ntt.go 6.5 KB

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  1. // ntt.go - NewHope Number Theoretic Transform.
  2. //
  3. // To the extent possible under law, Yawning Angel has waived all copyright
  4. // and related or neighboring rights to newhope, using the Creative
  5. // Commons "CC0" public domain dedication. See LICENSE or
  6. // <http://creativecommons.org/publicdomain/zero/1.0/> for full details.
  7. package newhope
  8. var bitrevTable = [paramN]uint16{
  9. 0, 512, 256, 768, 128, 640, 384, 896, 64, 576, 320, 832, 192, 704, 448, 960,
  10. 32, 544, 288, 800, 160, 672, 416, 928, 96, 608, 352, 864, 224, 736, 480,
  11. 992, 16, 528, 272, 784, 144, 656, 400, 912, 80, 592, 336, 848, 208, 720,
  12. 464, 976, 48, 560, 304, 816, 176, 688, 432, 944, 112, 624, 368, 880,
  13. 240, 752, 496, 1008, 8, 520, 264, 776, 136, 648, 392, 904, 72, 584, 328,
  14. 840, 200, 712, 456, 968, 40, 552, 296, 808, 168, 680, 424, 936, 104,
  15. 616, 360, 872, 232, 744, 488, 1000, 24, 536, 280, 792, 152, 664, 408,
  16. 920, 88, 600, 344, 856, 216, 728, 472, 984, 56, 568, 312, 824, 184, 696,
  17. 440, 952, 120, 632, 376, 888, 248, 760, 504, 1016, 4, 516, 260, 772,
  18. 132, 644, 388, 900, 68, 580, 324, 836, 196, 708, 452, 964, 36, 548, 292,
  19. 804, 164, 676, 420, 932, 100, 612, 356, 868, 228, 740, 484, 996, 20,
  20. 532, 276, 788, 148, 660, 404, 916, 84, 596, 340, 852, 212, 724, 468,
  21. 980, 52, 564, 308, 820, 180, 692, 436, 948, 116, 628, 372, 884, 244,
  22. 756, 500, 1012, 12, 524, 268, 780, 140, 652, 396, 908, 76, 588, 332,
  23. 844, 204, 716, 460, 972, 44, 556, 300, 812, 172, 684, 428, 940, 108,
  24. 620, 364, 876, 236, 748, 492, 1004, 28, 540, 284, 796, 156, 668, 412,
  25. 924, 92, 604, 348, 860, 220, 732, 476, 988, 60, 572, 316, 828, 188, 700,
  26. 444, 956, 124, 636, 380, 892, 252, 764, 508, 1020, 2, 514, 258, 770,
  27. 130, 642, 386, 898, 66, 578, 322, 834, 194, 706, 450, 962, 34, 546, 290,
  28. 802, 162, 674, 418, 930, 98, 610, 354, 866, 226, 738, 482, 994, 18, 530,
  29. 274, 786, 146, 658, 402, 914, 82, 594, 338, 850, 210, 722, 466, 978, 50,
  30. 562, 306, 818, 178, 690, 434, 946, 114, 626, 370, 882, 242, 754, 498,
  31. 1010, 10, 522, 266, 778, 138, 650, 394, 906, 74, 586, 330, 842, 202,
  32. 714, 458, 970, 42, 554, 298, 810, 170, 682, 426, 938, 106, 618, 362,
  33. 874, 234, 746, 490, 1002, 26, 538, 282, 794, 154, 666, 410, 922, 90,
  34. 602, 346, 858, 218, 730, 474, 986, 58, 570, 314, 826, 186, 698, 442,
  35. 954, 122, 634, 378, 890, 250, 762, 506, 1018, 6, 518, 262, 774, 134,
  36. 646, 390, 902, 70, 582, 326, 838, 198, 710, 454, 966, 38, 550, 294, 806,
  37. 166, 678, 422, 934, 102, 614, 358, 870, 230, 742, 486, 998, 22, 534,
  38. 278, 790, 150, 662, 406, 918, 86, 598, 342, 854, 214, 726, 470, 982, 54,
  39. 566, 310, 822, 182, 694, 438, 950, 118, 630, 374, 886, 246, 758, 502,
  40. 1014, 14, 526, 270, 782, 142, 654, 398, 910, 78, 590, 334, 846, 206,
  41. 718, 462, 974, 46, 558, 302, 814, 174, 686, 430, 942, 110, 622, 366,
  42. 878, 238, 750, 494, 1006, 30, 542, 286, 798, 158, 670, 414, 926, 94,
  43. 606, 350, 862, 222, 734, 478, 990, 62, 574, 318, 830, 190, 702, 446,
  44. 958, 126, 638, 382, 894, 254, 766, 510, 1022, 1, 513, 257, 769, 129,
  45. 641, 385, 897, 65, 577, 321, 833, 193, 705, 449, 961, 33, 545, 289, 801,
  46. 161, 673, 417, 929, 97, 609, 353, 865, 225, 737, 481, 993, 17, 529, 273,
  47. 785, 145, 657, 401, 913, 81, 593, 337, 849, 209, 721, 465, 977, 49, 561,
  48. 305, 817, 177, 689, 433, 945, 113, 625, 369, 881, 241, 753, 497, 1009,
  49. 9, 521, 265, 777, 137, 649, 393, 905, 73, 585, 329, 841, 201, 713, 457,
  50. 969, 41, 553, 297, 809, 169, 681, 425, 937, 105, 617, 361, 873, 233,
  51. 745, 489, 1001, 25, 537, 281, 793, 153, 665, 409, 921, 89, 601, 345,
  52. 857, 217, 729, 473, 985, 57, 569, 313, 825, 185, 697, 441, 953, 121,
  53. 633, 377, 889, 249, 761, 505, 1017, 5, 517, 261, 773, 133, 645, 389,
  54. 901, 69, 581, 325, 837, 197, 709, 453, 965, 37, 549, 293, 805, 165, 677,
  55. 421, 933, 101, 613, 357, 869, 229, 741, 485, 997, 21, 533, 277, 789,
  56. 149, 661, 405, 917, 85, 597, 341, 853, 213, 725, 469, 981, 53, 565, 309,
  57. 821, 181, 693, 437, 949, 117, 629, 373, 885, 245, 757, 501, 1013, 13,
  58. 525, 269, 781, 141, 653, 397, 909, 77, 589, 333, 845, 205, 717, 461,
  59. 973, 45, 557, 301, 813, 173, 685, 429, 941, 109, 621, 365, 877, 237,
  60. 749, 493, 1005, 29, 541, 285, 797, 157, 669, 413, 925, 93, 605, 349,
  61. 861, 221, 733, 477, 989, 61, 573, 317, 829, 189, 701, 445, 957, 125,
  62. 637, 381, 893, 253, 765, 509, 1021, 3, 515, 259, 771, 131, 643, 387,
  63. 899, 67, 579, 323, 835, 195, 707, 451, 963, 35, 547, 291, 803, 163, 675,
  64. 419, 931, 99, 611, 355, 867, 227, 739, 483, 995, 19, 531, 275, 787, 147,
  65. 659, 403, 915, 83, 595, 339, 851, 211, 723, 467, 979, 51, 563, 307, 819,
  66. 179, 691, 435, 947, 115, 627, 371, 883, 243, 755, 499, 1011, 11, 523,
  67. 267, 779, 139, 651, 395, 907, 75, 587, 331, 843, 203, 715, 459, 971, 43,
  68. 555, 299, 811, 171, 683, 427, 939, 107, 619, 363, 875, 235, 747, 491,
  69. 1003, 27, 539, 283, 795, 155, 667, 411, 923, 91, 603, 347, 859, 219,
  70. 731, 475, 987, 59, 571, 315, 827, 187, 699, 443, 955, 123, 635, 379,
  71. 891, 251, 763, 507, 1019, 7, 519, 263, 775, 135, 647, 391, 903, 71, 583,
  72. 327, 839, 199, 711, 455, 967, 39, 551, 295, 807, 167, 679, 423, 935,
  73. 103, 615, 359, 871, 231, 743, 487, 999, 23, 535, 279, 791, 151, 663,
  74. 407, 919, 87, 599, 343, 855, 215, 727, 471, 983, 55, 567, 311, 823, 183,
  75. 695, 439, 951, 119, 631, 375, 887, 247, 759, 503, 1015, 15, 527, 271,
  76. 783, 143, 655, 399, 911, 79, 591, 335, 847, 207, 719, 463, 975, 47, 559,
  77. 303, 815, 175, 687, 431, 943, 111, 623, 367, 879, 239, 751, 495, 1007,
  78. 31, 543, 287, 799, 159, 671, 415, 927, 95, 607, 351, 863, 223, 735, 479,
  79. 991, 63, 575, 319, 831, 191, 703, 447, 959, 127, 639, 383, 895, 255,
  80. 767, 511, 1023,
  81. }
  82. func (p *poly) bitrev() {
  83. for i, v := range p.coeffs {
  84. r := bitrevTable[i]
  85. if uint16(i) < r {
  86. p.coeffs[i] = p.coeffs[r]
  87. p.coeffs[r] = v
  88. }
  89. }
  90. }
  91. func (p *poly) mulCoefficients(factors *[paramN]uint16) {
  92. for i, v := range factors {
  93. p.coeffs[i] = montgomeryReduce(uint32(p.coeffs[i]) * uint32(v))
  94. }
  95. }
  96. func ntt(a *[paramN]uint16, omega *[paramN / 2]uint16) {
  97. var distance uint
  98. for i := uint(0); i < 10; i += 2 {
  99. // Even level.
  100. distance = (1 << i)
  101. for start := uint(0); start < distance; start++ {
  102. jTwiddle := 0
  103. for j := start; j < paramN-1; j += 2 * distance {
  104. w := uint32(omega[jTwiddle])
  105. jTwiddle++
  106. tmp := a[j]
  107. a[j] = tmp + a[j+distance]
  108. a[j+distance] = montgomeryReduce(w * (uint32(tmp) + 3*paramQ - uint32(a[j+distance])))
  109. }
  110. }
  111. // Odd level.
  112. distance <<= 1
  113. for start := uint(0); start < distance; start++ {
  114. jTwiddle := 0
  115. for j := start; j < paramN-1; j += 2 * distance {
  116. w := uint32(omega[jTwiddle])
  117. jTwiddle++
  118. tmp := a[j]
  119. a[j] = barrettReduce(tmp + a[j+distance])
  120. a[j+distance] = montgomeryReduce(w * (uint32(tmp) + 3*paramQ - uint32(a[j+distance])))
  121. }
  122. }
  123. }
  124. }