galois_table.c

//
// Created by 理 傅 on 2017/1/3.
//

#include "galois.h"

// The number of elements in the field.
const int fieldSize = 256;

// The polynomial used to generate the logarithm table.
//
// There are a number of polynomials that work to generate
// a Galois field of 256 elements.  The choice is arbitrary,
// and we just use the first one.
//
// The possibilities are: 29, 43, 45, 77, 95, 99, 101, 105,
//* 113, 135, 141, 169, 195, 207, 231, and 245.
const int generatingPolynomial = 29;


byte logTable[fieldSize] = {
        0, 0, 1, 25, 2, 50, 26, 198,
        3, 223, 51, 238, 27, 104, 199, 75,
        4, 100, 224, 14, 52, 141, 239, 129,
        28, 193, 105, 248, 200, 8, 76, 113,
        5, 138, 101, 47, 225, 36, 15, 33,
        53, 147, 142, 218, 240, 18, 130, 69,
        29, 181, 194, 125, 106, 39, 249, 185,
        201, 154, 9, 120, 77, 228, 114, 166,
        6, 191, 139, 98, 102, 221, 48, 253,
        226, 152, 37, 179, 16, 145, 34, 136,
        54, 208, 148, 206, 143, 150, 219, 189,
        241, 210, 19, 92, 131, 56, 70, 64,
        30, 66, 182, 163, 195, 72, 126, 110,
        107, 58, 40, 84, 250, 133, 186, 61,
        202, 94, 155, 159, 10, 21, 121, 43,
        78, 212, 229, 172, 115, 243, 167, 87,
        7, 112, 192, 247, 140, 128, 99, 13,
        103, 74, 222, 237, 49, 197, 254, 24,
        227, 165, 153, 119, 38, 184, 180, 124,
        17, 68, 146, 217, 35, 32, 137, 46,
        55, 63, 209, 91, 149, 188, 207, 205,
        144, 135, 151, 178, 220, 252, 190, 97,
        242, 86, 211, 171, 20, 42, 93, 158,
        132, 60, 57, 83, 71, 109, 65, 162,
        31, 45, 67, 216, 183, 123, 164, 118,
        196, 23, 73, 236, 127, 12, 111, 246,
        108, 161, 59, 82, 41, 157, 85, 170,
        251, 96, 134, 177, 187, 204, 62, 90,
        203, 89, 95, 176, 156, 169, 160, 81,
        11, 245, 22, 235, 122, 117, 44, 215,
        79, 174, 213, 233, 230, 231, 173, 232,
        116, 214, 244, 234, 168, 80, 88, 175,
};

/**
 * Inverse of the logarithm table.  Maps integer logarithms
 * to members of the field.  There is no entry for 255
 * because the highest log is 254.
 *
 * This table was generated by `go run gentables.go`
 */
byte expTable[]= {0x1, 0x2, 0x4, 0x8, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x3, 0x6, 0xc, 0x18, 0x30, 0x60, 0xc0, 0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46, 0x8c, 0x5, 0xa, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0xf, 0x1e, 0x3c, 0x78, 0xf0, 0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0xd, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x7, 0xe, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x9, 0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0xb, 0x16, 0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e, 0x1, 0x2, 0x4, 0x8, 0x10, 0x20, 0x40, 0x80, 0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26, 0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9, 0x8f, 0x3, 0x6, 0xc, 0x18, 0x30, 0x60, 0xc0, 0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35, 0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23, 0x46, 0x8c, 0x5, 0xa, 0x14, 0x28, 0x50, 0xa0, 0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1, 0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc, 0x65, 0xca, 0x89, 0xf, 0x1e, 0x3c, 0x78, 0xf0, 0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f, 0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2, 0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0xd, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce, 0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93, 0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc, 0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9, 0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54, 0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa, 0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73, 0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e, 0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff, 0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4, 0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41, 0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x7, 0xe, 0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6, 0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef, 0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x9, 0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5, 0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0xb, 0x16, 0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83, 0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e};


byte mulTable[256][256] = {{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}, {0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8, 0x9, 0xa, 0xb, 0xc, 0xd, 0xe, 0xf, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f, 0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47, 0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f, 0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57, 0x58, 0x59, 0x5a, 0x5b, 0x5c, 0x5d, 0x5e, 0x5f, 0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67, 0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f, 0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77, 0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f, 0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87, 0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f, 0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97, 0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f, 0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7, 0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf, 0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7, 0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf, 0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7, 0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf, 0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7, 0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf, 0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7, 0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef, 0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7, 0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff}, {0x0, 0x2, 0x4, 0x6, 0x8, 0xa, 0xc, 0xe, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1a, 0x1c, 0x1e, 0x20, 0x22, 0x24, 0x26, 0x28, 0x2a, 0x2c, 0x2e, 0x30, 0x32, 0x34, 0x36, 0x38, 0x3a, 0x3c, 0x3e, 0x40, 0x42, 0x44, 0x46, 0x48, 0x4a, 0x4c, 0x4e, 0x50, 0x52, 0x54, 0x56, 0x58, 0x5a, 0x5c, 0x5e, 0x60, 0x62, 0x64, 0x66, 0x68, 0x6a, 0x6c, 0x6e, 0x70, 0x72, 0x74, 0x76, 0x78, 0x7a, 0x7c, 0x7e, 0x80, 0x82, 0x84, 0x86, 0x88, 0x8a, 0x8c, 0x8e, 0x90, 0x92, 0x94, 0x96, 0x98, 0x9a, 0x9c, 0x9e, 0xa0, 0xa2, 0xa4, 0xa6, 0xa8, 0xaa, 0xac, 0xae, 0xb0, 0xb2, 0xb4, 0xb6, 0xb8, 0xba, 0xbc, 0xbe, 0xc0, 0xc2, 0xc4, 0xc6, 0xc8, 0xca, 0xcc, 0xce, 0xd0, 0xd2, 0xd4, 0xd6, 0xd8, 0xda, 0xdc, 0xde, 0xe0, 0xe2, 0xe4, 0xe6, 0xe8, 0xea, 0xec, 0xee, 0xf0, 0xf2, 0xf4, 0xf6, 0xf8, 0xfa, 0xfc, 0xfe, 0x1d, 0x1f, 0x19, 0x1b, 0x15, 0x17, 0x11, 0x13, 0xd, 0xf, 0x9, 0xb, 0x5, 0x7, 0x1, 0x3, 0x3d, 0x3f, 0x39, 0x3b, 0x35, 0x37, 0x31, 0x33, 0x2d, 0x2f, 0x29, 0x2b, 0x25, 0x27, 0x21, 0x23, 0x5d, 0x5f, 0x59, 0x5b, 0x55, 0x57, 0x51, 0x53, 0x4d, 0x4f, 0x49, 0x4b, 0x45, 0x47, 0x41, 0x43, 0x7d, 0x7f, 0x79, 0x7b, 0x75, 0x77, 0x71, 0x73, 0x6d, 0x6f, 0x69, 0x6b, 0x65, 0x67, 0x61, 0x63, 0x9d, 0x9f, 0x99, 0x9b, 0x95, 0x97, 0x91, 0x93, 0x8d, 0x8f, 0x89, 0x8b, 0x85, 0x87, 0x81, 0x83, 0xbd, 0xbf, 0xb9, 0xbb, 0xb5, 0xb7, 0xb1, 0xb3, 0xad, 0xaf, 0xa9, 0xab, 0xa5, 0xa7, 0xa1, 0xa3, 0xdd, 0xdf, 0xd9, 0xdb, 0xd5, 0xd7, 0xd1, 0xd3, 0xcd, 0xcf, 0xc9, 0xcb, 0xc5, 0xc7, 0xc1, 0xc3, 0xfd, 0xff, 0xf9, 0xfb, 0xf5, 0xf7, 0xf1, 0xf3, 0xed, 0xef, 0xe9, 0xeb, 0xe5, 0xe7, 0xe1, 0xe3}, {0x0, 0x3, 0x6, 0x5, 0xc, 0xf, 0xa, 0x9, 0x18, 0x1b, 0x1e, 0x1d, 0x14, 0x17, 0x12, 0x11, 0x30, 0x33, 0x36, 0x35, 0x3c, 0x3f, 0x3a, 0x39, 0x28, 0x2b, 0x2e, 0x2d, 0x24, 0x27, 0x22, 0x21, 0x60, 0x63, 0x66, 0x65, 0x6c, 0x6f, 0x6a, 0x69, 0x78, 0x7b, 0x7e, 0x7d, 0x74, 0x77, 0x72, 0x71, 0x50, 0x53, 0x56, 0x55, 0x5c, 0x5f, 0x5a, 0x59, 0x48, 0x4b, 0x4e, 0x4d, 0x44, 0x47, 0x42, 0x41, 0xc0, 0xc3, 0xc6, 0xc5, 0xcc, 0xcf, 0xca, 0xc9, 0xd8, 0xdb, 0xde, 0xdd, 0xd4, 0xd7, 0xd2, 0xd1, 0xf0, 0xf3, 0xf6, 0xf5, 0xfc, 0xff, 0xfa, 0xf9, 0xe8, 0xeb, 0xee, 0xed, 0xe4, 0xe7, 0xe2, 0xe1, 0xa0, 0xa3, 0xa6, 0xa5, 0xac, 0xaf, 0xaa, 0xa9, 0xb8, 0xbb, 0xbe, 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0xf3, 0xf, 0xe, 0xf2, 0xeb, 0x17, 0xd9, 0x25, 0x3c, 0xc0, 0xbd, 0x41, 0x58, 0xa4, 0x6a, 0x96, 0x8f, 0x73, 0x75, 0x89, 0x90, 0x6c, 0xa2, 0x5e, 0x47, 0xbb, 0xc6, 0x3a, 0x23, 0xdf, 0x11, 0xed, 0xf4, 0x8, 0xf8, 0x4, 0x1d, 0xe1, 0x2f, 0xd3, 0xca, 0x36, 0x4b, 0xb7, 0xae, 0x52, 0x9c, 0x60, 0x79, 0x85, 0x83, 0x7f, 0x66, 0x9a, 0x54, 0xa8, 0xb1, 0x4d, 0x30, 0xcc, 0xd5, 0x29, 0xe7, 0x1b, 0x2, 0xfe}, {0x0, 0xfd, 0xe7, 0x1a, 0xd3, 0x2e, 0x34, 0xc9, 0xbb, 0x46, 0x5c, 0xa1, 0x68, 0x95, 0x8f, 0x72, 0x6b, 0x96, 0x8c, 0x71, 0xb8, 0x45, 0x5f, 0xa2, 0xd0, 0x2d, 0x37, 0xca, 0x3, 0xfe, 0xe4, 0x19, 0xd6, 0x2b, 0x31, 0xcc, 0x5, 0xf8, 0xe2, 0x1f, 0x6d, 0x90, 0x8a, 0x77, 0xbe, 0x43, 0x59, 0xa4, 0xbd, 0x40, 0x5a, 0xa7, 0x6e, 0x93, 0x89, 0x74, 0x6, 0xfb, 0xe1, 0x1c, 0xd5, 0x28, 0x32, 0xcf, 0xb1, 0x4c, 0x56, 0xab, 0x62, 0x9f, 0x85, 0x78, 0xa, 0xf7, 0xed, 0x10, 0xd9, 0x24, 0x3e, 0xc3, 0xda, 0x27, 0x3d, 0xc0, 0x9, 0xf4, 0xee, 0x13, 0x61, 0x9c, 0x86, 0x7b, 0xb2, 0x4f, 0x55, 0xa8, 0x67, 0x9a, 0x80, 0x7d, 0xb4, 0x49, 0x53, 0xae, 0xdc, 0x21, 0x3b, 0xc6, 0xf, 0xf2, 0xe8, 0x15, 0xc, 0xf1, 0xeb, 0x16, 0xdf, 0x22, 0x38, 0xc5, 0xb7, 0x4a, 0x50, 0xad, 0x64, 0x99, 0x83, 0x7e, 0x7f, 0x82, 0x98, 0x65, 0xac, 0x51, 0x4b, 0xb6, 0xc4, 0x39, 0x23, 0xde, 0x17, 0xea, 0xf0, 0xd, 0x14, 0xe9, 0xf3, 0xe, 0xc7, 0x3a, 0x20, 0xdd, 0xaf, 0x52, 0x48, 0xb5, 0x7c, 0x81, 0x9b, 0x66, 0xa9, 0x54, 0x4e, 0xb3, 0x7a, 0x87, 0x9d, 0x60, 0x12, 0xef, 0xf5, 0x8, 0xc1, 0x3c, 0x26, 0xdb, 0xc2, 0x3f, 0x25, 0xd8, 0x11, 0xec, 0xf6, 0xb, 0x79, 0x84, 0x9e, 0x63, 0xaa, 0x57, 0x4d, 0xb0, 0xce, 0x33, 0x29, 0xd4, 0x1d, 0xe0, 0xfa, 0x7, 0x75, 0x88, 0x92, 0x6f, 0xa6, 0x5b, 0x41, 0xbc, 0xa5, 0x58, 0x42, 0xbf, 0x76, 0x8b, 0x91, 0x6c, 0x1e, 0xe3, 0xf9, 0x4, 0xcd, 0x30, 0x2a, 0xd7, 0x18, 0xe5, 0xff, 0x2, 0xcb, 0x36, 0x2c, 0xd1, 0xa3, 0x5e, 0x44, 0xb9, 0x70, 0x8d, 0x97, 0x6a, 0x73, 0x8e, 0x94, 0x69, 0xa0, 0x5d, 0x47, 0xba, 0xc8, 0x35, 0x2f, 0xd2, 0x1b, 0xe6, 0xfc, 0x1}, {0x0, 0xfe, 0xe1, 0x1f, 0xdf, 0x21, 0x3e, 0xc0, 0xa3, 0x5d, 0x42, 0xbc, 0x7c, 0x82, 0x9d, 0x63, 0x5b, 0xa5, 0xba, 0x44, 0x84, 0x7a, 0x65, 0x9b, 0xf8, 0x6, 0x19, 0xe7, 0x27, 0xd9, 0xc6, 0x38, 0xb6, 0x48, 0x57, 0xa9, 0x69, 0x97, 0x88, 0x76, 0x15, 0xeb, 0xf4, 0xa, 0xca, 0x34, 0x2b, 0xd5, 0xed, 0x13, 0xc, 0xf2, 0x32, 0xcc, 0xd3, 0x2d, 0x4e, 0xb0, 0xaf, 0x51, 0x91, 0x6f, 0x70, 0x8e, 0x71, 0x8f, 0x90, 0x6e, 0xae, 0x50, 0x4f, 0xb1, 0xd2, 0x2c, 0x33, 0xcd, 0xd, 0xf3, 0xec, 0x12, 0x2a, 0xd4, 0xcb, 0x35, 0xf5, 0xb, 0x14, 0xea, 0x89, 0x77, 0x68, 0x96, 0x56, 0xa8, 0xb7, 0x49, 0xc7, 0x39, 0x26, 0xd8, 0x18, 0xe6, 0xf9, 0x7, 0x64, 0x9a, 0x85, 0x7b, 0xbb, 0x45, 0x5a, 0xa4, 0x9c, 0x62, 0x7d, 0x83, 0x43, 0xbd, 0xa2, 0x5c, 0x3f, 0xc1, 0xde, 0x20, 0xe0, 0x1e, 0x1, 0xff, 0xe2, 0x1c, 0x3, 0xfd, 0x3d, 0xc3, 0xdc, 0x22, 0x41, 0xbf, 0xa0, 0x5e, 0x9e, 0x60, 0x7f, 0x81, 0xb9, 0x47, 0x58, 0xa6, 0x66, 0x98, 0x87, 0x79, 0x1a, 0xe4, 0xfb, 0x5, 0xc5, 0x3b, 0x24, 0xda, 0x54, 0xaa, 0xb5, 0x4b, 0x8b, 0x75, 0x6a, 0x94, 0xf7, 0x9, 0x16, 0xe8, 0x28, 0xd6, 0xc9, 0x37, 0xf, 0xf1, 0xee, 0x10, 0xd0, 0x2e, 0x31, 0xcf, 0xac, 0x52, 0x4d, 0xb3, 0x73, 0x8d, 0x92, 0x6c, 0x93, 0x6d, 0x72, 0x8c, 0x4c, 0xb2, 0xad, 0x53, 0x30, 0xce, 0xd1, 0x2f, 0xef, 0x11, 0xe, 0xf0, 0xc8, 0x36, 0x29, 0xd7, 0x17, 0xe9, 0xf6, 0x8, 0x6b, 0x95, 0x8a, 0x74, 0xb4, 0x4a, 0x55, 0xab, 0x25, 0xdb, 0xc4, 0x3a, 0xfa, 0x4, 0x1b, 0xe5, 0x86, 0x78, 0x67, 0x99, 0x59, 0xa7, 0xb8, 0x46, 0x7e, 0x80, 0x9f, 0x61, 0xa1, 0x5f, 0x40, 0xbe, 0xdd, 0x23, 0x3c, 0xc2, 0x2, 0xfc, 0xe3, 0x1d}, {0x0, 0xff, 0xe3, 0x1c, 0xdb, 0x24, 0x38, 0xc7, 0xab, 0x54, 0x48, 0xb7, 0x70, 0x8f, 0x93, 0x6c, 0x4b, 0xb4, 0xa8, 0x57, 0x90, 0x6f, 0x73, 0x8c, 0xe0, 0x1f, 0x3, 0xfc, 0x3b, 0xc4, 0xd8, 0x27, 0x96, 0x69, 0x75, 0x8a, 0x4d, 0xb2, 0xae, 0x51, 0x3d, 0xc2, 0xde, 0x21, 0xe6, 0x19, 0x5, 0xfa, 0xdd, 0x22, 0x3e, 0xc1, 0x6, 0xf9, 0xe5, 0x1a, 0x76, 0x89, 0x95, 0x6a, 0xad, 0x52, 0x4e, 0xb1, 0x31, 0xce, 0xd2, 0x2d, 0xea, 0x15, 0x9, 0xf6, 0x9a, 0x65, 0x79, 0x86, 0x41, 0xbe, 0xa2, 0x5d, 0x7a, 0x85, 0x99, 0x66, 0xa1, 0x5e, 0x42, 0xbd, 0xd1, 0x2e, 0x32, 0xcd, 0xa, 0xf5, 0xe9, 0x16, 0xa7, 0x58, 0x44, 0xbb, 0x7c, 0x83, 0x9f, 0x60, 0xc, 0xf3, 0xef, 0x10, 0xd7, 0x28, 0x34, 0xcb, 0xec, 0x13, 0xf, 0xf0, 0x37, 0xc8, 0xd4, 0x2b, 0x47, 0xb8, 0xa4, 0x5b, 0x9c, 0x63, 0x7f, 0x80, 0x62, 0x9d, 0x81, 0x7e, 0xb9, 0x46, 0x5a, 0xa5, 0xc9, 0x36, 0x2a, 0xd5, 0x12, 0xed, 0xf1, 0xe, 0x29, 0xd6, 0xca, 0x35, 0xf2, 0xd, 0x11, 0xee, 0x82, 0x7d, 0x61, 0x9e, 0x59, 0xa6, 0xba, 0x45, 0xf4, 0xb, 0x17, 0xe8, 0x2f, 0xd0, 0xcc, 0x33, 0x5f, 0xa0, 0xbc, 0x43, 0x84, 0x7b, 0x67, 0x98, 0xbf, 0x40, 0x5c, 0xa3, 0x64, 0x9b, 0x87, 0x78, 0x14, 0xeb, 0xf7, 0x8, 0xcf, 0x30, 0x2c, 0xd3, 0x53, 0xac, 0xb0, 0x4f, 0x88, 0x77, 0x6b, 0x94, 0xf8, 0x7, 0x1b, 0xe4, 0x23, 0xdc, 0xc0, 0x3f, 0x18, 0xe7, 0xfb, 0x4, 0xc3, 0x3c, 0x20, 0xdf, 0xb3, 0x4c, 0x50, 0xaf, 0x68, 0x97, 0x8b, 0x74, 0xc5, 0x3a, 0x26, 0xd9, 0x1e, 0xe1, 0xfd, 0x2, 0x6e, 0x91, 0x8d, 0x72, 0xb5, 0x4a, 0x56, 0xa9, 0x8e, 0x71, 0x6d, 0x92, 0x55, 0xaa, 0xb6, 0x49, 0x25, 0xda, 0xc6, 0x39, 0xfe, 0x1, 0x1d, 0xe2}};

const byte mulTableLow[256][16] = {{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}, {0x0, 0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8, 0x9, 0xa, 0xb, 0xc, 0xd, 0xe, 0xf}, {0x0, 0x2, 0x4, 0x6, 0x8, 0xa, 0xc, 0xe, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1a, 0x1c, 0x1e}, {0x0, 0x3, 0x6, 0x5, 0xc, 0xf, 0xa, 0x9, 0x18, 0x1b, 0x1e, 0x1d, 0x14, 0x17, 0x12, 0x11}, {0x0, 0x4, 0x8, 0xc, 0x10, 0x14, 0x18, 0x1c, 0x20, 0x24, 0x28, 0x2c, 0x30, 0x34, 0x38, 0x3c}, {0x0, 0x5, 0xa, 0xf, 0x14, 0x11, 0x1e, 0x1b, 0x28, 0x2d, 0x22, 0x27, 0x3c, 0x39, 0x36, 0x33}, {0x0, 0x6, 0xc, 0xa, 0x18, 0x1e, 0x14, 0x12, 0x30, 0x36, 0x3c, 0x3a, 0x28, 0x2e, 0x24, 0x22}, {0x0, 0x7, 0xe, 0x9, 0x1c, 0x1b, 0x12, 0x15, 0x38, 0x3f, 0x36, 0x31, 0x24, 0x23, 0x2a, 0x2d}, {0x0, 0x8, 0x10, 0x18, 0x20, 0x28, 0x30, 0x38, 0x40, 0x48, 0x50, 0x58, 0x60, 0x68, 0x70, 0x78}, {0x0, 0x9, 0x12, 0x1b, 0x24, 0x2d, 0x36, 0x3f, 0x48, 0x41, 0x5a, 0x53, 0x6c, 0x65, 0x7e, 0x77}, {0x0, 0xa, 0x14, 0x1e, 0x28, 0x22, 0x3c, 0x36, 0x50, 0x5a, 0x44, 0x4e, 0x78, 0x72, 0x6c, 0x66}, {0x0, 0xb, 0x16, 0x1d, 0x2c, 0x27, 0x3a, 0x31, 0x58, 0x53, 0x4e, 0x45, 0x74, 0x7f, 0x62, 0x69}, {0x0, 0xc, 0x18, 0x14, 0x30, 0x3c, 0x28, 0x24, 0x60, 0x6c, 0x78, 0x74, 0x50, 0x5c, 0x48, 0x44}, {0x0, 0xd, 0x1a, 0x17, 0x34, 0x39, 0x2e, 0x23, 0x68, 0x65, 0x72, 0x7f, 0x5c, 0x51, 0x46, 0x4b}, {0x0, 0xe, 0x1c, 0x12, 0x38, 0x36, 0x24, 0x2a, 0x70, 0x7e, 0x6c, 0x62, 0x48, 0x46, 0x54, 0x5a}, {0x0, 0xf, 0x1e, 0x11, 0x3c, 0x33, 0x22, 0x2d, 0x78, 0x77, 0x66, 0x69, 0x44, 0x4b, 0x5a, 0x55}, {0x0, 0x10, 0x20, 0x30, 0x40, 0x50, 0x60, 0x70, 0x80, 0x90, 0xa0, 0xb0, 0xc0, 0xd0, 0xe0, 0xf0}, {0x0, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77, 0x88, 0x99, 0xaa, 0xbb, 0xcc, 0xdd, 0xee, 0xff}, {0x0, 0x12, 0x24, 0x36, 0x48, 0x5a, 0x6c, 0x7e, 0x90, 0x82, 0xb4, 0xa6, 0xd8, 0xca, 0xfc, 0xee}, {0x0, 0x13, 0x26, 0x35, 0x4c, 0x5f, 0x6a, 0x79, 0x98, 0x8b, 0xbe, 0xad, 0xd4, 0xc7, 0xf2, 0xe1}, {0x0, 0x14, 0x28, 0x3c, 0x50, 0x44, 0x78, 0x6c, 0xa0, 0xb4, 0x88, 0x9c, 0xf0, 0xe4, 0xd8, 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