/* This file is for the Gao-Mateer FFT sse http://www.math.clemson.edu/~sgao/papers/GM10.pdf */ #include "fft.h" #include "transpose.h" #include /* input: in, polynomial in bitsliced form */ /* output: in, result of applying the radix conversions on in */ static void radix_conversions(vec in[][GFBITS]) { int i, j, k; const vec mask[5][2] = { {0x8888888888888888, 0x4444444444444444}, {0xC0C0C0C0C0C0C0C0, 0x3030303030303030}, {0xF000F000F000F000, 0x0F000F000F000F00}, {0xFF000000FF000000, 0x00FF000000FF0000}, {0xFFFF000000000000, 0x0000FFFF00000000} }; const vec s[5][2][GFBITS] = { #include "scalars_2x.inc" }; for (j = 0; j <= 5; j++) { for (i = 0; i < GFBITS; i++) { in[1][i] ^= in[1][i] >> 32; in[0][i] ^= in[1][i] << 32; } for (i = 0; i < GFBITS; i++) { for (k = 4; k >= j; k--) { in[0][i] ^= (in[0][i] & mask[k][0]) >> (1 << k); in[0][i] ^= (in[0][i] & mask[k][1]) >> (1 << k); in[1][i] ^= (in[1][i] & mask[k][0]) >> (1 << k); in[1][i] ^= (in[1][i] & mask[k][1]) >> (1 << k); } } if (j < 5) { PQCLEAN_MCELIECE460896F_VEC_vec_mul(in[0], in[0], s[j][0]); PQCLEAN_MCELIECE460896F_VEC_vec_mul(in[1], in[1], s[j][1]); } } } /* input: in, result of applying the radix conversions to the input polynomial */ /* output: out, evaluation results (by applying the FFT butterflies) */ static void butterflies(vec out[][ GFBITS ], vec in[][ GFBITS ]) { int i, j, k, s, b; vec tmp[ GFBITS ]; vec pre[8][ GFBITS ]; vec buf[128]; uint64_t consts_ptr = 2; const vec consts[ 128 ][ GFBITS ] = { #include "consts.inc" }; const unsigned char reversal[128] = { 0, 64, 32, 96, 16, 80, 48, 112, 8, 72, 40, 104, 24, 88, 56, 120, 4, 68, 36, 100, 20, 84, 52, 116, 12, 76, 44, 108, 28, 92, 60, 124, 2, 66, 34, 98, 18, 82, 50, 114, 10, 74, 42, 106, 26, 90, 58, 122, 6, 70, 38, 102, 22, 86, 54, 118, 14, 78, 46, 110, 30, 94, 62, 126, 1, 65, 33, 97, 17, 81, 49, 113, 9, 73, 41, 105, 25, 89, 57, 121, 5, 69, 37, 101, 21, 85, 53, 117, 13, 77, 45, 109, 29, 93, 61, 125, 3, 67, 35, 99, 19, 83, 51, 115, 11, 75, 43, 107, 27, 91, 59, 123, 7, 71, 39, 103, 23, 87, 55, 119, 15, 79, 47, 111, 31, 95, 63, 127 }; const uint16_t beta[7] = {2522, 7827, 7801, 8035, 6897, 8167, 3476}; // for (i = 0; i < 7; i++) { for (j = 0; j < GFBITS; j++) { pre[i][j] = (beta[i] >> j) & 1; pre[i][j] = -pre[i][j]; } PQCLEAN_MCELIECE460896F_VEC_vec_mul(pre[i], in[1], pre[i]); } for (i = 0; i < GFBITS; i++) { buf[0] = in[0][i]; buf[1] = buf[0] ^ pre[0][i]; buf[32] = in[0][i] ^ pre[5][i]; buf[3] = buf[1] ^ pre[1][i]; buf[96] = buf[32] ^ pre[6][i]; buf[97] = buf[96] ^ pre[0][i]; buf[2] = in[0][i] ^ pre[1][i]; buf[99] = buf[97] ^ pre[1][i]; buf[6] = buf[2] ^ pre[2][i]; buf[98] = buf[99] ^ pre[0][i]; buf[7] = buf[6] ^ pre[0][i]; buf[102] = buf[98] ^ pre[2][i]; buf[5] = buf[7] ^ pre[1][i]; buf[103] = buf[102] ^ pre[0][i]; buf[101] = buf[103] ^ pre[1][i]; buf[4] = in[0][i] ^ pre[2][i]; buf[100] = buf[101] ^ pre[0][i]; buf[12] = buf[4] ^ pre[3][i]; buf[108] = buf[100] ^ pre[3][i]; buf[13] = buf[12] ^ pre[0][i]; buf[109] = buf[108] ^ pre[0][i]; buf[15] = buf[13] ^ pre[1][i]; buf[111] = buf[109] ^ pre[1][i]; buf[14] = buf[15] ^ pre[0][i]; buf[110] = buf[111] ^ pre[0][i]; buf[10] = buf[14] ^ pre[2][i]; buf[106] = buf[110] ^ pre[2][i]; buf[11] = buf[10] ^ pre[0][i]; buf[107] = buf[106] ^ pre[0][i]; buf[9] = buf[11] ^ pre[1][i]; buf[105] = buf[107] ^ pre[1][i]; buf[104] = buf[105] ^ pre[0][i]; buf[8] = in[0][i] ^ pre[3][i]; buf[120] = buf[104] ^ pre[4][i]; buf[24] = buf[8] ^ pre[4][i]; buf[121] = buf[120] ^ pre[0][i]; buf[25] = buf[24] ^ pre[0][i]; buf[123] = buf[121] ^ pre[1][i]; buf[27] = buf[25] ^ pre[1][i]; buf[122] = buf[123] ^ pre[0][i]; buf[26] = buf[27] ^ pre[0][i]; buf[126] = buf[122] ^ pre[2][i]; buf[30] = buf[26] ^ pre[2][i]; buf[127] = buf[126] ^ pre[0][i]; buf[31] = buf[30] ^ pre[0][i]; buf[125] = buf[127] ^ pre[1][i]; buf[29] = buf[31] ^ pre[1][i]; buf[124] = buf[125] ^ pre[0][i]; buf[28] = buf[29] ^ pre[0][i]; buf[116] = buf[124] ^ pre[3][i]; buf[20] = buf[28] ^ pre[3][i]; buf[117] = buf[116] ^ pre[0][i]; buf[21] = buf[20] ^ pre[0][i]; buf[119] = buf[117] ^ pre[1][i]; buf[23] = buf[21] ^ pre[1][i]; buf[118] = buf[119] ^ pre[0][i]; buf[22] = buf[23] ^ pre[0][i]; buf[114] = buf[118] ^ pre[2][i]; buf[18] = buf[22] ^ pre[2][i]; buf[115] = buf[114] ^ pre[0][i]; buf[19] = buf[18] ^ pre[0][i]; buf[113] = buf[115] ^ pre[1][i]; buf[17] = buf[19] ^ pre[1][i]; buf[112] = buf[113] ^ pre[0][i]; buf[80] = buf[112] ^ pre[5][i]; buf[16] = in[0][i] ^ pre[4][i]; buf[81] = buf[80] ^ pre[0][i]; buf[48] = buf[16] ^ pre[5][i]; buf[83] = buf[81] ^ pre[1][i]; buf[49] = buf[48] ^ pre[0][i]; buf[82] = buf[83] ^ pre[0][i]; buf[51] = buf[49] ^ pre[1][i]; buf[86] = buf[82] ^ pre[2][i]; buf[50] = buf[51] ^ pre[0][i]; buf[87] = buf[86] ^ pre[0][i]; buf[54] = buf[50] ^ pre[2][i]; buf[85] = buf[87] ^ pre[1][i]; buf[55] = buf[54] ^ pre[0][i]; buf[84] = buf[85] ^ pre[0][i]; buf[53] = buf[55] ^ pre[1][i]; buf[92] = buf[84] ^ pre[3][i]; buf[52] = buf[53] ^ pre[0][i]; buf[93] = buf[92] ^ pre[0][i]; buf[60] = buf[52] ^ pre[3][i]; buf[95] = buf[93] ^ pre[1][i]; buf[61] = buf[60] ^ pre[0][i]; buf[94] = buf[95] ^ pre[0][i]; buf[63] = buf[61] ^ pre[1][i]; buf[90] = buf[94] ^ pre[2][i]; buf[62] = buf[63] ^ pre[0][i]; buf[91] = buf[90] ^ pre[0][i]; buf[58] = buf[62] ^ pre[2][i]; buf[89] = buf[91] ^ pre[1][i]; buf[59] = buf[58] ^ pre[0][i]; buf[88] = buf[89] ^ pre[0][i]; buf[57] = buf[59] ^ pre[1][i]; buf[72] = buf[88] ^ pre[4][i]; buf[56] = buf[57] ^ pre[0][i]; buf[73] = buf[72] ^ pre[0][i]; buf[40] = buf[56] ^ pre[4][i]; buf[75] = buf[73] ^ pre[1][i]; buf[41] = buf[40] ^ pre[0][i]; buf[74] = buf[75] ^ pre[0][i]; buf[43] = buf[41] ^ pre[1][i]; buf[78] = buf[74] ^ pre[2][i]; buf[42] = buf[43] ^ pre[0][i]; buf[79] = buf[78] ^ pre[0][i]; buf[46] = buf[42] ^ pre[2][i]; buf[77] = buf[79] ^ pre[1][i]; buf[47] = buf[46] ^ pre[0][i]; buf[76] = buf[77] ^ pre[0][i]; buf[45] = buf[47] ^ pre[1][i]; buf[68] = buf[76] ^ pre[3][i]; buf[44] = buf[45] ^ pre[0][i]; buf[69] = buf[68] ^ pre[0][i]; buf[36] = buf[44] ^ pre[3][i]; buf[71] = buf[69] ^ pre[1][i]; buf[37] = buf[36] ^ pre[0][i]; buf[70] = buf[71] ^ pre[0][i]; buf[39] = buf[37] ^ pre[1][i]; buf[66] = buf[70] ^ pre[2][i]; buf[38] = buf[39] ^ pre[0][i]; buf[67] = buf[66] ^ pre[0][i]; buf[34] = buf[38] ^ pre[2][i]; buf[65] = buf[67] ^ pre[1][i]; buf[35] = buf[34] ^ pre[0][i]; buf[33] = buf[35] ^ pre[1][i]; buf[64] = in[0][i] ^ pre[6][i]; PQCLEAN_MCELIECE460896F_VEC_transpose_64x64(buf + 0, buf + 0); PQCLEAN_MCELIECE460896F_VEC_transpose_64x64(buf + 64, buf + 64); for (j = 0; j < 128; j++) { out[ reversal[j] ][i] = buf[j]; } } for (i = 1; i <= 6; i++) { s = 1 << i; for (j = 0; j < 128; j += 2 * s) { for (k = j; k < j + s; k++) { PQCLEAN_MCELIECE460896F_VEC_vec_mul(tmp, out[k + s], consts[ consts_ptr + (k - j) ]); for (b = 0; b < GFBITS; b++) { out[k ][b] ^= tmp[b]; } for (b = 0; b < GFBITS; b++) { out[k + s][b] ^= out[k][b]; } } } consts_ptr += ((uint64_t)1 << i); } // adding the part contributed by x^128 // for (i = 0; i < 128; i++) // for (b = 0; b < GFBITS; b++) // out[i][b] ^= powers[i][b]; } /* input: in, polynomial in bitsliced form */ /* output: out, bitsliced results of evaluating in all the field elements */ void PQCLEAN_MCELIECE460896F_VEC_fft(vec out[][GFBITS], vec in[][GFBITS]) { radix_conversions(in); butterflies(out, in); }