
4886    }
4887
4888#if defined(WOLFSSL_SP_SMALL) || defined(WOLFSSL_SMALL_STACK)
4889    XFREE(d, NULL, DYNAMIC_TYPE_ECC);
4890#endif
4891
4892    return err;
4893}
4894#endif
4895#endif /* !WOLFSSL_SP_NO_256 */
4896#endif /* WOLFSSL_HAVE_SP_ECC */
4897#endif /* WOLFSSL_DSP */
4898#endif /* WOLFSSL_HAVE_SP_ECC */
4899