#include "mycrypt.h" #ifdef MPI #ifdef SMALL_PRIME_TAB static const mp_digit prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083, 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137 }; #else static const mp_digit prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083, 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199, 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9, 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7, 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239, 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265, 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293, 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF, 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301, 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B, 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371, 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD, 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5, 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419, 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449, 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B, 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7, 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503, 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529, 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F, 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3, 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653, 0x0655, 0x065B, 0x0665, 0x0679, 0x067F, 0x0683, 0x0685, 0x069D, 0x06A1, 0x06A3, 0x06AD, 0x06B9, 0x06BB, 0x06C5, 0x06CD, 0x06D3, 0x06D9, 0x06DF, 0x06F1, 0x06F7, 0x06FB, 0x06FD, 0x0709, 0x0713, 0x071F, 0x0727, 0x0737, 0x0745, 0x074B, 0x074F, 0x0751, 0x0755, 0x0757, 0x0761, 0x076D, 0x0773, 0x0779, 0x078B, 0x078D, 0x079D, 0x079F, 0x07B5, 0x07BB, 0x07C3, 0x07C9, 0x07CD, 0x07CF, 0x07D3, 0x07DB, 0x07E1, 0x07EB, 0x07ED, 0x07F7, 0x0805, 0x080F, 0x0815, 0x0821, 0x0823, 0x0827, 0x0829, 0x0833, 0x083F, 0x0841, 0x0851, 0x0853, 0x0859, 0x085D, 0x085F, 0x0869, 0x0871, 0x0883, 0x089B, 0x089F, 0x08A5, 0x08AD, 0x08BD, 0x08BF, 0x08C3, 0x08CB, 0x08DB, 0x08DD, 0x08E1, 0x08E9, 0x08EF, 0x08F5, 0x08F9, 0x0905, 0x0907, 0x091D, 0x0923, 0x0925, 0x092B, 0x092F, 0x0935, 0x0943, 0x0949, 0x094D, 0x094F, 0x0955, 0x0959, 0x095F, 0x096B, 0x0971, 0x0977, 0x0985, 0x0989, 0x098F, 0x099B, 0x09A3, 0x09A9, 0x09AD, 0x09C7, 0x09D9, 0x09E3, 0x09EB, 0x09EF, 0x09F5, 0x09F7, 0x09FD, 0x0A13, 0x0A1F, 0x0A21, 0x0A31, 0x0A39, 0x0A3D, 0x0A49, 0x0A57, 0x0A61, 0x0A63, 0x0A67, 0x0A6F, 0x0A75, 0x0A7B, 0x0A7F, 0x0A81, 0x0A85, 0x0A8B, 0x0A93, 0x0A97, 0x0A99, 0x0A9F, 0x0AA9, 0x0AAB, 0x0AB5, 0x0ABD, 0x0AC1, 0x0ACF, 0x0AD9, 0x0AE5, 0x0AE7, 0x0AED, 0x0AF1, 0x0AF3, 0x0B03, 0x0B11, 0x0B15, 0x0B1B, 0x0B23, 0x0B29, 0x0B2D, 0x0B3F, 0x0B47, 0x0B51, 0x0B57, 0x0B5D, 0x0B65, 0x0B6F, 0x0B7B, 0x0B89, 0x0B8D, 0x0B93, 0x0B99, 0x0B9B, 0x0BB7, 0x0BB9, 0x0BC3, 0x0BCB, 0x0BCF, 0x0BDD, 0x0BE1, 0x0BE9, 0x0BF5, 0x0BFB, 0x0C07, 0x0C0B, 0x0C11, 0x0C25, 0x0C2F, 0x0C31, 0x0C41, 0x0C5B, 0x0C5F, 0x0C61, 0x0C6D, 0x0C73, 0x0C77, 0x0C83, 0x0C89, 0x0C91, 0x0C95, 0x0C9D, 0x0CB3, 0x0CB5, 0x0CB9, 0x0CBB, 0x0CC7, 0x0CE3, 0x0CE5, 0x0CEB, 0x0CF1, 0x0CF7, 0x0CFB, 0x0D01, 0x0D03, 0x0D0F, 0x0D13, 0x0D1F, 0x0D21, 0x0D2B, 0x0D2D, 0x0D3D, 0x0D3F, 0x0D4F, 0x0D55, 0x0D69, 0x0D79, 0x0D81, 0x0D85, 0x0D87, 0x0D8B, 0x0D8D, 0x0DA3, 0x0DAB, 0x0DB7, 0x0DBD, 0x0DC7, 0x0DC9, 0x0DCD, 0x0DD3, 0x0DD5, 0x0DDB, 0x0DE5, 0x0DE7, 0x0DF3, 0x0DFD, 0x0DFF, 0x0E09, 0x0E17, 0x0E1D, 0x0E21, 0x0E27, 0x0E2F, 0x0E35, 0x0E3B, 0x0E4B, 0x0E57, 0x0E59, 0x0E5D, 0x0E6B, 0x0E71, 0x0E75, 0x0E7D, 0x0E87, 0x0E8F, 0x0E95, 0x0E9B, 0x0EB1, 0x0EB7, 0x0EB9, 0x0EC3, 0x0ED1, 0x0ED5, 0x0EDB, 0x0EED, 0x0EEF, 0x0EF9, 0x0F07, 0x0F0B, 0x0F0D, 0x0F17, 0x0F25, 0x0F29, 0x0F31, 0x0F43, 0x0F47, 0x0F4D, 0x0F4F, 0x0F53, 0x0F59, 0x0F5B, 0x0F67, 0x0F6B, 0x0F7F, 0x0F95, 0x0FA1, 0x0FA3, 0x0FA7, 0x0FAD, 0x0FB3, 0x0FB5, 0x0FBB, 0x0FD1, 0x0FD3, 0x0FD9, 0x0FE9, 0x0FEF, 0x0FFB, 0x0FFD, 0x1003, 0x100F, 0x101F, 0x1021, 0x1025, 0x102B, 0x1039, 0x103D, 0x103F, 0x1051, 0x1069, 0x1073, 0x1079, 0x107B, 0x1085, 0x1087, 0x1091, 0x1093, 0x109D, 0x10A3, 0x10A5, 0x10AF, 0x10B1, 0x10BB, 0x10C1, 0x10C9, 0x10E7, 0x10F1, 0x10F3, 0x10FD, 0x1105, 0x110B, 0x1115, 0x1127, 0x112D, 0x1139, 0x1145, 0x1147, 0x1159, 0x115F, 0x1163, 0x1169, 0x116F, 0x1181, 0x1183, 0x118D, 0x119B, 0x11A1, 0x11A5, 0x11A7, 0x11AB, 0x11C3, 0x11C5, 0x11D1, 0x11D7, 0x11E7, 0x11EF, 0x11F5, 0x11FB, 0x120D, 0x121D, 0x121F, 0x1223, 0x1229, 0x122B, 0x1231, 0x1237, 0x1241, 0x1247, 0x1253, 0x125F, 0x1271, 0x1273, 0x1279, 0x127D, 0x128F, 0x1297, 0x12AF, 0x12B3, 0x12B5, 0x12B9, 0x12BF, 0x12C1, 0x12CD, 0x12D1, 0x12DF, 0x12FD, 0x1307, 0x130D, 0x1319, 0x1327, 0x132D, 0x1337, 0x1343, 0x1345, 0x1349, 0x134F, 0x1357, 0x135D, 0x1367, 0x1369, 0x136D, 0x137B, 0x1381, 0x1387, 0x138B, 0x1391, 0x1393, 0x139D, 0x139F, 0x13AF, 0x13BB, 0x13C3, 0x13D5, 0x13D9, 0x13DF, 0x13EB, 0x13ED, 0x13F3, 0x13F9, 0x13FF, 0x141B, 0x1421, 0x142F, 0x1433, 0x143B, 0x1445, 0x144D, 0x1459, 0x146B, 0x146F, 0x1471, 0x1475, 0x148D, 0x1499, 0x149F, 0x14A1, 0x14B1, 0x14B7, 0x14BD, 0x14CB, 0x14D5, 0x14E3, 0x14E7, 0x1505, 0x150B, 0x1511, 0x1517, 0x151F, 0x1525, 0x1529, 0x152B, 0x1537, 0x153D, 0x1541, 0x1543, 0x1549, 0x155F, 0x1565, 0x1567, 0x156B, 0x157D, 0x157F, 0x1583, 0x158F, 0x1591, 0x1597, 0x159B, 0x15B5, 0x15BB, 0x15C1, 0x15C5, 0x15CD, 0x15D7, 0x15F7, 0x1607, 0x1609, 0x160F, 0x1613, 0x1615, 0x1619, 0x161B, 0x1625, 0x1633, 0x1639, 0x163D, 0x1645, 0x164F, 0x1655, 0x1669, 0x166D, 0x166F, 0x1675, 0x1693, 0x1697, 0x169F, 0x16A9, 0x16AF, 0x16B5, 0x16BD, 0x16C3, 0x16CF, 0x16D3, 0x16D9, 0x16DB, 0x16E1, 0x16E5, 0x16EB, 0x16ED, 0x16F7, 0x16F9, 0x1709, 0x170F, 0x1723, 0x1727, 0x1733, 0x1741, 0x175D, 0x1763, 0x1777, 0x177B, 0x178D, 0x1795, 0x179B, 0x179F, 0x17A5, 0x17B3, 0x17B9, 0x17BF, 0x17C9, 0x17CB, 0x17D5, 0x17E1, 0x17E9, 0x17F3, 0x17F5, 0x17FF, 0x1807, 0x1813, 0x181D, 0x1835, 0x1837, 0x183B, 0x1843, 0x1849, 0x184D, 0x1855, 0x1867, 0x1871, 0x1877, 0x187D, 0x187F, 0x1885, 0x188F, 0x189B, 0x189D, 0x18A7, 0x18AD, 0x18B3, 0x18B9, 0x18C1, 0x18C7, 0x18D1, 0x18D7, 0x18D9, 0x18DF, 0x18E5, 0x18EB, 0x18F5, 0x18FD, 0x1915, 0x191B, 0x1931, 0x1933, 0x1945, 0x1949, 0x1951, 0x195B, 0x1979, 0x1981, 0x1993, 0x1997, 0x1999, 0x19A3, 0x19A9, 0x19AB, 0x19B1, 0x19B5, 0x19C7, 0x19CF, 0x19DB, 0x19ED, 0x19FD, 0x1A03, 0x1A05, 0x1A11, 0x1A17, 0x1A21, 0x1A23, 0x1A2D, 0x1A2F, 0x1A35, 0x1A3F, 0x1A4D, 0x1A51, 0x1A69, 0x1A6B, 0x1A7B, 0x1A7D, 0x1A87, 0x1A89, 0x1A93, 0x1AA7, 0x1AAB, 0x1AAD, 0x1AB1, 0x1AB9, 0x1AC9, 0x1ACF, 0x1AD5, 0x1AD7, 0x1AE3, 0x1AF3, 0x1AFB, 0x1AFF, 0x1B05, 0x1B23, 0x1B25, 0x1B2F, 0x1B31, 0x1B37, 0x1B3B, 0x1B41, 0x1B47, 0x1B4F, 0x1B55, 0x1B59, 0x1B65, 0x1B6B, 0x1B73, 0x1B7F, 0x1B83, 0x1B91, 0x1B9D, 0x1BA7, 0x1BBF, 0x1BC5, 0x1BD1, 0x1BD7, 0x1BD9, 0x1BEF, 0x1BF7, 0x1C09, 0x1C13, 0x1C19, 0x1C27, 0x1C2B, 0x1C2D, 0x1C33, 0x1C3D, 0x1C45, 0x1C4B, 0x1C4F, 0x1C55, 0x1C73, 0x1C81, 0x1C8B, 0x1C8D, 0x1C99, 0x1CA3, 0x1CA5, 0x1CB5, 0x1CB7, 0x1CC9, 0x1CE1, 0x1CF3, 0x1CF9, 0x1D09, 0x1D1B, 0x1D21, 0x1D23, 0x1D35, 0x1D39, 0x1D3F, 0x1D41, 0x1D4B, 0x1D53, 0x1D5D, 0x1D63, 0x1D69, 0x1D71, 0x1D75, 0x1D7B, 0x1D7D, 0x1D87, 0x1D89, 0x1D95, 0x1D99, 0x1D9F, 0x1DA5, 0x1DA7, 0x1DB3, 0x1DB7, 0x1DC5, 0x1DD7, 0x1DDB, 0x1DE1, 0x1DF5, 0x1DF9, 0x1E01, 0x1E07, 0x1E0B, 0x1E13, 0x1E17, 0x1E25, 0x1E2B, 0x1E2F, 0x1E3D, 0x1E49, 0x1E4D, 0x1E4F, 0x1E6D, 0x1E71, 0x1E89, 0x1E8F, 0x1E95, 0x1EA1, 0x1EAD, 0x1EBB, 0x1EC1, 0x1EC5, 0x1EC7, 0x1ECB, 0x1EDD, 0x1EE3, 0x1EEF, 0x1EF7, 0x1EFD, 0x1F01, 0x1F0D, 0x1F0F, 0x1F1B, 0x1F39, 0x1F49, 0x1F4B, 0x1F51, 0x1F67, 0x1F75, 0x1F7B, 0x1F85, 0x1F91, 0x1F97, 0x1F99, 0x1F9D, 0x1FA5, 0x1FAF, 0x1FB5, 0x1FBB, 0x1FD3, 0x1FE1, 0x1FE7, 0x1FEB, 0x1FF3, 0x1FFF, 0x2011, 0x201B, 0x201D, 0x2027, 0x2029, 0x202D, 0x2033, 0x2047, 0x204D, 0x2051, 0x205F, 0x2063, 0x2065, 0x2069, 0x2077, 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0xE453, 0xE455, 0xE46D, 0xE471, 0xE48F, 0xE4A9, 0xE4AF, 0xE4B5, 0xE4C7, 0xE4CD, 0xE4D3, 0xE4E9, 0xE4EB, 0xE4F5, 0xE507, 0xE521, 0xE525, 0xE537, 0xE53F, 0xE545, 0xE54B, 0xE557, 0xE567, 0xE56D, 0xE575, 0xE585, 0xE58B, 0xE593, 0xE5A3, 0xE5A5, 0xE5CF, 0xE609, 0xE611, 0xE615, 0xE61B, 0xE61D, 0xE621, 0xE629, 0xE639, 0xE63F, 0xE653, 0xE657, 0xE663, 0xE66F, 0xE675, 0xE681, 0xE683, 0xE68D, 0xE68F, 0xE695, 0xE6AB, 0xE6AD, 0xE6B7, 0xE6BD, 0xE6C5, 0xE6CB, 0xE6D5, 0xE6E3, 0xE6E9, 0xE6EF, 0xE6F3, 0xE705, 0xE70D, 0xE717, 0xE71F, 0xE72F, 0xE73D, 0xE747, 0xE749, 0xE753, 0xE755, 0xE761, 0xE767, 0xE76B, 0xE77F, 0xE789, 0xE791, 0xE7C5, 0xE7CD, 0xE7D7, 0xE7DD, 0xE7DF, 0xE7E9, 0xE7F1, 0xE7FB, 0xE801, 0xE807, 0xE80F, 0xE819, 0xE81B, 0xE831, 0xE833, 0xE837, 0xE83D, 0xE84B, 0xE84F, 0xE851, 0xE869, 0xE875, 0xE879, 0xE893, 0xE8A5, 0xE8A9, 0xE8AF, 0xE8BD, 0xE8DB, 0xE8E1, 0xE8E5, 0xE8EB, 0xE8ED, 0xE903, 0xE90B, 0xE90F, 0xE915, 0xE917, 0xE92D, 0xE933, 0xE93B, 0xE94B, 0xE951, 0xE95F, 0xE963, 0xE969, 0xE97B, 0xE983, 0xE98F, 0xE995, 0xE9A1, 0xE9B9, 0xE9D7, 0xE9E7, 0xE9EF, 0xEA11, 0xEA19, 0xEA2F, 0xEA35, 0xEA43, 0xEA4D, 0xEA5F, 0xEA6D, 0xEA71, 0xEA7D, 0xEA85, 0xEA89, 0xEAAD, 0xEAB3, 0xEAB9, 0xEABB, 0xEAC5, 0xEAC7, 0xEACB, 0xEADF, 0xEAE5, 0xEAEB, 0xEAF5, 0xEB01, 0xEB07, 0xEB09, 0xEB31, 0xEB39, 0xEB3F, 0xEB5B, 0xEB61, 0xEB63, 0xEB6F, 0xEB81, 0xEB85, 0xEB9D, 0xEBAB, 0xEBB1, 0xEBB7, 0xEBC1, 0xEBD5, 0xEBDF, 0xEBED, 0xEBFD, 0xEC0B, 0xEC1B, 0xEC21, 0xEC29, 0xEC4D, 0xEC51, 0xEC5D, 0xEC69, 0xEC6F, 0xEC7B, 0xECAD, 0xECB9, 0xECBF, 0xECC3, 0xECC9, 0xECCF, 0xECD7, 0xECDD, 0xECE7, 0xECE9, 0xECF3, 0xECF5, 0xED07, 0xED11, 0xED1F, 0xED2F, 0xED37, 0xED3D, 0xED41, 0xED55, 0xED59, 0xED5B, 0xED65, 0xED6B, 0xED79, 0xED8B, 0xED95, 0xEDBB, 0xEDC5, 0xEDD7, 0xEDD9, 0xEDE3, 0xEDE5, 0xEDF1, 0xEDF5, 0xEDF7, 0xEDFB, 0xEE09, 0xEE0F, 0xEE19, 0xEE21, 0xEE49, 0xEE4F, 0xEE63, 0xEE67, 0xEE73, 0xEE7B, 0xEE81, 0xEEA3, 0xEEAB, 0xEEC1, 0xEEC9, 0xEED5, 0xEEDF, 0xEEE1, 0xEEF1, 0xEF1B, 0xEF27, 0xEF2F, 0xEF45, 0xEF4D, 0xEF63, 0xEF6B, 0xEF71, 0xEF93, 0xEF95, 0xEF9B, 0xEF9F, 0xEFAD, 0xEFB3, 0xEFC3, 0xEFC5, 0xEFDB, 0xEFE1, 0xEFE9, 0xF001, 0xF017, 0xF01D, 0xF01F, 0xF02B, 0xF02F, 0xF035, 0xF043, 0xF047, 0xF04F, 0xF067, 0xF06B, 0xF071, 0xF077, 0xF079, 0xF08F, 0xF0A3, 0xF0A9, 0xF0AD, 0xF0BB, 0xF0BF, 0xF0C5, 0xF0CB, 0xF0D3, 0xF0D9, 0xF0E3, 0xF0E9, 0xF0F1, 0xF0F7, 0xF107, 0xF115, 0xF11B, 0xF121, 0xF137, 0xF13D, 0xF155, 0xF175, 0xF17B, 0xF18D, 0xF193, 0xF1A5, 0xF1AF, 0xF1B7, 0xF1D5, 0xF1E7, 0xF1ED, 0xF1FD, 0xF209, 0xF20F, 0xF21B, 0xF21D, 0xF223, 0xF227, 0xF233, 0xF23B, 0xF241, 0xF257, 0xF25F, 0xF265, 0xF269, 0xF277, 0xF281, 0xF293, 0xF2A7, 0xF2B1, 0xF2B3, 0xF2B9, 0xF2BD, 0xF2BF, 0xF2DB, 0xF2ED, 0xF2EF, 0xF2F9, 0xF2FF, 0xF305, 0xF30B, 0xF319, 0xF341, 0xF359, 0xF35B, 0xF35F, 0xF367, 0xF373, 0xF377, 0xF38B, 0xF38F, 0xF3AF, 0xF3C1, 0xF3D1, 0xF3D7, 0xF3FB, 0xF403, 0xF409, 0xF40D, 0xF413, 0xF421, 0xF425, 0xF42B, 0xF445, 0xF44B, 0xF455, 0xF463, 0xF475, 0xF47F, 0xF485, 0xF48B, 0xF499, 0xF4A3, 0xF4A9, 0xF4AF, 0xF4BD, 0xF4C3, 0xF4DB, 0xF4DF, 0xF4ED, 0xF503, 0xF50B, 0xF517, 0xF521, 0xF529, 0xF535, 0xF547, 0xF551, 0xF563, 0xF56B, 0xF583, 0xF58D, 0xF595, 0xF599, 0xF5B1, 0xF5B7, 0xF5C9, 0xF5CF, 0xF5D1, 0xF5DB, 0xF5F9, 0xF5FB, 0xF605, 0xF607, 0xF60B, 0xF60D, 0xF635, 0xF637, 0xF653, 0xF65B, 0xF661, 0xF667, 0xF679, 0xF67F, 0xF689, 0xF697, 0xF69B, 0xF6AD, 0xF6CB, 0xF6DD, 0xF6DF, 0xF6EB, 0xF709, 0xF70F, 0xF72D, 0xF731, 0xF743, 0xF74F, 0xF751, 0xF755, 0xF763, 0xF769, 0xF773, 0xF779, 0xF781, 0xF787, 0xF791, 0xF79D, 0xF79F, 0xF7A5, 0xF7B1, 0xF7BB, 0xF7BD, 0xF7CF, 0xF7D3, 0xF7E7, 0xF7EB, 0xF7F1, 0xF7FF, 0xF805, 0xF80B, 0xF821, 0xF827, 0xF82D, 0xF835, 0xF847, 0xF859, 0xF863, 0xF865, 0xF86F, 0xF871, 0xF877, 0xF87B, 0xF881, 0xF88D, 0xF89F, 0xF8A1, 0xF8AB, 0xF8B3, 0xF8B7, 0xF8C9, 0xF8CB, 0xF8D1, 0xF8D7, 0xF8DD, 0xF8E7, 0xF8EF, 0xF8F9, 0xF8FF, 0xF911, 0xF91D, 0xF925, 0xF931, 0xF937, 0xF93B, 0xF941, 0xF94F, 0xF95F, 0xF961, 0xF96D, 0xF971, 0xF977, 0xF99D, 0xF9A3, 0xF9A9, 0xF9B9, 0xF9CD, 0xF9E9, 0xF9FD, 0xFA07, 0xFA0D, 0xFA13, 0xFA21, 0xFA25, 0xFA3F, 0xFA43, 0xFA51, 0xFA5B, 0xFA6D, 0xFA7B, 0xFA97, 0xFA99, 0xFA9D, 0xFAAB, 0xFABB, 0xFABD, 0xFAD9, 0xFADF, 0xFAE7, 0xFAED, 0xFB0F, 0xFB17, 0xFB1B, 0xFB2D, 0xFB2F, 0xFB3F, 0xFB47, 0xFB4D, 0xFB75, 0xFB7D, 0xFB8F, 0xFB93, 0xFBB1, 0xFBB7, 0xFBC3, 0xFBC5, 0xFBE3, 0xFBE9, 0xFBF3, 0xFC01, 0xFC29, 0xFC37, 0xFC41, 0xFC43, 0xFC4F, 0xFC59, 0xFC61, 0xFC65, 0xFC6D, 0xFC73, 0xFC79, 0xFC95, 0xFC97, 0xFC9B, 0xFCA7, 0xFCB5, 0xFCC5, 0xFCCD, 0xFCEB, 0xFCFB, 0xFD0D, 0xFD0F, 0xFD19, 0xFD2B, 0xFD31, 0xFD51, 0xFD55, 0xFD67, 0xFD6D, 0xFD6F, 0xFD7B, 0xFD85, 0xFD97, 0xFD99, 0xFD9F, 0xFDA9, 0xFDB7, 0xFDC9, 0xFDE5, 0xFDEB, 0xFDF3, 0xFE03, 0xFE05, 0xFE09, 0xFE1D, 0xFE27, 0xFE2F, 0xFE41, 0xFE4B, 0xFE4D, 0xFE57, 0xFE5F, 0xFE63, 0xFE69, 0xFE75, 0xFE7B, 0xFE8F, 0xFE93, 0xFE95, 0xFE9B, 0xFE9F, 0xFEB3, 0xFEBD, 0xFED7, 0xFEE9, 0xFEF3, 0xFEF5, 0xFF07, 0xFF0D, 0xFF1D, 0xFF2B, 0xFF2F, 0xFF49, 0xFF4D, 0xFF5B, 0xFF65, 0xFF71, 0xFF7F, 0xFF85, 0xFF8B, 0xFF8F, 0xFF9D, 0xFFA7, 0xFFA9, 0xFFC7, 0xFFD9, 0xFFEF, 0xFFF1 }; #endif #define UPPER_LIMIT (sizeof(prime_tab) / sizeof(prime_tab[0])) /* figures out if a number is prime (MR test) */ #ifdef CLEAN_STACK static int _is_prime(mp_int *N, int *result) #else int is_prime(mp_int *N, int *result) #endif { long x, s, j; int res; mp_int n1, a, y, r; mp_digit d; _ARGCHK(N != NULL); _ARGCHK(result != NULL); /* default to answer of no */ *result = 0; /* divisible by any of the first primes? */ for (x = 0; x < (long)UPPER_LIMIT; x++) { /* is N equal to a small prime? */ if (mp_cmp_d(N, prime_tab[x]) == 0) { *result = 1; return CRYPT_OK; } /* is N mod prime_tab[x] == 0, then its divisible by it */ if (mp_mod_d(N, prime_tab[x], &d) != MP_OKAY) { return CRYPT_MEM; } if (d == 0) { return CRYPT_OK; } } /* init variables */ if (mp_init_multi(&r, &n1, &a, &y, NULL) != MP_OKAY) { return CRYPT_MEM; } /* n1 = N - 1 */ if (mp_sub_d(N, 1, &n1) != MP_OKAY) { goto error; } /* r = N - 1 */ if (mp_copy(&n1, &r) != MP_OKAY) { goto error; } /* find s such that N = (2^s)r */ s = 0; while (mp_iseven(&r) && mp_cmp_d(&r, 0)) { ++s; if (mp_div_2(&r, &r) != MP_OKAY) { goto error; } } for (x = 0; x < 16; x++) { /* choose a */ mp_set(&a, prime_tab[x]); /* compute y = a^r mod n */ if (mp_exptmod(&a, &r, N, &y) != MP_OKAY) { goto error; } /* (y != 1) AND (y != N-1) */ if ((mp_cmp_d(&y, 1) != 0) && (mp_cmp(&y, &n1) != 0)) { /* while j <= s-1 and y != n-1 */ for (j = 1; (j <= (s-1)) && (mp_cmp(&y, &n1) != 0); j++) { /* y = y^2 mod N */ if (mp_sqrmod(&y, N, &y) != MP_OKAY) { goto error; } /* if y == 1 return false */ if (mp_cmp_d(&y, 1) == 0) { goto ok; } } /* if y != n-1 return false */ if (mp_cmp(&y, &n1) != 0) { goto ok; } } } *result = 1; ok: res = CRYPT_OK; goto done; error: res = CRYPT_MEM; done: mp_clear_multi(&a, &y, &n1, &r, NULL); return res; } #ifdef CLEAN_STACK int is_prime(mp_int *N, int *result) { int x; x = _is_prime(N, result); burn_stack(sizeof(long) * 3 + sizeof(int) + sizeof(mp_int) * 4 + sizeof(mp_digit)); return x; } #endif int rand_prime(mp_int *N, long len, prng_state *prng, int wprng) { unsigned char buf[260]; int errno, step, ormask, res; _ARGCHK(N != NULL); /* pass a negative size if you want a prime congruent to 3 mod 4 */ if (len < 0) { step = 4; ormask = 3; len = -len; } else { step = 2; ormask = 1; } /* allow sizes between 2 and 256 bytes for a prime size */ if (len < 2 || len > 256) { return CRYPT_INVALID_PRIME_SIZE; } /* valid PRNG? */ if ((errno = prng_is_valid(wprng)) != CRYPT_OK) { return errno; } /* read the prng */ if (prng_descriptor[wprng].read(buf+2, len, prng) != (unsigned long)len) { return CRYPT_ERROR_READPRNG; } /* set sign byte to zero */ buf[0] = 0; /* Set the top byte to 0x01 which makes the number a len*8 bit number */ buf[1] = 0x01; /* set the LSB to the desired settings * (1 for any prime, 3 for primes congruent to 3 mod 4) */ buf[len+1] |= ormask; /* read the number in */ if (mp_read_raw(N, buf, 2+len) != MP_OKAY) { return CRYPT_MEM; } /* add the step size to it while N is not prime */ do { if (mp_add_d(N, (mp_digit)step, N) != MP_OKAY) { return CRYPT_MEM; } if ((errno = is_prime(N, &res)) != CRYPT_OK) { return errno; } } while (res == 0); #ifdef CLEAN_STACK zeromem(buf, sizeof(buf)); #endif return CRYPT_OK; } #endif