| /* Copyright (c) 2016, Google Inc. |
| * |
| * Permission to use, copy, modify, and/or distribute this software for any |
| * purpose with or without fee is hereby granted, provided that the above |
| * copyright notice and this permission notice appear in all copies. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY |
| * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION |
| * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN |
| * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ |
| |
| #include "internal.h" |
| |
| |
| static uint16_t bitrev_table[1024] = { |
| 0, 512, 256, 768, 128, 640, 384, 896, 64, 576, 320, 832, 192, 704, |
| 448, 960, 32, 544, 288, 800, 160, 672, 416, 928, 96, 608, 352, 864, |
| 224, 736, 480, 992, 16, 528, 272, 784, 144, 656, 400, 912, 80, 592, |
| 336, 848, 208, 720, 464, 976, 48, 560, 304, 816, 176, 688, 432, 944, |
| 112, 624, 368, 880, 240, 752, 496, 1008, 8, 520, 264, 776, 136, 648, |
| 392, 904, 72, 584, 328, 840, 200, 712, 456, 968, 40, 552, 296, 808, |
| 168, 680, 424, 936, 104, 616, 360, 872, 232, 744, 488, 1000, 24, 536, |
| 280, 792, 152, 664, 408, 920, 88, 600, 344, 856, 216, 728, 472, 984, |
| 56, 568, 312, 824, 184, 696, 440, 952, 120, 632, 376, 888, 248, 760, |
| 504, 1016, 4, 516, 260, 772, 132, 644, 388, 900, 68, 580, 324, 836, |
| 196, 708, 452, 964, 36, 548, 292, 804, 164, 676, 420, 932, 100, 612, |
| 356, 868, 228, 740, 484, 996, 20, 532, 276, 788, 148, 660, 404, 916, |
| 84, 596, 340, 852, 212, 724, 468, 980, 52, 564, 308, 820, 180, 692, |
| 436, 948, 116, 628, 372, 884, 244, 756, 500, 1012, 12, 524, 268, 780, |
| 140, 652, 396, 908, 76, 588, 332, 844, 204, 716, 460, 972, 44, 556, |
| 300, 812, 172, 684, 428, 940, 108, 620, 364, 876, 236, 748, 492, 1004, |
| 28, 540, 284, 796, 156, 668, 412, 924, 92, 604, 348, 860, 220, 732, |
| 476, 988, 60, 572, 316, 828, 188, 700, 444, 956, 124, 636, 380, 892, |
| 252, 764, 508, 1020, 2, 514, 258, 770, 130, 642, 386, 898, 66, 578, |
| 322, 834, 194, 706, 450, 962, 34, 546, 290, 802, 162, 674, 418, 930, |
| 98, 610, 354, 866, 226, 738, 482, 994, 18, 530, 274, 786, 146, 658, |
| 402, 914, 82, 594, 338, 850, 210, 722, 466, 978, 50, 562, 306, 818, |
| 178, 690, 434, 946, 114, 626, 370, 882, 242, 754, 498, 1010, 10, 522, |
| 266, 778, 138, 650, 394, 906, 74, 586, 330, 842, 202, 714, 458, 970, |
| 42, 554, 298, 810, 170, 682, 426, 938, 106, 618, 362, 874, 234, 746, |
| 490, 1002, 26, 538, 282, 794, 154, 666, 410, 922, 90, 602, 346, 858, |
| 218, 730, 474, 986, 58, 570, 314, 826, 186, 698, 442, 954, 122, 634, |
| 378, 890, 250, 762, 506, 1018, 6, 518, 262, 774, 134, 646, 390, 902, |
| 70, 582, 326, 838, 198, 710, 454, 966, 38, 550, 294, 806, 166, 678, |
| 422, 934, 102, 614, 358, 870, 230, 742, 486, 998, 22, 534, 278, 790, |
| 150, 662, 406, 918, 86, 598, 342, 854, 214, 726, 470, 982, 54, 566, |
| 310, 822, 182, 694, 438, 950, 118, 630, 374, 886, 246, 758, 502, 1014, |
| 14, 526, 270, 782, 142, 654, 398, 910, 78, 590, 334, 846, 206, 718, |
| 462, 974, 46, 558, 302, 814, 174, 686, 430, 942, 110, 622, 366, 878, |
| 238, 750, 494, 1006, 30, 542, 286, 798, 158, 670, 414, 926, 94, 606, |
| 350, 862, 222, 734, 478, 990, 62, 574, 318, 830, 190, 702, 446, 958, |
| 126, 638, 382, 894, 254, 766, 510, 1022, 1, 513, 257, 769, 129, 641, |
| 385, 897, 65, 577, 321, 833, 193, 705, 449, 961, 33, 545, 289, 801, |
| 161, 673, 417, 929, 97, 609, 353, 865, 225, 737, 481, 993, 17, 529, |
| 273, 785, 145, 657, 401, 913, 81, 593, 337, 849, 209, 721, 465, 977, |
| 49, 561, 305, 817, 177, 689, 433, 945, 113, 625, 369, 881, 241, 753, |
| 497, 1009, 9, 521, 265, 777, 137, 649, 393, 905, 73, 585, 329, 841, |
| 201, 713, 457, 969, 41, 553, 297, 809, 169, 681, 425, 937, 105, 617, |
| 361, 873, 233, 745, 489, 1001, 25, 537, 281, 793, 153, 665, 409, 921, |
| 89, 601, 345, 857, 217, 729, 473, 985, 57, 569, 313, 825, 185, 697, |
| 441, 953, 121, 633, 377, 889, 249, 761, 505, 1017, 5, 517, 261, 773, |
| 133, 645, 389, 901, 69, 581, 325, 837, 197, 709, 453, 965, 37, 549, |
| 293, 805, 165, 677, 421, 933, 101, 613, 357, 869, 229, 741, 485, 997, |
| 21, 533, 277, 789, 149, 661, 405, 917, 85, 597, 341, 853, 213, 725, |
| 469, 981, 53, 565, 309, 821, 181, 693, 437, 949, 117, 629, 373, 885, |
| 245, 757, 501, 1013, 13, 525, 269, 781, 141, 653, 397, 909, 77, 589, |
| 333, 845, 205, 717, 461, 973, 45, 557, 301, 813, 173, 685, 429, 941, |
| 109, 621, 365, 877, 237, 749, 493, 1005, 29, 541, 285, 797, 157, 669, |
| 413, 925, 93, 605, 349, 861, 221, 733, 477, 989, 61, 573, 317, 829, |
| 189, 701, 445, 957, 125, 637, 381, 893, 253, 765, 509, 1021, 3, 515, |
| 259, 771, 131, 643, 387, 899, 67, 579, 323, 835, 195, 707, 451, 963, |
| 35, 547, 291, 803, 163, 675, 419, 931, 99, 611, 355, 867, 227, 739, |
| 483, 995, 19, 531, 275, 787, 147, 659, 403, 915, 83, 595, 339, 851, |
| 211, 723, 467, 979, 51, 563, 307, 819, 179, 691, 435, 947, 115, 627, |
| 371, 883, 243, 755, 499, 1011, 11, 523, 267, 779, 139, 651, 395, 907, |
| 75, 587, 331, 843, 203, 715, 459, 971, 43, 555, 299, 811, 171, 683, |
| 427, 939, 107, 619, 363, 875, 235, 747, 491, 1003, 27, 539, 283, 795, |
| 155, 667, 411, 923, 91, 603, 347, 859, 219, 731, 475, 987, 59, 571, |
| 315, 827, 187, 699, 443, 955, 123, 635, 379, 891, 251, 763, 507, 1019, |
| 7, 519, 263, 775, 135, 647, 391, 903, 71, 583, 327, 839, 199, 711, |
| 455, 967, 39, 551, 295, 807, 167, 679, 423, 935, 103, 615, 359, 871, |
| 231, 743, 487, 999, 23, 535, 279, 791, 151, 663, 407, 919, 87, 599, |
| 343, 855, 215, 727, 471, 983, 55, 567, 311, 823, 183, 695, 439, 951, |
| 119, 631, 375, 887, 247, 759, 503, 1015, 15, 527, 271, 783, 143, 655, |
| 399, 911, 79, 591, 335, 847, 207, 719, 463, 975, 47, 559, 303, 815, |
| 175, 687, 431, 943, 111, 623, 367, 879, 239, 751, 495, 1007, 31, 543, |
| 287, 799, 159, 671, 415, 927, 95, 607, 351, 863, 223, 735, 479, 991, |
| 63, 575, 319, 831, 191, 703, 447, 959, 127, 639, 383, 895, 255, 767, |
| 511, 1023}; |
| |
| void newhope_bitrev_vector(uint16_t* poly) { |
| unsigned int i, r; |
| uint16_t tmp; |
| |
| for (i = 0; i < PARAM_N; i++) { |
| r = bitrev_table[i]; |
| if (i < r) { |
| tmp = poly[i]; |
| poly[i] = poly[r]; |
| poly[r] = tmp; |
| } |
| } |
| } |
| |
| void newhope_mul_coefficients(uint16_t* poly, const uint16_t* factors) { |
| unsigned int i; |
| |
| for (i = 0; i < PARAM_N; i++) { |
| poly[i] = newhope_montgomery_reduce((poly[i] * factors[i])); |
| } |
| } |
| |
| /* GS_bo_to_no; omegas need to be in Montgomery domain */ |
| void newhope_ntt(uint16_t* a, const uint16_t* omega) { |
| int i, start, j, jTwiddle, distance; |
| uint16_t temp, W; |
| |
| for (i = 0; i < 10; i += 2) { |
| /* Even level */ |
| distance = (1 << i); |
| for (start = 0; start < distance; start++) { |
| jTwiddle = 0; |
| for (j = start; j < PARAM_N - 1; j += 2 * distance) { |
| W = omega[jTwiddle++]; |
| temp = a[j]; |
| a[j] = (temp + a[j + distance]); /* Omit reduction (be lazy) */ |
| a[j + distance] = newhope_montgomery_reduce( |
| (W * ((uint32_t)temp + 3 * PARAM_Q - a[j + distance]))); |
| } |
| } |
| |
| /* Odd level */ |
| distance <<= 1; |
| for (start = 0; start < distance; start++) { |
| jTwiddle = 0; |
| for (j = start; j < PARAM_N - 1; j += 2 * distance) { |
| W = omega[jTwiddle++]; |
| temp = a[j]; |
| a[j] = newhope_barrett_reduce((temp + a[j + distance])); |
| a[j + distance] = newhope_montgomery_reduce( |
| (W * ((uint32_t)temp + 3 * PARAM_Q - a[j + distance]))); |
| } |
| } |
| } |
| } |
