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8ad60658e4
Personal note: imo a factor for 256 would have been useful Signed-off-by: Tanguy Pruvot <tanguy.pruvot@gmail.com>
1155 lines
50 KiB
C
1155 lines
50 KiB
C
///////////////////////////////////////////////////////////////////////////////////////////////
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//
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// SWIFFTX ANSI C OPTIMIZED 32BIT IMPLEMENTATION FOR NIST SHA-3 COMPETITION
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//
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// SWIFFTX.c
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//
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// October 2008
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//
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// This is the source file of the OPTIMIZED 32BIT implementation of SWIFFTX hash function.
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// SWIFFTX is a candidate function for SHA-3 NIST competition.
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// More details about SWIFFTX can be found in the accompanying submission documents.
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//
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///////////////////////////////////////////////////////////////////////////////////////////////
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#include "SWIFFTX.h"
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// See the remarks concerning compatibility issues inside stdint.h.
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#include "stdint.h"
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// Remove this while using gcc:
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//#include "stdbool.h"
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#include <memory.h>
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///////////////////////////////////////////////////////////////////////////////////////////////
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// Constants and static tables portion.
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///////////////////////////////////////////////////////////////////////////////////////////////
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// In SWIFFTX we work over Z_257, so this is the modulus and the arithmetic is performed modulo
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// this number.
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#define FIELD_SIZE 257
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// The size of FFT we use:
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#define N 64
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#define LOGN 6
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#define EIGHTH_N (N / 8)
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// The number of FFTS done on the input.
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#define M (SWIFFTX_INPUT_BLOCK_SIZE / 8) // 32
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// Omega is the 128th root of unity in Z_257.
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// We choose w = 42.
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#define OMEGA 42
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// The size of the inner FFT lookup table:
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#define W 8
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// Calculates the sum and the difference of two numbers.
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//
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// Parameters:
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// - A: the first operand. After the operation stores the sum of the two operands.
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// - B: the second operand. After the operation stores the difference between the first and the
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// second operands.
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#define ADD_SUB(A, B) {register int temp = (B); B = ((A) - (B)); A = ((A) + (temp));}
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// Quickly reduces an integer modulo 257.
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//
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// Parameters:
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// - A: the input.
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#define Q_REDUCE(A) (((A) & 0xff) - ((A) >> 8))
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// Since we need to do the setup only once, this is the indicator variable:
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static bool wasSetupDone = false;
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// This array stores the powers of omegas that correspond to the indices, which are the input
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// values. Known also as the "outer FFT twiddle factors".
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swift_int16_t multipliers[N];
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// This array stores the powers of omegas, multiplied by the corresponding values.
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// We store this table to save computation time.
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//
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// To calculate the intermediate value of the compression function (the first out of two
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// stages), we multiply the k-th bit of x_i by w^[(2i + 1) * k]. {x_i} is the input to the
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// compression function, i is between 0 and 31, x_i is a 64-bit value.
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// One can see the formula for this (intermediate) stage in the SWIFFT FSE 2008 paper --
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// formula (2), section 3, page 6.
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swift_int16_t fftTable[256 * EIGHTH_N];
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// The A's we use in SWIFFTX shall be random elements of Z_257.
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// We generated these A's from the decimal expansion of PI as follows: we converted each
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// triple of digits into a decimal number d. If d < (257 * 3) we used (d % 257) for the next A
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// element, otherwise move to the next triple of digits in the expansion. This guarntees that
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// the A's are random, provided that PI digits are.
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const swift_int16_t As[3 * M * N] =
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{141, 78, 139, 75, 238, 205, 129, 126, 22, 245, 197, 169, 142, 118, 105, 78,
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50, 149, 29, 208, 114, 34, 85, 117, 67, 148, 86, 256, 25, 49, 133, 93,
|
|
95, 36, 68, 231, 211, 102, 151, 128, 224, 117, 193, 27, 102, 187, 7, 105,
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|
45, 130, 108, 124, 171, 151, 189, 128, 218, 134, 233, 165, 14, 201, 145, 134,
|
|
52, 203, 91, 96, 197, 69, 134, 213, 136, 93, 3, 249, 141, 16, 210, 73,
|
|
6, 92, 58, 74, 174, 6, 254, 91, 201, 107, 110, 76, 103, 11, 73, 16,
|
|
34, 209, 7, 127, 146, 254, 95, 176, 57, 13, 108, 245, 77, 92, 186, 117,
|
|
124, 97, 105, 118, 34, 74, 205, 122, 235, 53, 94, 238, 210, 227, 183, 11,
|
|
129, 159, 105, 183, 142, 129, 86, 21, 137, 138, 224, 223, 190, 188, 179, 188,
|
|
256, 25, 217, 176, 36, 176, 238, 127, 160, 210, 155, 148, 132, 0, 54, 127,
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|
145, 6, 46, 85, 243, 95, 173, 123, 178, 207, 211, 183, 224, 173, 146, 35,
|
|
71, 114, 50, 22, 175, 1, 28, 19, 112, 129, 21, 34, 161, 159, 115, 52,
|
|
4, 193, 211, 92, 115, 49, 59, 217, 218, 96, 61, 81, 24, 202, 198, 89,
|
|
45, 128, 8, 51, 253, 87, 171, 35, 4, 188, 171, 10, 3, 137, 238, 73,
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|
19, 208, 124, 163, 103, 177, 155, 147, 46, 84, 253, 233, 171, 241, 211, 217,
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|
159, 48, 96, 79, 237, 18, 171, 226, 99, 1, 97, 195, 216, 163, 198, 95,
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|
0, 201, 65, 228, 21, 153, 124, 230, 44, 35, 44, 108, 85, 156, 249, 207,
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|
26, 222, 131, 1, 60, 242, 197, 150, 181, 19, 116, 213, 75, 98, 124, 240,
|
|
123, 207, 62, 255, 60, 143, 187, 157, 139, 9, 12, 104, 89, 49, 193, 146,
|
|
104, 196, 181, 82, 198, 253, 192, 191, 255, 122, 212, 104, 47, 20, 132, 208,
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|
46, 170, 2, 69, 234, 36, 56, 163, 28, 152, 104, 238, 162, 56, 24, 58,
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|
38, 150, 193, 254, 253, 125, 173, 35, 73, 126, 247, 239, 216, 6, 199, 15,
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|
90, 12, 97, 122, 9, 84, 207, 127, 219, 72, 58, 30, 29, 182, 41, 192,
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|
235, 248, 237, 74, 72, 176, 210, 252, 45, 64, 165, 87, 202, 241, 236, 223,
|
|
151, 242, 119, 239, 52, 112, 169, 28, 13, 37, 160, 60, 158, 81, 133, 60,
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|
16, 145, 249, 192, 173, 217, 214, 93, 141, 184, 54, 34, 161, 104, 157, 95,
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38, 133, 218, 227, 211, 181, 9, 66, 137, 143, 77, 33, 248, 159, 4, 55,
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|
228, 48, 99, 219, 222, 184, 15, 36, 254, 256, 157, 237, 87, 139, 209, 113,
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|
232, 85, 126, 167, 197, 100, 103, 166, 64, 225, 125, 205, 117, 135, 84, 128,
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231, 112, 90, 241, 28, 22, 210, 147, 186, 49, 230, 21, 108, 39, 194, 47,
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123, 199, 107, 114, 30, 210, 250, 143, 59, 156, 131, 133, 221, 27, 76, 99,
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208, 250, 78, 12, 211, 141, 95, 81, 195, 106, 8, 232, 150, 212, 205, 221,
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11, 225, 87, 219, 126, 136, 137, 180, 198, 48, 68, 203, 239, 252, 194, 235,
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142, 137, 174, 172, 190, 145, 250, 221, 182, 204, 1, 195, 130, 153, 83, 241,
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161, 239, 211, 138, 11, 169, 155, 245, 174, 49, 10, 166, 16, 130, 181, 139,
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222, 222, 112, 99, 124, 94, 51, 243, 133, 194, 244, 136, 35, 248, 201, 177,
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178, 186, 129, 102, 89, 184, 180, 41, 149, 96, 165, 72, 225, 231, 134, 158,
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199, 28, 249, 16, 225, 195, 10, 210, 164, 252, 138, 8, 35, 152, 213, 199,
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82, 116, 97, 230, 63, 199, 241, 35, 79, 120, 54, 174, 67, 112, 1, 76,
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69, 222, 194, 96, 82, 94, 25, 228, 196, 145, 155, 136, 228, 234, 46, 101,
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246, 51, 103, 166, 246, 75, 9, 200, 161, 4, 108, 35, 129, 168, 208, 144,
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50, 14, 13, 220, 41, 132, 122, 127, 194, 9, 232, 234, 107, 28, 187, 8,
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|
51, 141, 97, 221, 225, 9, 113, 170, 166, 102, 135, 22, 231, 185, 227, 187,
|
|
110, 145, 251, 146, 76, 22, 146, 228, 7, 53, 64, 25, 62, 198, 130, 190,
|
|
221, 232, 169, 64, 188, 199, 237, 249, 173, 218, 196, 191, 48, 224, 5, 113,
|
|
100, 166, 160, 21, 191, 197, 61, 162, 149, 171, 240, 183, 129, 231, 123, 204,
|
|
192, 179, 134, 15, 47, 161, 142, 177, 239, 234, 186, 237, 231, 53, 208, 95,
|
|
146, 36, 225, 231, 89, 142, 93, 248, 137, 124, 83, 39, 69, 77, 89, 208,
|
|
182, 48, 85, 147, 244, 164, 246, 68, 38, 190, 220, 35, 202, 91, 157, 151,
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|
201, 240, 185, 218, 4, 152, 2, 132, 177, 88, 190, 196, 229, 74, 220, 135,
|
|
137, 196, 11, 47, 5, 251, 106, 144, 163, 60, 222, 127, 52, 57, 202, 102,
|
|
64, 140, 110, 206, 23, 182, 39, 245, 1, 163, 157, 186, 163, 80, 7, 230,
|
|
44, 249, 176, 102, 164, 125, 147, 120, 18, 191, 186, 125, 64, 65, 198, 157,
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164, 213, 95, 61, 13, 181, 208, 91, 242, 197, 158, 34, 98, 169, 91, 14,
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17, 93, 157, 17, 65, 30, 183, 6, 139, 58, 255, 108, 100, 136, 209, 144,
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164, 6, 237, 33, 210, 110, 57, 126, 197, 136, 125, 244, 165, 151, 168, 3,
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143, 251, 247, 155, 136, 130, 88, 14, 74, 121, 250, 133, 21, 226, 185, 232,
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118, 132, 89, 64, 204, 161, 2, 70, 224, 159, 35, 204, 123, 180, 13, 52,
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231, 57, 25, 78, 66, 69, 97, 42, 198, 84, 176, 59, 8, 232, 125, 134,
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193, 2, 232, 109, 216, 69, 90, 142, 32, 38, 249, 37, 75, 180, 184, 188,
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|
19, 47, 120, 87, 146, 70, 232, 120, 191, 45, 33, 38, 19, 248, 110, 110,
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|
44, 64, 2, 84, 244, 228, 252, 228, 170, 123, 38, 144, 213, 144, 171, 212,
|
|
243, 87, 189, 46, 128, 110, 84, 77, 65, 183, 61, 184, 101, 44, 168, 68,
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|
14, 106, 105, 8, 227, 211, 166, 39, 152, 43, 52, 254, 197, 55, 119, 89,
|
|
168, 65, 53, 138, 177, 56, 219, 0, 58, 121, 148, 18, 44, 100, 215, 103,
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|
145, 229, 117, 196, 91, 89, 113, 143, 172, 239, 249, 184, 154, 39, 112, 65,
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|
204, 42, 84, 38, 155, 151, 151, 16, 100, 87, 174, 162, 145, 147, 149, 186,
|
|
237, 145, 134, 144, 198, 235, 213, 163, 48, 230, 24, 47, 57, 71, 127, 0,
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|
150, 219, 12, 81, 197, 150, 131, 13, 169, 63, 175, 184, 48, 235, 65, 243,
|
|
149, 200, 163, 254, 202, 114, 247, 67, 143, 250, 126, 228, 80, 130, 216, 214,
|
|
36, 2, 230, 33, 119, 125, 3, 142, 237, 100, 3, 152, 197, 174, 244, 129,
|
|
232, 30, 206, 199, 39, 210, 220, 43, 237, 221, 201, 54, 179, 42, 28, 133,
|
|
246, 203, 198, 177, 0, 28, 194, 85, 223, 109, 155, 147, 221, 60, 133, 108,
|
|
157, 254, 26, 75, 157, 185, 49, 142, 31, 137, 71, 43, 63, 64, 237, 148,
|
|
237, 172, 159, 160, 155, 254, 234, 224, 140, 193, 114, 140, 62, 109, 136, 39,
|
|
255, 8, 158, 146, 128, 49, 222, 96, 57, 209, 180, 249, 202, 127, 113, 231,
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|
78, 178, 46, 33, 228, 215, 104, 31, 207, 186, 82, 41, 42, 39, 103, 119,
|
|
123, 133, 243, 254, 238, 156, 90, 186, 37, 212, 33, 107, 252, 51, 177, 36,
|
|
237, 76, 159, 245, 93, 214, 97, 56, 190, 38, 160, 94, 105, 222, 220, 158,
|
|
49, 16, 191, 52, 120, 87, 179, 2, 27, 144, 223, 230, 184, 6, 129, 227,
|
|
69, 47, 215, 181, 162, 139, 72, 200, 45, 163, 159, 62, 2, 221, 124, 40,
|
|
159, 242, 35, 208, 179, 166, 98, 67, 178, 68, 143, 225, 178, 146, 187, 159,
|
|
57, 66, 176, 192, 236, 250, 168, 224, 122, 43, 159, 120, 133, 165, 122, 64,
|
|
87, 74, 161, 241, 9, 87, 90, 24, 255, 113, 203, 220, 57, 139, 197, 159,
|
|
31, 151, 27, 140, 77, 162, 7, 27, 84, 228, 187, 220, 53, 126, 162, 242,
|
|
84, 181, 223, 103, 86, 177, 207, 31, 140, 18, 207, 256, 201, 166, 96, 23,
|
|
233, 103, 197, 84, 161, 75, 59, 149, 138, 154, 119, 92, 16, 53, 116, 97,
|
|
220, 114, 35, 45, 77, 209, 40, 196, 71, 22, 81, 178, 110, 14, 3, 180,
|
|
110, 129, 112, 47, 18, 61, 134, 78, 73, 79, 254, 232, 125, 180, 205, 54,
|
|
220, 119, 63, 89, 181, 52, 77, 109, 151, 77, 80, 207, 144, 25, 20, 6,
|
|
208, 47, 201, 206, 192, 14, 73, 176, 256, 201, 207, 87, 216, 60, 56, 73,
|
|
92, 243, 179, 113, 49, 59, 55, 168, 121, 137, 69, 154, 95, 57, 187, 47,
|
|
129, 4, 15, 92, 6, 116, 69, 196, 48, 134, 84, 81, 111, 56, 38, 176,
|
|
239, 6, 128, 72, 242, 134, 36, 221, 59, 48, 242, 68, 130, 110, 171, 89,
|
|
13, 220, 48, 29, 5, 75, 104, 233, 91, 129, 105, 162, 44, 113, 163, 163,
|
|
85, 147, 190, 111, 197, 80, 213, 153, 81, 68, 203, 33, 161, 165, 10, 61,
|
|
120, 252, 0, 205, 28, 42, 193, 64, 39, 37, 83, 175, 5, 218, 215, 174,
|
|
128, 121, 231, 11, 150, 145, 135, 197, 136, 91, 193, 5, 107, 88, 82, 6,
|
|
4, 188, 256, 70, 40, 2, 167, 57, 169, 203, 115, 254, 215, 172, 84, 80,
|
|
188, 167, 34, 137, 43, 243, 2, 79, 178, 38, 188, 135, 233, 194, 208, 13,
|
|
11, 151, 231, 196, 12, 122, 162, 56, 17, 114, 191, 207, 90, 132, 64, 238,
|
|
187, 6, 198, 176, 240, 88, 118, 236, 15, 226, 166, 22, 193, 229, 82, 246,
|
|
213, 64, 37, 63, 31, 243, 252, 37, 156, 38, 175, 204, 138, 141, 211, 82,
|
|
106, 217, 97, 139, 153, 56, 129, 218, 158, 9, 83, 26, 87, 112, 71, 21,
|
|
250, 5, 65, 141, 68, 116, 231, 113, 10, 218, 99, 205, 201, 92, 157, 4,
|
|
97, 46, 49, 220, 72, 139, 103, 171, 149, 129, 193, 19, 69, 245, 43, 31,
|
|
58, 68, 36, 195, 159, 22, 54, 34, 233, 141, 205, 100, 226, 96, 22, 192,
|
|
41, 231, 24, 79, 234, 138, 30, 120, 117, 216, 172, 197, 172, 107, 86, 29,
|
|
181, 151, 0, 6, 146, 186, 68, 55, 54, 58, 213, 182, 60, 231, 33, 232,
|
|
77, 210, 216, 154, 80, 51, 141, 122, 68, 148, 219, 122, 254, 48, 64, 175,
|
|
41, 115, 62, 243, 141, 81, 119, 121, 5, 68, 121, 88, 239, 29, 230, 90,
|
|
135, 159, 35, 223, 168, 112, 49, 37, 146, 60, 126, 134, 42, 145, 115, 90,
|
|
73, 133, 211, 86, 120, 141, 122, 241, 127, 56, 130, 36, 174, 75, 83, 246,
|
|
112, 45, 136, 194, 201, 115, 1, 156, 114, 167, 208, 12, 176, 147, 32, 170,
|
|
251, 100, 102, 220, 122, 210, 6, 49, 75, 201, 38, 105, 132, 135, 126, 102,
|
|
13, 121, 76, 228, 202, 20, 61, 213, 246, 13, 207, 42, 148, 168, 37, 253,
|
|
34, 94, 141, 185, 18, 234, 157, 109, 104, 64, 250, 125, 49, 236, 86, 48,
|
|
196, 77, 75, 237, 156, 103, 225, 19, 110, 229, 22, 68, 177, 93, 221, 181,
|
|
152, 153, 61, 108, 101, 74, 247, 195, 127, 216, 30, 166, 168, 61, 83, 229,
|
|
120, 156, 96, 120, 201, 124, 43, 27, 253, 250, 120, 143, 89, 235, 189, 243,
|
|
150, 7, 127, 119, 149, 244, 84, 185, 134, 34, 128, 193, 236, 234, 132, 117,
|
|
137, 32, 145, 184, 44, 121, 51, 76, 11, 228, 142, 251, 39, 77, 228, 251,
|
|
41, 58, 246, 107, 125, 187, 9, 240, 35, 8, 11, 162, 242, 220, 158, 163,
|
|
2, 184, 163, 227, 242, 2, 100, 101, 2, 78, 129, 34, 89, 28, 26, 157,
|
|
79, 31, 107, 250, 194, 156, 186, 69, 212, 66, 41, 180, 139, 42, 211, 253,
|
|
256, 239, 29, 129, 104, 248, 182, 68, 1, 189, 48, 226, 36, 229, 3, 158,
|
|
41, 53, 241, 22, 115, 174, 16, 163, 224, 19, 112, 219, 177, 233, 42, 27,
|
|
250, 134, 18, 28, 145, 122, 68, 34, 134, 31, 147, 17, 39, 188, 150, 76,
|
|
45, 42, 167, 249, 12, 16, 23, 182, 13, 79, 121, 3, 70, 197, 239, 44,
|
|
86, 177, 255, 81, 64, 171, 138, 131, 73, 110, 44, 201, 254, 198, 146, 91,
|
|
48, 9, 104, 31, 29, 161, 101, 31, 138, 180, 231, 233, 79, 137, 61, 236,
|
|
140, 15, 249, 218, 234, 119, 99, 195, 110, 137, 237, 207, 8, 31, 45, 24,
|
|
90, 155, 203, 253, 192, 203, 65, 176, 210, 171, 142, 214, 220, 122, 136, 237,
|
|
189, 186, 147, 40, 80, 254, 173, 33, 191, 46, 192, 26, 108, 255, 228, 205,
|
|
61, 76, 39, 107, 225, 126, 228, 182, 140, 251, 143, 134, 252, 168, 221, 8,
|
|
185, 85, 60, 233, 147, 244, 87, 137, 8, 140, 96, 80, 53, 45, 175, 160,
|
|
124, 189, 112, 37, 144, 19, 70, 17, 170, 242, 2, 3, 28, 95, 120, 199,
|
|
212, 43, 9, 117, 86, 151, 101, 241, 200, 145, 241, 19, 178, 69, 204, 197,
|
|
227, 166, 94, 7, 193, 45, 247, 234, 19, 187, 212, 212, 236, 125, 33, 95,
|
|
198, 121, 122, 103, 77, 155, 235, 49, 25, 237, 249, 11, 162, 7, 238, 24,
|
|
16, 150, 129, 25, 152, 17, 42, 67, 247, 162, 77, 154, 31, 133, 55, 137,
|
|
79, 119, 153, 10, 86, 28, 244, 186, 41, 169, 106, 44, 10, 49, 110, 179,
|
|
32, 133, 155, 244, 61, 70, 131, 168, 170, 39, 231, 252, 32, 69, 92, 238,
|
|
239, 35, 132, 136, 236, 167, 90, 32, 123, 88, 69, 22, 20, 89, 145, 166,
|
|
30, 118, 75, 4, 49, 31, 225, 54, 11, 50, 56, 191, 246, 1, 187, 33,
|
|
119, 107, 139, 68, 19, 240, 131, 55, 94, 113, 31, 252, 12, 179, 121, 2,
|
|
120, 252, 0, 76, 41, 80, 185, 42, 62, 121, 105, 159, 121, 109, 111, 98,
|
|
7, 118, 86, 29, 210, 70, 231, 179, 223, 229, 164, 70, 62, 47, 0, 206,
|
|
204, 178, 168, 120, 224, 166, 99, 25, 103, 63, 246, 224, 117, 204, 75, 124,
|
|
140, 133, 110, 110, 222, 88, 151, 118, 46, 37, 22, 143, 158, 40, 2, 50,
|
|
153, 94, 190, 199, 13, 198, 127, 211, 180, 90, 183, 98, 0, 142, 210, 154,
|
|
100, 187, 67, 231, 202, 100, 198, 235, 252, 160, 247, 124, 247, 14, 121, 221,
|
|
57, 88, 253, 243, 185, 89, 45, 249, 221, 194, 108, 175, 193, 119, 50, 141,
|
|
223, 133, 136, 64, 176, 250, 129, 100, 124, 94, 181, 159, 99, 185, 177, 240,
|
|
135, 42, 103, 52, 202, 208, 143, 186, 193, 103, 154, 237, 102, 88, 225, 161,
|
|
50, 188, 191, 109, 12, 87, 19, 227, 247, 183, 13, 52, 205, 170, 205, 146,
|
|
89, 160, 18, 105, 192, 73, 231, 225, 184, 157, 252, 220, 61, 59, 169, 183,
|
|
221, 20, 141, 20, 158, 101, 245, 7, 245, 225, 118, 137, 84, 55, 19, 27,
|
|
164, 110, 35, 25, 202, 94, 150, 46, 91, 152, 130, 1, 7, 46, 16, 237,
|
|
171, 109, 19, 200, 65, 38, 10, 213, 70, 96, 126, 226, 185, 225, 181, 46,
|
|
10, 165, 11, 123, 53, 158, 22, 147, 64, 22, 227, 69, 182, 237, 197, 37,
|
|
39, 49, 186, 223, 139, 128, 55, 36, 166, 178, 220, 20, 98, 172, 166, 253,
|
|
45, 0, 120, 180, 189, 185, 158, 159, 196, 6, 214, 79, 141, 52, 156, 107,
|
|
5, 109, 142, 159, 33, 64, 190, 133, 95, 132, 95, 202, 160, 63, 186, 23,
|
|
231, 107, 163, 33, 234, 15, 244, 77, 108, 49, 51, 7, 164, 87, 142, 99,
|
|
240, 202, 47, 256, 118, 190, 196, 178, 217, 42, 39, 153, 21, 192, 232, 202,
|
|
14, 82, 179, 64, 233, 4, 219, 10, 133, 78, 43, 144, 146, 216, 202, 81,
|
|
71, 252, 8, 201, 68, 256, 85, 233, 164, 88, 176, 30, 5, 152, 126, 179,
|
|
249, 84, 140, 190, 159, 54, 118, 98, 2, 159, 27, 133, 74, 121, 239, 196,
|
|
71, 149, 119, 135, 102, 20, 87, 112, 44, 75, 221, 3, 151, 158, 5, 98,
|
|
152, 25, 97, 106, 63, 171, 240, 79, 234, 240, 230, 92, 76, 70, 173, 196,
|
|
36, 225, 218, 133, 64, 240, 150, 41, 146, 66, 133, 51, 134, 73, 170, 238,
|
|
140, 90, 45, 89, 46, 147, 96, 169, 174, 174, 244, 151, 90, 40, 32, 74,
|
|
38, 154, 246, 57, 31, 14, 189, 151, 83, 243, 197, 183, 220, 185, 53, 225,
|
|
51, 106, 188, 208, 222, 248, 93, 13, 93, 215, 131, 25, 142, 185, 113, 222,
|
|
131, 215, 149, 50, 159, 85, 32, 5, 205, 192, 2, 227, 42, 214, 197, 42,
|
|
126, 182, 68, 123, 109, 36, 237, 179, 170, 199, 77, 256, 5, 128, 214, 243,
|
|
137, 177, 170, 253, 179, 180, 153, 236, 100, 196, 216, 231, 198, 37, 192, 80,
|
|
121, 221, 246, 1, 16, 246, 29, 78, 64, 148, 124, 38, 96, 125, 28, 20,
|
|
48, 51, 73, 187, 139, 208, 98, 253, 221, 188, 84, 129, 1, 205, 95, 205,
|
|
117, 79, 71, 126, 134, 237, 19, 184, 137, 125, 129, 178, 223, 54, 188, 112,
|
|
30, 7, 225, 228, 205, 184, 233, 87, 117, 22, 58, 10, 8, 42, 2, 114,
|
|
254, 19, 17, 13, 150, 92, 233, 179, 63, 12, 60, 171, 127, 35, 50, 5,
|
|
195, 113, 241, 25, 249, 184, 166, 44, 221, 35, 151, 116, 8, 54, 195, 89,
|
|
218, 186, 132, 5, 41, 89, 226, 177, 11, 41, 87, 172, 5, 23, 20, 59,
|
|
228, 94, 76, 33, 137, 43, 151, 221, 61, 232, 4, 120, 93, 217, 80, 228,
|
|
228, 6, 58, 25, 62, 84, 91, 48, 209, 20, 247, 243, 55, 106, 80, 79,
|
|
235, 34, 20, 180, 146, 2, 236, 13, 236, 206, 243, 222, 204, 83, 148, 213,
|
|
214, 117, 237, 98, 0, 90, 204, 168, 32, 41, 126, 67, 191, 74, 27, 255,
|
|
26, 75, 240, 113, 185, 105, 167, 154, 112, 67, 151, 63, 161, 134, 239, 176,
|
|
42, 87, 249, 130, 45, 242, 17, 100, 107, 120, 212, 218, 237, 76, 231, 162,
|
|
175, 172, 118, 155, 92, 36, 124, 17, 121, 71, 13, 9, 82, 126, 147, 142,
|
|
218, 148, 138, 80, 163, 106, 164, 123, 140, 129, 35, 42, 186, 154, 228, 214,
|
|
75, 73, 8, 253, 42, 153, 232, 164, 95, 24, 110, 90, 231, 197, 90, 196,
|
|
57, 164, 252, 181, 31, 7, 97, 256, 35, 77, 200, 212, 99, 179, 92, 227,
|
|
17, 180, 49, 176, 9, 188, 13, 182, 93, 44, 128, 219, 134, 92, 151, 6,
|
|
23, 126, 200, 109, 66, 30, 140, 180, 146, 134, 67, 200, 7, 9, 223, 168,
|
|
186, 221, 3, 154, 150, 165, 43, 53, 138, 27, 86, 213, 235, 160, 70, 2,
|
|
240, 20, 89, 212, 84, 141, 168, 246, 183, 227, 30, 167, 138, 185, 253, 83,
|
|
52, 143, 236, 94, 59, 65, 89, 218, 194, 157, 164, 156, 111, 95, 202, 168,
|
|
245, 256, 151, 28, 222, 194, 72, 130, 217, 134, 253, 77, 246, 100, 76, 32,
|
|
254, 174, 182, 193, 14, 237, 74, 1, 74, 26, 135, 216, 152, 208, 112, 38,
|
|
181, 62, 25, 71, 61, 234, 254, 97, 191, 23, 92, 256, 190, 205, 6, 16,
|
|
134, 147, 210, 219, 148, 59, 73, 185, 24, 247, 174, 143, 116, 220, 128, 144,
|
|
111, 126, 101, 98, 130, 136, 101, 102, 69, 127, 24, 168, 146, 226, 226, 207,
|
|
176, 122, 149, 254, 134, 196, 22, 151, 197, 21, 50, 205, 116, 154, 65, 116,
|
|
177, 224, 127, 77, 177, 159, 225, 69, 176, 54, 100, 104, 140, 8, 11, 126,
|
|
11, 188, 185, 159, 107, 16, 254, 142, 80, 28, 5, 157, 104, 57, 109, 82,
|
|
102, 80, 173, 242, 238, 207, 57, 105, 237, 160, 59, 189, 189, 199, 26, 11,
|
|
190, 156, 97, 118, 20, 12, 254, 189, 165, 147, 142, 199, 5, 213, 64, 133,
|
|
108, 217, 133, 60, 94, 28, 116, 136, 47, 165, 125, 42, 183, 143, 14, 129,
|
|
223, 70, 212, 205, 181, 180, 3, 201, 182, 46, 57, 104, 239, 60, 99, 181,
|
|
220, 231, 45, 79, 156, 89, 149, 143, 190, 103, 153, 61, 235, 73, 136, 20,
|
|
89, 243, 16, 130, 247, 141, 134, 93, 80, 68, 85, 84, 8, 72, 194, 4,
|
|
242, 110, 19, 133, 199, 70, 172, 92, 132, 254, 67, 74, 36, 94, 13, 90,
|
|
154, 184, 9, 109, 118, 243, 214, 71, 36, 95, 0, 90, 201, 105, 112, 215,
|
|
69, 196, 224, 210, 236, 242, 155, 211, 37, 134, 69, 113, 157, 97, 68, 26,
|
|
230, 149, 219, 180, 20, 76, 172, 145, 154, 40, 129, 8, 93, 56, 162, 124,
|
|
207, 233, 105, 19, 3, 183, 155, 134, 8, 244, 213, 78, 139, 88, 156, 37,
|
|
51, 152, 111, 102, 112, 250, 114, 252, 201, 241, 133, 24, 136, 153, 5, 90,
|
|
210, 197, 216, 24, 131, 17, 147, 246, 13, 86, 3, 253, 179, 237, 101, 114,
|
|
243, 191, 207, 2, 220, 133, 244, 53, 87, 125, 154, 158, 197, 20, 8, 83,
|
|
32, 191, 38, 241, 204, 22, 168, 59, 217, 123, 162, 82, 21, 50, 130, 89,
|
|
239, 253, 195, 56, 253, 74, 147, 125, 234, 199, 250, 28, 65, 193, 22, 237,
|
|
193, 94, 58, 229, 139, 176, 69, 42, 179, 164, 150, 168, 246, 214, 86, 174,
|
|
59, 117, 15, 19, 76, 37, 214, 238, 153, 226, 154, 45, 109, 114, 198, 107,
|
|
45, 70, 238, 196, 142, 252, 244, 71, 123, 136, 134, 188, 99, 132, 25, 42,
|
|
240, 0, 196, 33, 26, 124, 256, 145, 27, 102, 153, 35, 28, 132, 221, 167,
|
|
138, 133, 41, 170, 95, 224, 40, 139, 239, 153, 1, 106, 255, 106, 170, 163,
|
|
127, 44, 155, 232, 194, 119, 232, 117, 239, 143, 108, 41, 3, 9, 180, 256,
|
|
144, 113, 133, 200, 79, 69, 128, 216, 31, 50, 102, 209, 249, 136, 150, 154,
|
|
182, 51, 228, 39, 127, 142, 87, 15, 94, 92, 187, 245, 31, 236, 64, 58,
|
|
114, 11, 17, 166, 189, 152, 218, 34, 123, 39, 58, 37, 153, 91, 63, 121,
|
|
31, 34, 12, 254, 106, 96, 171, 14, 155, 247, 214, 69, 24, 98, 3, 204,
|
|
202, 194, 207, 30, 253, 44, 119, 70, 14, 96, 82, 250, 63, 6, 232, 38,
|
|
89, 144, 102, 191, 82, 254, 20, 222, 96, 162, 110, 6, 159, 58, 200, 226,
|
|
98, 128, 42, 70, 84, 247, 128, 211, 136, 54, 143, 166, 60, 118, 99, 218,
|
|
27, 193, 85, 81, 219, 223, 46, 41, 23, 233, 152, 222, 36, 236, 54, 181,
|
|
56, 50, 4, 207, 129, 92, 78, 88, 197, 251, 131, 105, 31, 172, 38, 131,
|
|
19, 204, 129, 47, 227, 106, 202, 183, 23, 6, 77, 224, 102, 147, 11, 218,
|
|
131, 132, 60, 192, 208, 223, 236, 23, 103, 115, 89, 18, 185, 171, 70, 174,
|
|
139, 0, 100, 160, 221, 11, 228, 60, 12, 122, 114, 12, 157, 235, 148, 57,
|
|
83, 62, 173, 131, 169, 126, 85, 99, 93, 243, 81, 80, 29, 245, 206, 82,
|
|
236, 227, 166, 14, 230, 213, 144, 97, 27, 111, 99, 164, 105, 150, 89, 111,
|
|
252, 118, 140, 232, 120, 183, 137, 213, 232, 157, 224, 33, 134, 118, 186, 80,
|
|
159, 2, 186, 193, 54, 242, 25, 237, 232, 249, 226, 213, 90, 149, 90, 160,
|
|
118, 69, 64, 37, 10, 183, 109, 246, 30, 52, 219, 69, 189, 26, 116, 220,
|
|
50, 244, 243, 243, 139, 137, 232, 98, 38, 45, 256, 143, 171, 101, 73, 238,
|
|
123, 45, 194, 167, 250, 123, 12, 29, 136, 237, 141, 21, 89, 96, 199, 44,
|
|
8, 214, 208, 17, 113, 41, 137, 26, 166, 155, 89, 85, 54, 58, 97, 160,
|
|
50, 239, 58, 71, 21, 157, 139, 12, 37, 198, 182, 131, 149, 134, 16, 204,
|
|
164, 181, 248, 166, 52, 216, 136, 201, 37, 255, 187, 240, 5, 101, 147, 231,
|
|
14, 163, 253, 134, 146, 216, 8, 54, 224, 90, 220, 195, 75, 215, 186, 58,
|
|
71, 204, 124, 105, 239, 53, 16, 85, 69, 163, 195, 223, 33, 38, 69, 88,
|
|
88, 203, 99, 55, 176, 13, 156, 204, 236, 99, 194, 134, 75, 247, 126, 129,
|
|
160, 124, 233, 206, 139, 144, 154, 45, 233, 51, 206, 61, 60, 55, 205, 107,
|
|
84, 108, 96, 188, 203, 31, 89, 20, 115, 144, 137, 90, 237, 78, 231, 185,
|
|
120, 217, 1, 176, 169, 30, 155, 176, 100, 113, 53, 42, 193, 108, 14, 121,
|
|
176, 158, 137, 92, 178, 44, 110, 249, 108, 234, 94, 101, 128, 12, 250, 173,
|
|
72, 202, 232, 66, 139, 152, 189, 18, 32, 197, 9, 238, 246, 55, 119, 183,
|
|
196, 119, 113, 247, 191, 100, 200, 245, 46, 16, 234, 112, 136, 116, 232, 48,
|
|
176, 108, 11, 237, 14, 153, 93, 177, 124, 72, 67, 121, 135, 143, 45, 18,
|
|
97, 251, 184, 172, 136, 55, 213, 8, 103, 12, 221, 212, 13, 160, 116, 91,
|
|
237, 127, 218, 190, 103, 131, 77, 82, 36, 100, 22, 252, 79, 69, 54, 26,
|
|
65, 182, 115, 142, 247, 20, 89, 81, 188, 244, 27, 120, 240, 248, 13, 230,
|
|
67, 133, 32, 201, 129, 87, 9, 245, 66, 88, 166, 34, 46, 184, 119, 218,
|
|
144, 235, 163, 40, 138, 134, 127, 217, 64, 227, 116, 67, 55, 202, 130, 48,
|
|
199, 42, 251, 112, 124, 153, 123, 194, 243, 49, 250, 12, 78, 157, 167, 134,
|
|
210, 73, 156, 102, 21, 88, 216, 123, 45, 11, 208, 18, 47, 187, 20, 43,
|
|
3, 180, 124, 2, 136, 176, 77, 111, 138, 139, 91, 225, 126, 8, 74, 255,
|
|
88, 192, 193, 239, 138, 204, 139, 194, 166, 130, 252, 184, 140, 168, 30, 177,
|
|
121, 98, 131, 124, 69, 171, 75, 49, 184, 34, 76, 122, 202, 115, 184, 253,
|
|
120, 182, 33, 251, 1, 74, 216, 217, 243, 168, 70, 162, 119, 158, 197, 198,
|
|
61, 89, 7, 5, 54, 199, 211, 170, 23, 226, 44, 247, 165, 195, 7, 225,
|
|
91, 23, 50, 15, 51, 208, 106, 94, 12, 31, 43, 112, 146, 139, 246, 182,
|
|
113, 1, 97, 15, 66, 2, 51, 76, 164, 184, 237, 200, 218, 176, 72, 98,
|
|
33, 135, 38, 147, 140, 229, 50, 94, 81, 187, 129, 17, 238, 168, 146, 203,
|
|
181, 99, 164, 3, 104, 98, 255, 189, 114, 142, 86, 102, 229, 102, 80, 129,
|
|
64, 84, 79, 161, 81, 156, 128, 111, 164, 197, 18, 15, 55, 196, 198, 191,
|
|
28, 113, 117, 96, 207, 253, 19, 158, 231, 13, 53, 130, 252, 211, 58, 180,
|
|
212, 142, 7, 219, 38, 81, 62, 109, 167, 113, 33, 56, 97, 185, 157, 130,
|
|
186, 129, 119, 182, 196, 26, 54, 110, 65, 170, 166, 236, 30, 22, 162, 0,
|
|
106, 12, 248, 33, 48, 72, 159, 17, 76, 244, 172, 132, 89, 171, 196, 76,
|
|
254, 166, 76, 218, 226, 3, 52, 220, 238, 181, 179, 144, 225, 23, 3, 166,
|
|
158, 35, 228, 154, 204, 23, 203, 71, 134, 189, 18, 168, 236, 141, 117, 138,
|
|
2, 132, 78, 57, 154, 21, 250, 196, 184, 40, 161, 40, 10, 178, 134, 120,
|
|
132, 123, 101, 82, 205, 121, 55, 140, 231, 56, 231, 71, 206, 246, 198, 150,
|
|
146, 192, 45, 105, 242, 1, 125, 18, 176, 46, 222, 122, 19, 80, 113, 133,
|
|
131, 162, 81, 51, 98, 168, 247, 161, 139, 39, 63, 162, 22, 153, 170, 92,
|
|
91, 130, 174, 200, 45, 112, 99, 164, 132, 184, 191, 186, 200, 167, 86, 145,
|
|
167, 227, 130, 44, 12, 158, 172, 249, 204, 17, 54, 249, 16, 200, 21, 174,
|
|
67, 223, 105, 201, 50, 36, 133, 203, 244, 131, 228, 67, 29, 195, 91, 91,
|
|
55, 107, 167, 154, 170, 137, 218, 183, 169, 61, 99, 175, 128, 23, 142, 183,
|
|
66, 255, 59, 187, 66, 85, 212, 109, 168, 82, 16, 43, 67, 139, 114, 176,
|
|
216, 255, 130, 94, 152, 79, 183, 64, 100, 23, 214, 82, 34, 230, 48, 15,
|
|
242, 130, 50, 241, 81, 32, 5, 125, 183, 182, 184, 99, 248, 109, 159, 210,
|
|
226, 61, 119, 129, 39, 149, 78, 214, 107, 78, 147, 124, 228, 18, 143, 188,
|
|
84, 180, 233, 119, 64, 39, 158, 133, 177, 168, 6, 150, 80, 117, 150, 56,
|
|
49, 72, 49, 37, 30, 242, 49, 142, 33, 156, 34, 44, 44, 72, 58, 22,
|
|
249, 46, 168, 80, 25, 196, 64, 174, 97, 179, 244, 134, 213, 105, 63, 151,
|
|
21, 90, 168, 90, 245, 28, 157, 65, 250, 232, 188, 27, 99, 160, 156, 127,
|
|
68, 193, 10, 80, 205, 36, 138, 229, 12, 223, 70, 169, 251, 41, 48, 94,
|
|
41, 177, 99, 256, 158, 0, 6, 83, 231, 191, 120, 135, 157, 146, 218, 213,
|
|
160, 7, 47, 234, 98, 211, 79, 225, 179, 95, 175, 105, 185, 79, 115, 0,
|
|
104, 14, 65, 124, 15, 188, 52, 9, 253, 27, 132, 137, 13, 127, 75, 238,
|
|
185, 253, 33, 8, 52, 157, 164, 68, 232, 188, 69, 28, 209, 233, 5, 129,
|
|
216, 90, 252, 212, 33, 200, 222, 9, 112, 15, 43, 36, 226, 114, 15, 249,
|
|
217, 8, 148, 22, 147, 23, 143, 67, 222, 116, 235, 250, 212, 210, 39, 142,
|
|
108, 64, 209, 83, 73, 66, 99, 34, 17, 29, 45, 151, 244, 114, 28, 241,
|
|
144, 208, 146, 179, 132, 89, 217, 198, 252, 219, 205, 165, 75, 107, 11, 173,
|
|
76, 6, 196, 247, 152, 216, 248, 91, 209, 178, 57, 250, 174, 60, 79, 123,
|
|
18, 135, 9, 241, 230, 159, 184, 68, 156, 251, 215, 9, 113, 234, 75, 235,
|
|
103, 194, 205, 129, 230, 45, 96, 73, 157, 20, 200, 212, 212, 228, 161, 7,
|
|
231, 228, 108, 43, 198, 87, 140, 140, 4, 182, 164, 3, 53, 104, 250, 213,
|
|
85, 38, 89, 61, 52, 187, 35, 204, 86, 249, 100, 71, 248, 213, 163, 215,
|
|
66, 106, 252, 129, 40, 111, 47, 24, 186, 221, 85, 205, 199, 237, 122, 181,
|
|
32, 46, 182, 135, 33, 251, 142, 34, 208, 242, 128, 255, 4, 234, 15, 33,
|
|
167, 222, 32, 186, 191, 34, 255, 244, 98, 240, 228, 204, 30, 142, 32, 70,
|
|
69, 83, 110, 151, 10, 243, 141, 21, 223, 69, 61, 37, 59, 209, 102, 114,
|
|
223, 33, 129, 254, 255, 103, 86, 247, 235, 72, 126, 177, 102, 226, 102, 30,
|
|
149, 221, 62, 247, 251, 120, 163, 173, 57, 202, 204, 24, 39, 106, 120, 143,
|
|
202, 176, 191, 147, 37, 38, 51, 133, 47, 245, 157, 132, 154, 71, 183, 111,
|
|
30, 180, 18, 202, 82, 96, 170, 91, 157, 181, 212, 140, 256, 8, 196, 121,
|
|
149, 79, 66, 127, 113, 78, 4, 197, 84, 256, 111, 222, 102, 63, 228, 104,
|
|
136, 223, 67, 193, 93, 154, 249, 83, 204, 101, 200, 234, 84, 252, 230, 195,
|
|
43, 140, 120, 242, 89, 63, 166, 233, 209, 94, 43, 170, 126, 5, 205, 78,
|
|
112, 80, 143, 151, 146, 248, 137, 203, 45, 183, 61, 1, 155, 8, 102, 59,
|
|
68, 212, 230, 61, 254, 191, 128, 223, 176, 123, 229, 27, 146, 120, 96, 165,
|
|
213, 12, 232, 40, 186, 225, 66, 105, 200, 195, 212, 110, 237, 238, 151, 19,
|
|
12, 171, 150, 82, 7, 228, 79, 52, 15, 78, 62, 43, 21, 154, 114, 21,
|
|
12, 212, 256, 232, 125, 127, 5, 51, 37, 252, 136, 13, 47, 195, 168, 191,
|
|
231, 55, 57, 251, 214, 116, 15, 86, 210, 41, 249, 242, 119, 27, 250, 203,
|
|
107, 69, 90, 43, 206, 154, 127, 54, 100, 78, 187, 54, 244, 177, 234, 167,
|
|
202, 136, 209, 171, 69, 114, 133, 173, 26, 139, 78, 141, 128, 32, 124, 39,
|
|
45, 218, 96, 68, 90, 44, 67, 62, 83, 190, 188, 256, 103, 42, 102, 64,
|
|
249, 0, 141, 11, 61, 69, 70, 66, 233, 237, 29, 200, 251, 157, 71, 51,
|
|
64, 133, 113, 76, 35, 125, 76, 137, 217, 145, 35, 69, 226, 180, 56, 249,
|
|
156, 163, 176, 237, 81, 54, 85, 169, 115, 211, 129, 70, 248, 40, 252, 192,
|
|
194, 101, 247, 8, 181, 124, 217, 191, 194, 93, 99, 127, 117, 177, 144, 151,
|
|
228, 121, 32, 11, 89, 81, 26, 29, 183, 76, 249, 132, 179, 70, 34, 102,
|
|
20, 66, 87, 63, 124, 205, 174, 177, 87, 219, 73, 218, 91, 87, 176, 72,
|
|
15, 211, 47, 61, 251, 165, 39, 247, 146, 70, 150, 57, 1, 212, 36, 162,
|
|
39, 38, 16, 216, 3, 50, 116, 200, 32, 234, 77, 181, 155, 19, 90, 188,
|
|
36, 6, 254, 46, 46, 203, 25, 230, 181, 196, 4, 151, 225, 65, 122, 216,
|
|
168, 86, 158, 131, 136, 16, 49, 102, 233, 64, 154, 88, 228, 52, 146, 69,
|
|
93, 157, 243, 121, 70, 209, 126, 213, 88, 145, 236, 65, 70, 96, 204, 47,
|
|
10, 200, 77, 8, 103, 150, 48, 153, 5, 37, 52, 235, 209, 31, 181, 126,
|
|
83, 142, 224, 140, 6, 32, 200, 171, 160, 179, 115, 229, 75, 194, 208, 39,
|
|
59, 223, 52, 247, 38, 197, 135, 1, 6, 189, 106, 114, 168, 5, 211, 222,
|
|
44, 63, 90, 160, 116, 172, 170, 133, 125, 138, 39, 131, 23, 178, 10, 214,
|
|
36, 93, 28, 59, 68, 17, 123, 25, 255, 184, 204, 102, 194, 214, 129, 94,
|
|
159, 245, 112, 141, 62, 11, 61, 197, 124, 221, 205, 11, 79, 71, 201, 54,
|
|
58, 150, 29, 121, 87, 46, 240, 201, 68, 20, 194, 209, 47, 152, 158, 174,
|
|
193, 164, 120, 255, 216, 165, 247, 58, 85, 130, 220, 23, 122, 223, 188, 98,
|
|
21, 70, 72, 170, 150, 237, 76, 143, 112, 238, 206, 146, 215, 110, 4, 250,
|
|
68, 44, 174, 177, 30, 98, 143, 241, 180, 127, 113, 48, 0, 1, 179, 199,
|
|
59, 106, 201, 114, 29, 86, 173, 133, 217, 44, 200, 141, 107, 172, 16, 60,
|
|
82, 58, 239, 94, 141, 234, 186, 235, 109, 173, 249, 139, 141, 59, 100, 248,
|
|
84, 144, 49, 160, 51, 207, 164, 103, 74, 97, 146, 202, 193, 125, 168, 134,
|
|
236, 111, 135, 121, 59, 145, 168, 200, 181, 173, 109, 2, 255, 6, 9, 245,
|
|
90, 202, 214, 143, 121, 65, 85, 232, 132, 77, 228, 84, 26, 54, 184, 15,
|
|
161, 29, 177, 79, 43, 0, 156, 184, 163, 165, 62, 90, 179, 93, 45, 239,
|
|
1, 16, 120, 189, 127, 47, 74, 166, 20, 214, 233, 226, 89, 217, 229, 26,
|
|
156, 53, 162, 60, 21, 3, 192, 72, 111, 51, 53, 101, 181, 208, 88, 82,
|
|
179, 160, 219, 113, 240, 108, 43, 224, 162, 147, 62, 14, 95, 81, 205, 4,
|
|
160, 177, 225, 115, 29, 69, 235, 168, 148, 29, 128, 114, 124, 129, 172, 165,
|
|
215, 231, 214, 86, 160, 44, 157, 91, 248, 183, 73, 164, 56, 181, 162, 92,
|
|
141, 118, 127, 240, 196, 77, 0, 9, 244, 79, 250, 100, 195, 25, 255, 85,
|
|
94, 35, 212, 137, 107, 34, 110, 20, 200, 104, 17, 32, 231, 43, 150, 159,
|
|
231, 216, 223, 190, 226, 109, 162, 197, 87, 92, 224, 11, 111, 73, 60, 225,
|
|
238, 73, 246, 169, 19, 217, 119, 38, 121, 118, 70, 82, 99, 241, 110, 67,
|
|
31, 76, 146, 215, 124, 240, 31, 103, 139, 224, 75, 160, 31, 78, 93, 4,
|
|
64, 9, 103, 223, 6, 227, 119, 85, 116, 81, 21, 43, 46, 206, 234, 132,
|
|
85, 99, 22, 131, 135, 97, 86, 13, 234, 188, 21, 14, 89, 169, 207, 238,
|
|
219, 177, 190, 72, 157, 41, 114, 140, 92, 141, 186, 1, 63, 107, 225, 184,
|
|
118, 150, 153, 254, 241, 106, 120, 210, 104, 144, 151, 161, 88, 206, 125, 164,
|
|
15, 211, 173, 49, 146, 241, 71, 36, 58, 201, 46, 27, 33, 187, 91, 162,
|
|
117, 19, 210, 213, 187, 97, 193, 50, 190, 114, 217, 60, 61, 167, 207, 213,
|
|
213, 53, 135, 34, 156, 91, 115, 119, 46, 99, 242, 1, 90, 52, 198, 227,
|
|
201, 91, 216, 146, 210, 82, 121, 38, 73, 133, 182, 193, 132, 148, 246, 75,
|
|
109, 157, 179, 113, 176, 134, 205, 159, 148, 58, 103, 171, 132, 156, 133, 147,
|
|
161, 231, 39, 100, 175, 97, 125, 28, 183, 129, 135, 191, 202, 181, 29, 218,
|
|
43, 104, 148, 203, 189, 204, 4, 182, 169, 1, 134, 122, 141, 202, 13, 187,
|
|
177, 112, 162, 35, 231, 6, 8, 241, 99, 6, 191, 45, 113, 113, 101, 104};
|
|
|
|
// The S-Box we use for further linearity breaking.
|
|
// We created it by taking the digits of decimal expansion of e.
|
|
// The code that created it can be found in 'ProduceRandomSBox.c'.
|
|
unsigned char SBox[256] = {
|
|
//0 1 2 3 4 5 6 7 8 9 A B C D E F
|
|
0x7d, 0xd1, 0x70, 0x0b, 0xfa, 0x39, 0x18, 0xc3, 0xf3, 0xbb, 0xa7, 0xd4, 0x84, 0x25, 0x3b, 0x3c, // 0
|
|
0x2c, 0x15, 0x69, 0x9a, 0xf9, 0x27, 0xfb, 0x02, 0x52, 0xba, 0xa8, 0x4b, 0x20, 0xb5, 0x8b, 0x3a, // 1
|
|
0x88, 0x8e, 0x26, 0xcb, 0x71, 0x5e, 0xaf, 0xad, 0x0c, 0xac, 0xa1, 0x93, 0xc6, 0x78, 0xce, 0xfc, // 2
|
|
0x2a, 0x76, 0x17, 0x1f, 0x62, 0xc2, 0x2e, 0x99, 0x11, 0x37, 0x65, 0x40, 0xfd, 0xa0, 0x03, 0xc1, // 3
|
|
0xca, 0x48, 0xe2, 0x9b, 0x81, 0xe4, 0x1c, 0x01, 0xec, 0x68, 0x7a, 0x5a, 0x50, 0xf8, 0x0e, 0xa3, // 4
|
|
0xe8, 0x61, 0x2b, 0xa2, 0xeb, 0xcf, 0x8c, 0x3d, 0xb4, 0x95, 0x13, 0x08, 0x46, 0xab, 0x91, 0x7b, // 5
|
|
0xea, 0x55, 0x67, 0x9d, 0xdd, 0x29, 0x6a, 0x8f, 0x9f, 0x22, 0x4e, 0xf2, 0x57, 0xd2, 0xa9, 0xbd, // 6
|
|
0x38, 0x16, 0x5f, 0x4c, 0xf7, 0x9e, 0x1b, 0x2f, 0x30, 0xc7, 0x41, 0x24, 0x5c, 0xbf, 0x05, 0xf6, // 7
|
|
0x0a, 0x31, 0xa5, 0x45, 0x21, 0x33, 0x6b, 0x6d, 0x6c, 0x86, 0xe1, 0xa4, 0xe6, 0x92, 0x9c, 0xdf, // 8
|
|
0xe7, 0xbe, 0x28, 0xe3, 0xfe, 0x06, 0x4d, 0x98, 0x80, 0x04, 0x96, 0x36, 0x3e, 0x14, 0x4a, 0x34, // 9
|
|
0xd3, 0xd5, 0xdb, 0x44, 0xcd, 0xf5, 0x54, 0xdc, 0x89, 0x09, 0x90, 0x42, 0x87, 0xff, 0x7e, 0x56, // A
|
|
0x5d, 0x59, 0xd7, 0x23, 0x75, 0x19, 0x97, 0x73, 0x83, 0x64, 0x53, 0xa6, 0x1e, 0xd8, 0xb0, 0x49, // B
|
|
0x3f, 0xef, 0xbc, 0x7f, 0x43, 0xf0, 0xc9, 0x72, 0x0f, 0x63, 0x79, 0x2d, 0xc0, 0xda, 0x66, 0xc8, // C
|
|
0x32, 0xde, 0x47, 0x07, 0xb8, 0xe9, 0x1d, 0xc4, 0x85, 0x74, 0x82, 0xcc, 0x60, 0x51, 0x77, 0x0d, // D
|
|
0xaa, 0x35, 0xed, 0x58, 0x7c, 0x5b, 0xb9, 0x94, 0x6e, 0x8d, 0xb1, 0xc5, 0xb7, 0xee, 0xb6, 0xae, // E
|
|
0x10, 0xe0, 0xd6, 0xd9, 0xe5, 0x4f, 0xf1, 0x12, 0x00, 0xd0, 0xf4, 0x1a, 0x6f, 0x8a, 0xb3, 0xb2 }; // F
|
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////
|
|
//
|
|
// Helper functions definition portion.
|
|
//
|
|
///////////////////////////////////////////////////////////////////////////////////////////////
|
|
|
|
// Translates an input array with values in base 257 to output array with values in base 256.
|
|
// Returns the carry bit.
|
|
//
|
|
// Parameters:
|
|
// - input: the input array of size EIGHTH_N. Each value in the array is a number in Z_257.
|
|
// The MSB is assumed to be the last one in the array.
|
|
// - output: the input array encoded in base 256.
|
|
//
|
|
// Returns:
|
|
// - The carry bit (MSB).
|
|
swift_int16_t TranslateToBase256(swift_int32_t input[EIGHTH_N], unsigned char output[EIGHTH_N]);
|
|
|
|
// Translates an input integer into the range (-FIELD_SIZE / 2) <= result <= (FIELD_SIZE / 2).
|
|
//
|
|
// Parameters:
|
|
// - x: the input integer.
|
|
//
|
|
// Returns:
|
|
// - The result, which equals (x MOD FIELD_SIZE), such that |result| <= (FIELD_SIZE / 2).
|
|
int Center(int x);
|
|
|
|
// Calculates bit reversal permutation.
|
|
//
|
|
// Parameters:
|
|
// - input: the input to reverse.
|
|
// - numOfBits: the number of bits in the input to reverse.
|
|
//
|
|
// Returns:
|
|
// - The resulting number, which is obtained from the input by reversing its bits.
|
|
int ReverseBits(int input, int numOfBits);
|
|
|
|
// Initializes the FFT fast lookup table.
|
|
// Shall be called only once.
|
|
void InitializeSWIFFTX();
|
|
|
|
// Calculates the FFT.
|
|
//
|
|
// Parameters:
|
|
// - input: the input to the FFT.
|
|
// - output: the resulting output.
|
|
void FFT(const unsigned char input[EIGHTH_N], swift_int32_t *output);
|
|
|
|
///////////////////////////////////////////////////////////////////////////////////////////////
|
|
// Helper functions implementation portion.
|
|
///////////////////////////////////////////////////////////////////////////////////////////////
|
|
|
|
swift_int16_t TranslateToBase256(swift_int32_t input[EIGHTH_N], unsigned char output[EIGHTH_N])
|
|
{
|
|
swift_int32_t pairs[EIGHTH_N / 2];
|
|
int i;
|
|
|
|
for (i = 0; i < EIGHTH_N; i += 2)
|
|
{
|
|
// input[i] + 257 * input[i + 1]
|
|
pairs[i >> 1] = input[i] + input[i + 1] + (input[i + 1] << 8);
|
|
}
|
|
|
|
for (i = (EIGHTH_N / 2) - 1; i > 0; --i)
|
|
{
|
|
int j;
|
|
|
|
for (j = i - 1; j < (EIGHTH_N / 2) - 1; ++j)
|
|
{
|
|
// pairs[j + 1] * 513, because 257^2 = 513 % 256^2.
|
|
register swift_int32_t temp = pairs[j] + pairs[j + 1] + (pairs[j + 1] << 9);
|
|
pairs[j] = temp & 0xffff;
|
|
pairs[j + 1] += (temp >> 16);
|
|
}
|
|
}
|
|
|
|
for (i = 0; i < EIGHTH_N; i += 2)
|
|
{
|
|
output[i] = (unsigned char) (pairs[i >> 1] & 0xff);
|
|
output[i + 1] = (unsigned char) ((pairs[i >> 1] >> 8) & 0xff);
|
|
}
|
|
|
|
return (pairs[EIGHTH_N/2 - 1] >> 16);
|
|
}
|
|
|
|
int Center(int x)
|
|
{
|
|
int result = x % FIELD_SIZE;
|
|
|
|
if (result > (FIELD_SIZE / 2))
|
|
result -= FIELD_SIZE;
|
|
|
|
if (result < (FIELD_SIZE / -2))
|
|
result += FIELD_SIZE;
|
|
|
|
return result;
|
|
}
|
|
|
|
int ReverseBits(int input, int numOfBits)
|
|
{
|
|
register int reversed = 0;
|
|
|
|
for (input |= numOfBits; input > 1; input >>= 1)
|
|
reversed = (reversed << 1) | (input & 1);
|
|
|
|
return reversed;
|
|
}
|
|
|
|
void InitializeSWIFFTX()
|
|
{
|
|
int i, j, k, x;
|
|
// The powers of OMEGA
|
|
int omegaPowers[2 * N];
|
|
omegaPowers[0] = 1;
|
|
|
|
if (wasSetupDone)
|
|
return;
|
|
|
|
for (i = 1; i < (2 * N); ++i)
|
|
{
|
|
omegaPowers[i] = Center(omegaPowers[i - 1] * OMEGA);
|
|
}
|
|
|
|
for (i = 0; i < (N / W); ++i)
|
|
{
|
|
for (j = 0; j < W; ++j)
|
|
{
|
|
multipliers[(i << 3) + j] = omegaPowers[ReverseBits(i, N / W) * (2 * j + 1)];
|
|
}
|
|
}
|
|
|
|
for (x = 0; x < 256; ++x)
|
|
{
|
|
for (j = 0; j < 8; ++j)
|
|
{
|
|
register int temp = 0;
|
|
for (k = 0; k < 8; ++k)
|
|
{
|
|
temp += omegaPowers[(EIGHTH_N * (2 * j + 1) * ReverseBits(k, W)) % (2 * N)]
|
|
* ((x >> k) & 1);
|
|
}
|
|
|
|
fftTable[(x << 3) + j] = Center(temp);
|
|
}
|
|
}
|
|
|
|
wasSetupDone = true;
|
|
}
|
|
|
|
void FFT(const unsigned char input[EIGHTH_N], swift_int32_t *output)
|
|
{
|
|
register swift_int16_t *mult = multipliers;
|
|
register swift_int32_t F0, F1, F2, F3, F4, F5, F6, F7, F8, F9,
|
|
F10, F11, F12, F13, F14, F15, F16, F17, F18, F19,
|
|
F20, F21, F22, F23, F24, F25, F26, F27, F28, F29,
|
|
F30, F31, F32, F33, F34, F35, F36, F37, F38, F39,
|
|
F40, F41, F42, F43, F44, F45, F46, F47, F48, F49,
|
|
F50, F51, F52, F53, F54, F55, F56, F57, F58, F59,
|
|
F60, F61, F62, F63;
|
|
|
|
// First loop unrolling:
|
|
register swift_int16_t *table = &(fftTable[input[0] << 3]);
|
|
|
|
F0 = mult[0] * table[0];
|
|
F8 = mult[1] * table[1];
|
|
F16 = mult[2] * table[2];
|
|
F24 = mult[3] * table[3];
|
|
F32 = mult[4] * table[4];
|
|
F40 = mult[5] * table[5];
|
|
F48 = mult[6] * table[6];
|
|
F56 = mult[7] * table[7];
|
|
|
|
mult += 8;
|
|
table = &(fftTable[input[1] << 3]);
|
|
|
|
F1 = mult[0] * table[0];
|
|
F9 = mult[1] * table[1];
|
|
F17 = mult[2] * table[2];
|
|
F25 = mult[3] * table[3];
|
|
F33 = mult[4] * table[4];
|
|
F41 = mult[5] * table[5];
|
|
F49 = mult[6] * table[6];
|
|
F57 = mult[7] * table[7];
|
|
|
|
mult += 8;
|
|
table = &(fftTable[input[2] << 3]);
|
|
|
|
F2 = mult[0] * table[0];
|
|
F10 = mult[1] * table[1];
|
|
F18 = mult[2] * table[2];
|
|
F26 = mult[3] * table[3];
|
|
F34 = mult[4] * table[4];
|
|
F42 = mult[5] * table[5];
|
|
F50 = mult[6] * table[6];
|
|
F58 = mult[7] * table[7];
|
|
|
|
mult += 8;
|
|
table = &(fftTable[input[3] << 3]);
|
|
|
|
F3 = mult[0] * table[0];
|
|
F11 = mult[1] * table[1];
|
|
F19 = mult[2] * table[2];
|
|
F27 = mult[3] * table[3];
|
|
F35 = mult[4] * table[4];
|
|
F43 = mult[5] * table[5];
|
|
F51 = mult[6] * table[6];
|
|
F59 = mult[7] * table[7];
|
|
|
|
mult += 8;
|
|
table = &(fftTable[input[4] << 3]);
|
|
|
|
F4 = mult[0] * table[0];
|
|
F12 = mult[1] * table[1];
|
|
F20 = mult[2] * table[2];
|
|
F28 = mult[3] * table[3];
|
|
F36 = mult[4] * table[4];
|
|
F44 = mult[5] * table[5];
|
|
F52 = mult[6] * table[6];
|
|
F60 = mult[7] * table[7];
|
|
|
|
mult += 8;
|
|
table = &(fftTable[input[5] << 3]);
|
|
|
|
F5 = mult[0] * table[0];
|
|
F13 = mult[1] * table[1];
|
|
F21 = mult[2] * table[2];
|
|
F29 = mult[3] * table[3];
|
|
F37 = mult[4] * table[4];
|
|
F45 = mult[5] * table[5];
|
|
F53 = mult[6] * table[6];
|
|
F61 = mult[7] * table[7];
|
|
|
|
mult += 8;
|
|
table = &(fftTable[input[6] << 3]);
|
|
|
|
F6 = mult[0] * table[0];
|
|
F14 = mult[1] * table[1];
|
|
F22 = mult[2] * table[2];
|
|
F30 = mult[3] * table[3];
|
|
F38 = mult[4] * table[4];
|
|
F46 = mult[5] * table[5];
|
|
F54 = mult[6] * table[6];
|
|
F62 = mult[7] * table[7];
|
|
|
|
mult += 8;
|
|
table = &(fftTable[input[7] << 3]);
|
|
|
|
F7 = mult[0] * table[0];
|
|
F15 = mult[1] * table[1];
|
|
F23 = mult[2] * table[2];
|
|
F31 = mult[3] * table[3];
|
|
F39 = mult[4] * table[4];
|
|
F47 = mult[5] * table[5];
|
|
F55 = mult[6] * table[6];
|
|
F63 = mult[7] * table[7];
|
|
|
|
// Second loop unrolling:
|
|
// Iteration 0:
|
|
ADD_SUB(F0, F1);
|
|
ADD_SUB(F2, F3);
|
|
ADD_SUB(F4, F5);
|
|
ADD_SUB(F6, F7);
|
|
|
|
F3 <<= 4;
|
|
F7 <<= 4;
|
|
|
|
ADD_SUB(F0, F2);
|
|
ADD_SUB(F1, F3);
|
|
ADD_SUB(F4, F6);
|
|
ADD_SUB(F5, F7);
|
|
|
|
F5 <<= 2;
|
|
F6 <<= 4;
|
|
F7 <<= 6;
|
|
|
|
ADD_SUB(F0, F4);
|
|
ADD_SUB(F1, F5);
|
|
ADD_SUB(F2, F6);
|
|
ADD_SUB(F3, F7);
|
|
|
|
output[0] = Q_REDUCE(F0);
|
|
output[8] = Q_REDUCE(F1);
|
|
output[16] = Q_REDUCE(F2);
|
|
output[24] = Q_REDUCE(F3);
|
|
output[32] = Q_REDUCE(F4);
|
|
output[40] = Q_REDUCE(F5);
|
|
output[48] = Q_REDUCE(F6);
|
|
output[56] = Q_REDUCE(F7);
|
|
|
|
// Iteration 1:
|
|
ADD_SUB(F8, F9);
|
|
ADD_SUB(F10, F11);
|
|
ADD_SUB(F12, F13);
|
|
ADD_SUB(F14, F15);
|
|
|
|
F11 <<= 4;
|
|
F15 <<= 4;
|
|
|
|
ADD_SUB(F8, F10);
|
|
ADD_SUB(F9, F11);
|
|
ADD_SUB(F12, F14);
|
|
ADD_SUB(F13, F15);
|
|
|
|
F13 <<= 2;
|
|
F14 <<= 4;
|
|
F15 <<= 6;
|
|
|
|
ADD_SUB(F8, F12);
|
|
ADD_SUB(F9, F13);
|
|
ADD_SUB(F10, F14);
|
|
ADD_SUB(F11, F15);
|
|
|
|
output[1] = Q_REDUCE(F8);
|
|
output[9] = Q_REDUCE(F9);
|
|
output[17] = Q_REDUCE(F10);
|
|
output[25] = Q_REDUCE(F11);
|
|
output[33] = Q_REDUCE(F12);
|
|
output[41] = Q_REDUCE(F13);
|
|
output[49] = Q_REDUCE(F14);
|
|
output[57] = Q_REDUCE(F15);
|
|
|
|
// Iteration 2:
|
|
ADD_SUB(F16, F17);
|
|
ADD_SUB(F18, F19);
|
|
ADD_SUB(F20, F21);
|
|
ADD_SUB(F22, F23);
|
|
|
|
F19 <<= 4;
|
|
F23 <<= 4;
|
|
|
|
ADD_SUB(F16, F18);
|
|
ADD_SUB(F17, F19);
|
|
ADD_SUB(F20, F22);
|
|
ADD_SUB(F21, F23);
|
|
|
|
F21 <<= 2;
|
|
F22 <<= 4;
|
|
F23 <<= 6;
|
|
|
|
ADD_SUB(F16, F20);
|
|
ADD_SUB(F17, F21);
|
|
ADD_SUB(F18, F22);
|
|
ADD_SUB(F19, F23);
|
|
|
|
output[2] = Q_REDUCE(F16);
|
|
output[10] = Q_REDUCE(F17);
|
|
output[18] = Q_REDUCE(F18);
|
|
output[26] = Q_REDUCE(F19);
|
|
output[34] = Q_REDUCE(F20);
|
|
output[42] = Q_REDUCE(F21);
|
|
output[50] = Q_REDUCE(F22);
|
|
output[58] = Q_REDUCE(F23);
|
|
|
|
// Iteration 3:
|
|
ADD_SUB(F24, F25);
|
|
ADD_SUB(F26, F27);
|
|
ADD_SUB(F28, F29);
|
|
ADD_SUB(F30, F31);
|
|
|
|
F27 <<= 4;
|
|
F31 <<= 4;
|
|
|
|
ADD_SUB(F24, F26);
|
|
ADD_SUB(F25, F27);
|
|
ADD_SUB(F28, F30);
|
|
ADD_SUB(F29, F31);
|
|
|
|
F29 <<= 2;
|
|
F30 <<= 4;
|
|
F31 <<= 6;
|
|
|
|
ADD_SUB(F24, F28);
|
|
ADD_SUB(F25, F29);
|
|
ADD_SUB(F26, F30);
|
|
ADD_SUB(F27, F31);
|
|
|
|
output[3] = Q_REDUCE(F24);
|
|
output[11] = Q_REDUCE(F25);
|
|
output[19] = Q_REDUCE(F26);
|
|
output[27] = Q_REDUCE(F27);
|
|
output[35] = Q_REDUCE(F28);
|
|
output[43] = Q_REDUCE(F29);
|
|
output[51] = Q_REDUCE(F30);
|
|
output[59] = Q_REDUCE(F31);
|
|
|
|
// Iteration 4:
|
|
ADD_SUB(F32, F33);
|
|
ADD_SUB(F34, F35);
|
|
ADD_SUB(F36, F37);
|
|
ADD_SUB(F38, F39);
|
|
|
|
F35 <<= 4;
|
|
F39 <<= 4;
|
|
|
|
ADD_SUB(F32, F34);
|
|
ADD_SUB(F33, F35);
|
|
ADD_SUB(F36, F38);
|
|
ADD_SUB(F37, F39);
|
|
|
|
F37 <<= 2;
|
|
F38 <<= 4;
|
|
F39 <<= 6;
|
|
|
|
ADD_SUB(F32, F36);
|
|
ADD_SUB(F33, F37);
|
|
ADD_SUB(F34, F38);
|
|
ADD_SUB(F35, F39);
|
|
|
|
output[4] = Q_REDUCE(F32);
|
|
output[12] = Q_REDUCE(F33);
|
|
output[20] = Q_REDUCE(F34);
|
|
output[28] = Q_REDUCE(F35);
|
|
output[36] = Q_REDUCE(F36);
|
|
output[44] = Q_REDUCE(F37);
|
|
output[52] = Q_REDUCE(F38);
|
|
output[60] = Q_REDUCE(F39);
|
|
|
|
// Iteration 5:
|
|
ADD_SUB(F40, F41);
|
|
ADD_SUB(F42, F43);
|
|
ADD_SUB(F44, F45);
|
|
ADD_SUB(F46, F47);
|
|
|
|
F43 <<= 4;
|
|
F47 <<= 4;
|
|
|
|
ADD_SUB(F40, F42);
|
|
ADD_SUB(F41, F43);
|
|
ADD_SUB(F44, F46);
|
|
ADD_SUB(F45, F47);
|
|
|
|
F45 <<= 2;
|
|
F46 <<= 4;
|
|
F47 <<= 6;
|
|
|
|
ADD_SUB(F40, F44);
|
|
ADD_SUB(F41, F45);
|
|
ADD_SUB(F42, F46);
|
|
ADD_SUB(F43, F47);
|
|
|
|
output[5] = Q_REDUCE(F40);
|
|
output[13] = Q_REDUCE(F41);
|
|
output[21] = Q_REDUCE(F42);
|
|
output[29] = Q_REDUCE(F43);
|
|
output[37] = Q_REDUCE(F44);
|
|
output[45] = Q_REDUCE(F45);
|
|
output[53] = Q_REDUCE(F46);
|
|
output[61] = Q_REDUCE(F47);
|
|
|
|
// Iteration 6:
|
|
ADD_SUB(F48, F49);
|
|
ADD_SUB(F50, F51);
|
|
ADD_SUB(F52, F53);
|
|
ADD_SUB(F54, F55);
|
|
|
|
F51 <<= 4;
|
|
F55 <<= 4;
|
|
|
|
ADD_SUB(F48, F50);
|
|
ADD_SUB(F49, F51);
|
|
ADD_SUB(F52, F54);
|
|
ADD_SUB(F53, F55);
|
|
|
|
F53 <<= 2;
|
|
F54 <<= 4;
|
|
F55 <<= 6;
|
|
|
|
ADD_SUB(F48, F52);
|
|
ADD_SUB(F49, F53);
|
|
ADD_SUB(F50, F54);
|
|
ADD_SUB(F51, F55);
|
|
|
|
output[6] = Q_REDUCE(F48);
|
|
output[14] = Q_REDUCE(F49);
|
|
output[22] = Q_REDUCE(F50);
|
|
output[30] = Q_REDUCE(F51);
|
|
output[38] = Q_REDUCE(F52);
|
|
output[46] = Q_REDUCE(F53);
|
|
output[54] = Q_REDUCE(F54);
|
|
output[62] = Q_REDUCE(F55);
|
|
|
|
// Iteration 7:
|
|
ADD_SUB(F56, F57);
|
|
ADD_SUB(F58, F59);
|
|
ADD_SUB(F60, F61);
|
|
ADD_SUB(F62, F63);
|
|
|
|
F59 <<= 4;
|
|
F63 <<= 4;
|
|
|
|
ADD_SUB(F56, F58);
|
|
ADD_SUB(F57, F59);
|
|
ADD_SUB(F60, F62);
|
|
ADD_SUB(F61, F63);
|
|
|
|
F61 <<= 2;
|
|
F62 <<= 4;
|
|
F63 <<= 6;
|
|
|
|
ADD_SUB(F56, F60);
|
|
ADD_SUB(F57, F61);
|
|
ADD_SUB(F58, F62);
|
|
ADD_SUB(F59, F63);
|
|
|
|
output[7] = Q_REDUCE(F56);
|
|
output[15] = Q_REDUCE(F57);
|
|
output[23] = Q_REDUCE(F58);
|
|
output[31] = Q_REDUCE(F59);
|
|
output[39] = Q_REDUCE(F60);
|
|
output[47] = Q_REDUCE(F61);
|
|
output[55] = Q_REDUCE(F62);
|
|
output[63] = Q_REDUCE(F63);
|
|
}
|
|
|
|
// Calculates the FFT part of SWIFFT.
|
|
// We divided the SWIFFT calculation into two, because that way we could save 2 computations of
|
|
// the FFT part, since in the first stage of SWIFFTX the difference between the first 3 SWIFFTs
|
|
// is only the A's part.
|
|
//
|
|
// Parameters:
|
|
// - input: the input to FFT.
|
|
// - m: the input size divided by 8. The function performs m FFTs.
|
|
// - output: will store the result.
|
|
void SWIFFTFFT(const unsigned char *input, int m, swift_int32_t *output)
|
|
{
|
|
int i;
|
|
|
|
for (i = 0;
|
|
i < m;
|
|
i++, input += EIGHTH_N, output += N)
|
|
{
|
|
FFT(input, output);
|
|
}
|
|
}
|
|
|
|
// Calculates the 'sum' part of SWIFFT, including the base change at the end.
|
|
// We divided the SWIFFT calculation into two, because that way we could save 2 computations of
|
|
// the FFT part, since in the first stage of SWIFFTX the difference between the first 3 SWIFFTs
|
|
// is only the A's part.
|
|
//
|
|
// Parameters:
|
|
// - input: the input. Of size 64 * m.
|
|
// - m: the input size divided by 64.
|
|
// - output: will store the result.
|
|
// - a: the coefficients in the sum. Of size 64 * m.
|
|
void SWIFFTSum(const swift_int32_t *input, int m, unsigned char *output, const swift_int16_t *a)
|
|
{
|
|
int i, j;
|
|
swift_int32_t result[N];
|
|
register swift_int16_t carry = 0;
|
|
|
|
for (j = 0; j < N; ++j)
|
|
{
|
|
register swift_int32_t sum = 0;
|
|
const register swift_int32_t *f = input + j;
|
|
const register swift_int16_t *k = a + j;
|
|
|
|
for (i = 0; i < m; i++, f += N,k += N)
|
|
{
|
|
sum += (*f) * (*k);
|
|
}
|
|
|
|
result[j] = sum;
|
|
}
|
|
|
|
for (j = 0; j < N; ++j)
|
|
{
|
|
result[j] = ((FIELD_SIZE << 22) + result[j]) % FIELD_SIZE;
|
|
}
|
|
|
|
for (j = 0; j < 8; ++j)
|
|
{
|
|
int register carryBit = TranslateToBase256(result + (j << 3), output + (j << 3));
|
|
carry |= carryBit << j;
|
|
}
|
|
|
|
output[N] = carry;
|
|
}
|
|
|
|
void ComputeSingleSWIFFTX(unsigned char input[SWIFFTX_INPUT_BLOCK_SIZE],
|
|
unsigned char output[SWIFFTX_OUTPUT_BLOCK_SIZE],
|
|
bool doSmooth)
|
|
{
|
|
int i;
|
|
// Will store the result of the FFT parts:
|
|
swift_int32_t fftOut[N * M];
|
|
unsigned char intermediate[N * 3 + 8];
|
|
unsigned char carry0,carry1,carry2;
|
|
|
|
// Do the three SWIFFTS while remembering the three carry bytes (each carry byte gets
|
|
// overriden by the following SWIFFT):
|
|
|
|
// 1. Compute the FFT of the input - the common part for the first 3 SWIFFTs:
|
|
SWIFFTFFT(input, M, fftOut);
|
|
|
|
// 2. Compute the sums of the 3 SWIFFTs, each using a different set of coefficients:
|
|
|
|
// 2a. The first SWIFFT:
|
|
SWIFFTSum(fftOut, M, intermediate, As);
|
|
// Remember the carry byte:
|
|
carry0 = intermediate[N];
|
|
|
|
// 2b. The second one:
|
|
SWIFFTSum(fftOut, M, intermediate + N, As + (M * N));
|
|
carry1 = intermediate[2 * N];
|
|
|
|
// 2c. The third one:
|
|
SWIFFTSum(fftOut, M, intermediate + (2 * N), As + 2 * (M * N));
|
|
carry2 = intermediate[3 * N];
|
|
|
|
//2d. Put three carry bytes in their place
|
|
intermediate[3 * N] = carry0;
|
|
intermediate[(3 * N) + 1] = carry1;
|
|
intermediate[(3 * N) + 2] = carry2;
|
|
|
|
// Padding intermediate output with 5 zeroes.
|
|
memset(intermediate + (3 * N) + 3, 0, 5);
|
|
|
|
// Apply the S-Box:
|
|
for (i = 0; i < (3 * N) + 8; ++i)
|
|
{
|
|
intermediate[i] = SBox[intermediate[i]];
|
|
}
|
|
|
|
// 3. The final and last SWIFFT:
|
|
SWIFFTFFT(intermediate, 3 * (N/8) + 1, fftOut);
|
|
SWIFFTSum(fftOut, 3 * (N/8) + 1, output, As);
|
|
|
|
if (doSmooth)
|
|
{
|
|
unsigned char sum[N];
|
|
register int i, j;
|
|
memset(sum, 0, N);
|
|
|
|
for (i = 0; i < (N + 1) * 8; ++i)
|
|
{
|
|
register const swift_int16_t *AsRow;
|
|
register int AShift;
|
|
|
|
if (!(output[i >> 3] & (1 << (i & 7))))
|
|
{
|
|
continue;
|
|
}
|
|
|
|
AsRow = As + N * M + (i & ~(N - 1)) ;
|
|
AShift = i & 63;
|
|
|
|
for (j = AShift; j < N; ++j)
|
|
{
|
|
sum[j] += AsRow[j - AShift];
|
|
}
|
|
|
|
for(j = 0; j < AShift; ++j)
|
|
{
|
|
sum[j] -= AsRow[N - AShift + j];
|
|
}
|
|
}
|
|
|
|
for (i = 0; i < N; ++i)
|
|
{
|
|
output[i] = sum[i];
|
|
}
|
|
|
|
output[N] = 0;
|
|
}
|
|
}
|