diff options
author | Jack Lloyd <[email protected]> | 2015-11-29 02:45:49 -0500 |
---|---|---|
committer | Jack Lloyd <[email protected]> | 2015-11-29 02:45:49 -0500 |
commit | ebf2164a972517ee405428d9d0641fe296aba745 (patch) | |
tree | b60831471a37219902d5d6a165b03700f550a402 /src/lib/block | |
parent | 0bc108a29fd2e7ff6fe992ea8e6c56a5cde27e34 (diff) |
Improve side channel attack resistance of table based AES impl
Diffstat (limited to 'src/lib/block')
-rw-r--r-- | src/lib/block/aes/aes.cpp | 561 |
1 files changed, 147 insertions, 414 deletions
diff --git a/src/lib/block/aes/aes.cpp b/src/lib/block/aes/aes.cpp index 61cc9d777..0da4ff0a0 100644 --- a/src/lib/block/aes/aes.cpp +++ b/src/lib/block/aes/aes.cpp @@ -1,14 +1,47 @@ /* * AES -* (C) 1999-2010 Jack Lloyd +* (C) 1999-2010,2015 Jack Lloyd * -* Based on the public domain reference implemenation +* Based on the public domain reference implementation by Paulo Baretto * * Botan is released under the Simplified BSD License (see license.txt) */ #include <botan/aes.h> #include <botan/loadstor.h> +#include <botan/cpuid.h> +#include <botan/internal/bit_ops.h> + +/* +* This implementation is based on table lookups which are known to be +* vulnerable to timing and cache based side channel attacks. Some +* countermeasures are used which may be helpful in some situations: +* +* - Small tables are used in the first and last rounds. +* +* - The TE and TD tables are computed at runtime to avoid flush+reload +* attacks using clflush. As different processes will not share the +* same underlying table data, an attacker can't manipulate another +* processes cache lines via their shared reference to the library +* read only segment. +* +* - Each cache line of the lookup tables is accessed at the beginning +* of each call to encrypt or decrypt. (See the Z variable below) +* +* If available SSSE3 or AES-NI are used instead of this version, as both +* are faster and immune to side channel attacks. +* +* Some AES cache timing papers for reference: +* +* "Software mitigations to hedge AES against cache-based software side +* channel vulnerabilities" https://eprint.iacr.org/2006/052.pdf +* +* "Cache Games - Bringing Access-Based Cache Attacks on AES to Practice" +* http://www.ieee-security.org/TC/SP2011/PAPERS/2011/paper031.pdf +* +* "Cache-Collision Timing Attacks Against AES" Bonneau, Mironov +* http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.4753 +*/ namespace Botan { @@ -62,351 +95,56 @@ const byte SD[256] = { 0x17, 0x2B, 0x04, 0x7E, 0xBA, 0x77, 0xD6, 0x26, 0xE1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0C, 0x7D }; -const u32bit TE[1024] = { - 0xC66363A5, 0xF87C7C84, 0xEE777799, 0xF67B7B8D, 0xFFF2F20D, 0xD66B6BBD, - 0xDE6F6FB1, 0x91C5C554, 0x60303050, 0x02010103, 0xCE6767A9, 0x562B2B7D, - 0xE7FEFE19, 0xB5D7D762, 0x4DABABE6, 0xEC76769A, 0x8FCACA45, 0x1F82829D, - 0x89C9C940, 0xFA7D7D87, 0xEFFAFA15, 0xB25959EB, 0x8E4747C9, 0xFBF0F00B, - 0x41ADADEC, 0xB3D4D467, 0x5FA2A2FD, 0x45AFAFEA, 0x239C9CBF, 0x53A4A4F7, - 0xE4727296, 0x9BC0C05B, 0x75B7B7C2, 0xE1FDFD1C, 0x3D9393AE, 0x4C26266A, - 0x6C36365A, 0x7E3F3F41, 0xF5F7F702, 0x83CCCC4F, 0x6834345C, 0x51A5A5F4, - 0xD1E5E534, 0xF9F1F108, 0xE2717193, 0xABD8D873, 0x62313153, 0x2A15153F, - 0x0804040C, 0x95C7C752, 0x46232365, 0x9DC3C35E, 0x30181828, 0x379696A1, - 0x0A05050F, 0x2F9A9AB5, 0x0E070709, 0x24121236, 0x1B80809B, 0xDFE2E23D, - 0xCDEBEB26, 0x4E272769, 0x7FB2B2CD, 0xEA75759F, 0x1209091B, 0x1D83839E, - 0x582C2C74, 0x341A1A2E, 0x361B1B2D, 0xDC6E6EB2, 0xB45A5AEE, 0x5BA0A0FB, - 0xA45252F6, 0x763B3B4D, 0xB7D6D661, 0x7DB3B3CE, 0x5229297B, 0xDDE3E33E, - 0x5E2F2F71, 0x13848497, 0xA65353F5, 0xB9D1D168, 0x00000000, 0xC1EDED2C, - 0x40202060, 0xE3FCFC1F, 0x79B1B1C8, 0xB65B5BED, 0xD46A6ABE, 0x8DCBCB46, - 0x67BEBED9, 0x7239394B, 0x944A4ADE, 0x984C4CD4, 0xB05858E8, 0x85CFCF4A, - 0xBBD0D06B, 0xC5EFEF2A, 0x4FAAAAE5, 0xEDFBFB16, 0x864343C5, 0x9A4D4DD7, - 0x66333355, 0x11858594, 0x8A4545CF, 0xE9F9F910, 0x04020206, 0xFE7F7F81, - 0xA05050F0, 0x783C3C44, 0x259F9FBA, 0x4BA8A8E3, 0xA25151F3, 0x5DA3A3FE, - 0x804040C0, 0x058F8F8A, 0x3F9292AD, 0x219D9DBC, 0x70383848, 0xF1F5F504, - 0x63BCBCDF, 0x77B6B6C1, 0xAFDADA75, 0x42212163, 0x20101030, 0xE5FFFF1A, - 0xFDF3F30E, 0xBFD2D26D, 0x81CDCD4C, 0x180C0C14, 0x26131335, 0xC3ECEC2F, - 0xBE5F5FE1, 0x359797A2, 0x884444CC, 0x2E171739, 0x93C4C457, 0x55A7A7F2, - 0xFC7E7E82, 0x7A3D3D47, 0xC86464AC, 0xBA5D5DE7, 0x3219192B, 0xE6737395, - 0xC06060A0, 0x19818198, 0x9E4F4FD1, 0xA3DCDC7F, 0x44222266, 0x542A2A7E, - 0x3B9090AB, 0x0B888883, 0x8C4646CA, 0xC7EEEE29, 0x6BB8B8D3, 0x2814143C, - 0xA7DEDE79, 0xBC5E5EE2, 0x160B0B1D, 0xADDBDB76, 0xDBE0E03B, 0x64323256, - 0x743A3A4E, 0x140A0A1E, 0x924949DB, 0x0C06060A, 0x4824246C, 0xB85C5CE4, - 0x9FC2C25D, 0xBDD3D36E, 0x43ACACEF, 0xC46262A6, 0x399191A8, 0x319595A4, - 0xD3E4E437, 0xF279798B, 0xD5E7E732, 0x8BC8C843, 0x6E373759, 0xDA6D6DB7, - 0x018D8D8C, 0xB1D5D564, 0x9C4E4ED2, 0x49A9A9E0, 0xD86C6CB4, 0xAC5656FA, - 0xF3F4F407, 0xCFEAEA25, 0xCA6565AF, 0xF47A7A8E, 0x47AEAEE9, 0x10080818, - 0x6FBABAD5, 0xF0787888, 0x4A25256F, 0x5C2E2E72, 0x381C1C24, 0x57A6A6F1, - 0x73B4B4C7, 0x97C6C651, 0xCBE8E823, 0xA1DDDD7C, 0xE874749C, 0x3E1F1F21, - 0x964B4BDD, 0x61BDBDDC, 0x0D8B8B86, 0x0F8A8A85, 0xE0707090, 0x7C3E3E42, - 0x71B5B5C4, 0xCC6666AA, 0x904848D8, 0x06030305, 0xF7F6F601, 0x1C0E0E12, - 0xC26161A3, 0x6A35355F, 0xAE5757F9, 0x69B9B9D0, 0x17868691, 0x99C1C158, - 0x3A1D1D27, 0x279E9EB9, 0xD9E1E138, 0xEBF8F813, 0x2B9898B3, 0x22111133, - 0xD26969BB, 0xA9D9D970, 0x078E8E89, 0x339494A7, 0x2D9B9BB6, 0x3C1E1E22, - 0x15878792, 0xC9E9E920, 0x87CECE49, 0xAA5555FF, 0x50282878, 0xA5DFDF7A, - 0x038C8C8F, 0x59A1A1F8, 0x09898980, 0x1A0D0D17, 0x65BFBFDA, 0xD7E6E631, - 0x844242C6, 0xD06868B8, 0x824141C3, 0x299999B0, 0x5A2D2D77, 0x1E0F0F11, - 0x7BB0B0CB, 0xA85454FC, 0x6DBBBBD6, 0x2C16163A, 0xA5C66363, 0x84F87C7C, - 0x99EE7777, 0x8DF67B7B, 0x0DFFF2F2, 0xBDD66B6B, 0xB1DE6F6F, 0x5491C5C5, - 0x50603030, 0x03020101, 0xA9CE6767, 0x7D562B2B, 0x19E7FEFE, 0x62B5D7D7, - 0xE64DABAB, 0x9AEC7676, 0x458FCACA, 0x9D1F8282, 0x4089C9C9, 0x87FA7D7D, - 0x15EFFAFA, 0xEBB25959, 0xC98E4747, 0x0BFBF0F0, 0xEC41ADAD, 0x67B3D4D4, - 0xFD5FA2A2, 0xEA45AFAF, 0xBF239C9C, 0xF753A4A4, 0x96E47272, 0x5B9BC0C0, - 0xC275B7B7, 0x1CE1FDFD, 0xAE3D9393, 0x6A4C2626, 0x5A6C3636, 0x417E3F3F, - 0x02F5F7F7, 0x4F83CCCC, 0x5C683434, 0xF451A5A5, 0x34D1E5E5, 0x08F9F1F1, - 0x93E27171, 0x73ABD8D8, 0x53623131, 0x3F2A1515, 0x0C080404, 0x5295C7C7, - 0x65462323, 0x5E9DC3C3, 0x28301818, 0xA1379696, 0x0F0A0505, 0xB52F9A9A, - 0x090E0707, 0x36241212, 0x9B1B8080, 0x3DDFE2E2, 0x26CDEBEB, 0x694E2727, - 0xCD7FB2B2, 0x9FEA7575, 0x1B120909, 0x9E1D8383, 0x74582C2C, 0x2E341A1A, - 0x2D361B1B, 0xB2DC6E6E, 0xEEB45A5A, 0xFB5BA0A0, 0xF6A45252, 0x4D763B3B, - 0x61B7D6D6, 0xCE7DB3B3, 0x7B522929, 0x3EDDE3E3, 0x715E2F2F, 0x97138484, - 0xF5A65353, 0x68B9D1D1, 0x00000000, 0x2CC1EDED, 0x60402020, 0x1FE3FCFC, - 0xC879B1B1, 0xEDB65B5B, 0xBED46A6A, 0x468DCBCB, 0xD967BEBE, 0x4B723939, - 0xDE944A4A, 0xD4984C4C, 0xE8B05858, 0x4A85CFCF, 0x6BBBD0D0, 0x2AC5EFEF, - 0xE54FAAAA, 0x16EDFBFB, 0xC5864343, 0xD79A4D4D, 0x55663333, 0x94118585, - 0xCF8A4545, 0x10E9F9F9, 0x06040202, 0x81FE7F7F, 0xF0A05050, 0x44783C3C, - 0xBA259F9F, 0xE34BA8A8, 0xF3A25151, 0xFE5DA3A3, 0xC0804040, 0x8A058F8F, - 0xAD3F9292, 0xBC219D9D, 0x48703838, 0x04F1F5F5, 0xDF63BCBC, 0xC177B6B6, - 0x75AFDADA, 0x63422121, 0x30201010, 0x1AE5FFFF, 0x0EFDF3F3, 0x6DBFD2D2, - 0x4C81CDCD, 0x14180C0C, 0x35261313, 0x2FC3ECEC, 0xE1BE5F5F, 0xA2359797, - 0xCC884444, 0x392E1717, 0x5793C4C4, 0xF255A7A7, 0x82FC7E7E, 0x477A3D3D, - 0xACC86464, 0xE7BA5D5D, 0x2B321919, 0x95E67373, 0xA0C06060, 0x98198181, - 0xD19E4F4F, 0x7FA3DCDC, 0x66442222, 0x7E542A2A, 0xAB3B9090, 0x830B8888, - 0xCA8C4646, 0x29C7EEEE, 0xD36BB8B8, 0x3C281414, 0x79A7DEDE, 0xE2BC5E5E, - 0x1D160B0B, 0x76ADDBDB, 0x3BDBE0E0, 0x56643232, 0x4E743A3A, 0x1E140A0A, - 0xDB924949, 0x0A0C0606, 0x6C482424, 0xE4B85C5C, 0x5D9FC2C2, 0x6EBDD3D3, - 0xEF43ACAC, 0xA6C46262, 0xA8399191, 0xA4319595, 0x37D3E4E4, 0x8BF27979, - 0x32D5E7E7, 0x438BC8C8, 0x596E3737, 0xB7DA6D6D, 0x8C018D8D, 0x64B1D5D5, - 0xD29C4E4E, 0xE049A9A9, 0xB4D86C6C, 0xFAAC5656, 0x07F3F4F4, 0x25CFEAEA, - 0xAFCA6565, 0x8EF47A7A, 0xE947AEAE, 0x18100808, 0xD56FBABA, 0x88F07878, - 0x6F4A2525, 0x725C2E2E, 0x24381C1C, 0xF157A6A6, 0xC773B4B4, 0x5197C6C6, - 0x23CBE8E8, 0x7CA1DDDD, 0x9CE87474, 0x213E1F1F, 0xDD964B4B, 0xDC61BDBD, - 0x860D8B8B, 0x850F8A8A, 0x90E07070, 0x427C3E3E, 0xC471B5B5, 0xAACC6666, - 0xD8904848, 0x05060303, 0x01F7F6F6, 0x121C0E0E, 0xA3C26161, 0x5F6A3535, - 0xF9AE5757, 0xD069B9B9, 0x91178686, 0x5899C1C1, 0x273A1D1D, 0xB9279E9E, - 0x38D9E1E1, 0x13EBF8F8, 0xB32B9898, 0x33221111, 0xBBD26969, 0x70A9D9D9, - 0x89078E8E, 0xA7339494, 0xB62D9B9B, 0x223C1E1E, 0x92158787, 0x20C9E9E9, - 0x4987CECE, 0xFFAA5555, 0x78502828, 0x7AA5DFDF, 0x8F038C8C, 0xF859A1A1, - 0x80098989, 0x171A0D0D, 0xDA65BFBF, 0x31D7E6E6, 0xC6844242, 0xB8D06868, - 0xC3824141, 0xB0299999, 0x775A2D2D, 0x111E0F0F, 0xCB7BB0B0, 0xFCA85454, - 0xD66DBBBB, 0x3A2C1616, 0x63A5C663, 0x7C84F87C, 0x7799EE77, 0x7B8DF67B, - 0xF20DFFF2, 0x6BBDD66B, 0x6FB1DE6F, 0xC55491C5, 0x30506030, 0x01030201, - 0x67A9CE67, 0x2B7D562B, 0xFE19E7FE, 0xD762B5D7, 0xABE64DAB, 0x769AEC76, - 0xCA458FCA, 0x829D1F82, 0xC94089C9, 0x7D87FA7D, 0xFA15EFFA, 0x59EBB259, - 0x47C98E47, 0xF00BFBF0, 0xADEC41AD, 0xD467B3D4, 0xA2FD5FA2, 0xAFEA45AF, - 0x9CBF239C, 0xA4F753A4, 0x7296E472, 0xC05B9BC0, 0xB7C275B7, 0xFD1CE1FD, - 0x93AE3D93, 0x266A4C26, 0x365A6C36, 0x3F417E3F, 0xF702F5F7, 0xCC4F83CC, - 0x345C6834, 0xA5F451A5, 0xE534D1E5, 0xF108F9F1, 0x7193E271, 0xD873ABD8, - 0x31536231, 0x153F2A15, 0x040C0804, 0xC75295C7, 0x23654623, 0xC35E9DC3, - 0x18283018, 0x96A13796, 0x050F0A05, 0x9AB52F9A, 0x07090E07, 0x12362412, - 0x809B1B80, 0xE23DDFE2, 0xEB26CDEB, 0x27694E27, 0xB2CD7FB2, 0x759FEA75, - 0x091B1209, 0x839E1D83, 0x2C74582C, 0x1A2E341A, 0x1B2D361B, 0x6EB2DC6E, - 0x5AEEB45A, 0xA0FB5BA0, 0x52F6A452, 0x3B4D763B, 0xD661B7D6, 0xB3CE7DB3, - 0x297B5229, 0xE33EDDE3, 0x2F715E2F, 0x84971384, 0x53F5A653, 0xD168B9D1, - 0x00000000, 0xED2CC1ED, 0x20604020, 0xFC1FE3FC, 0xB1C879B1, 0x5BEDB65B, - 0x6ABED46A, 0xCB468DCB, 0xBED967BE, 0x394B7239, 0x4ADE944A, 0x4CD4984C, - 0x58E8B058, 0xCF4A85CF, 0xD06BBBD0, 0xEF2AC5EF, 0xAAE54FAA, 0xFB16EDFB, - 0x43C58643, 0x4DD79A4D, 0x33556633, 0x85941185, 0x45CF8A45, 0xF910E9F9, - 0x02060402, 0x7F81FE7F, 0x50F0A050, 0x3C44783C, 0x9FBA259F, 0xA8E34BA8, - 0x51F3A251, 0xA3FE5DA3, 0x40C08040, 0x8F8A058F, 0x92AD3F92, 0x9DBC219D, - 0x38487038, 0xF504F1F5, 0xBCDF63BC, 0xB6C177B6, 0xDA75AFDA, 0x21634221, - 0x10302010, 0xFF1AE5FF, 0xF30EFDF3, 0xD26DBFD2, 0xCD4C81CD, 0x0C14180C, - 0x13352613, 0xEC2FC3EC, 0x5FE1BE5F, 0x97A23597, 0x44CC8844, 0x17392E17, - 0xC45793C4, 0xA7F255A7, 0x7E82FC7E, 0x3D477A3D, 0x64ACC864, 0x5DE7BA5D, - 0x192B3219, 0x7395E673, 0x60A0C060, 0x81981981, 0x4FD19E4F, 0xDC7FA3DC, - 0x22664422, 0x2A7E542A, 0x90AB3B90, 0x88830B88, 0x46CA8C46, 0xEE29C7EE, - 0xB8D36BB8, 0x143C2814, 0xDE79A7DE, 0x5EE2BC5E, 0x0B1D160B, 0xDB76ADDB, - 0xE03BDBE0, 0x32566432, 0x3A4E743A, 0x0A1E140A, 0x49DB9249, 0x060A0C06, - 0x246C4824, 0x5CE4B85C, 0xC25D9FC2, 0xD36EBDD3, 0xACEF43AC, 0x62A6C462, - 0x91A83991, 0x95A43195, 0xE437D3E4, 0x798BF279, 0xE732D5E7, 0xC8438BC8, - 0x37596E37, 0x6DB7DA6D, 0x8D8C018D, 0xD564B1D5, 0x4ED29C4E, 0xA9E049A9, - 0x6CB4D86C, 0x56FAAC56, 0xF407F3F4, 0xEA25CFEA, 0x65AFCA65, 0x7A8EF47A, - 0xAEE947AE, 0x08181008, 0xBAD56FBA, 0x7888F078, 0x256F4A25, 0x2E725C2E, - 0x1C24381C, 0xA6F157A6, 0xB4C773B4, 0xC65197C6, 0xE823CBE8, 0xDD7CA1DD, - 0x749CE874, 0x1F213E1F, 0x4BDD964B, 0xBDDC61BD, 0x8B860D8B, 0x8A850F8A, - 0x7090E070, 0x3E427C3E, 0xB5C471B5, 0x66AACC66, 0x48D89048, 0x03050603, - 0xF601F7F6, 0x0E121C0E, 0x61A3C261, 0x355F6A35, 0x57F9AE57, 0xB9D069B9, - 0x86911786, 0xC15899C1, 0x1D273A1D, 0x9EB9279E, 0xE138D9E1, 0xF813EBF8, - 0x98B32B98, 0x11332211, 0x69BBD269, 0xD970A9D9, 0x8E89078E, 0x94A73394, - 0x9BB62D9B, 0x1E223C1E, 0x87921587, 0xE920C9E9, 0xCE4987CE, 0x55FFAA55, - 0x28785028, 0xDF7AA5DF, 0x8C8F038C, 0xA1F859A1, 0x89800989, 0x0D171A0D, - 0xBFDA65BF, 0xE631D7E6, 0x42C68442, 0x68B8D068, 0x41C38241, 0x99B02999, - 0x2D775A2D, 0x0F111E0F, 0xB0CB7BB0, 0x54FCA854, 0xBBD66DBB, 0x163A2C16, - 0x6363A5C6, 0x7C7C84F8, 0x777799EE, 0x7B7B8DF6, 0xF2F20DFF, 0x6B6BBDD6, - 0x6F6FB1DE, 0xC5C55491, 0x30305060, 0x01010302, 0x6767A9CE, 0x2B2B7D56, - 0xFEFE19E7, 0xD7D762B5, 0xABABE64D, 0x76769AEC, 0xCACA458F, 0x82829D1F, - 0xC9C94089, 0x7D7D87FA, 0xFAFA15EF, 0x5959EBB2, 0x4747C98E, 0xF0F00BFB, - 0xADADEC41, 0xD4D467B3, 0xA2A2FD5F, 0xAFAFEA45, 0x9C9CBF23, 0xA4A4F753, - 0x727296E4, 0xC0C05B9B, 0xB7B7C275, 0xFDFD1CE1, 0x9393AE3D, 0x26266A4C, - 0x36365A6C, 0x3F3F417E, 0xF7F702F5, 0xCCCC4F83, 0x34345C68, 0xA5A5F451, - 0xE5E534D1, 0xF1F108F9, 0x717193E2, 0xD8D873AB, 0x31315362, 0x15153F2A, - 0x04040C08, 0xC7C75295, 0x23236546, 0xC3C35E9D, 0x18182830, 0x9696A137, - 0x05050F0A, 0x9A9AB52F, 0x0707090E, 0x12123624, 0x80809B1B, 0xE2E23DDF, - 0xEBEB26CD, 0x2727694E, 0xB2B2CD7F, 0x75759FEA, 0x09091B12, 0x83839E1D, - 0x2C2C7458, 0x1A1A2E34, 0x1B1B2D36, 0x6E6EB2DC, 0x5A5AEEB4, 0xA0A0FB5B, - 0x5252F6A4, 0x3B3B4D76, 0xD6D661B7, 0xB3B3CE7D, 0x29297B52, 0xE3E33EDD, - 0x2F2F715E, 0x84849713, 0x5353F5A6, 0xD1D168B9, 0x00000000, 0xEDED2CC1, - 0x20206040, 0xFCFC1FE3, 0xB1B1C879, 0x5B5BEDB6, 0x6A6ABED4, 0xCBCB468D, - 0xBEBED967, 0x39394B72, 0x4A4ADE94, 0x4C4CD498, 0x5858E8B0, 0xCFCF4A85, - 0xD0D06BBB, 0xEFEF2AC5, 0xAAAAE54F, 0xFBFB16ED, 0x4343C586, 0x4D4DD79A, - 0x33335566, 0x85859411, 0x4545CF8A, 0xF9F910E9, 0x02020604, 0x7F7F81FE, - 0x5050F0A0, 0x3C3C4478, 0x9F9FBA25, 0xA8A8E34B, 0x5151F3A2, 0xA3A3FE5D, - 0x4040C080, 0x8F8F8A05, 0x9292AD3F, 0x9D9DBC21, 0x38384870, 0xF5F504F1, - 0xBCBCDF63, 0xB6B6C177, 0xDADA75AF, 0x21216342, 0x10103020, 0xFFFF1AE5, - 0xF3F30EFD, 0xD2D26DBF, 0xCDCD4C81, 0x0C0C1418, 0x13133526, 0xECEC2FC3, - 0x5F5FE1BE, 0x9797A235, 0x4444CC88, 0x1717392E, 0xC4C45793, 0xA7A7F255, - 0x7E7E82FC, 0x3D3D477A, 0x6464ACC8, 0x5D5DE7BA, 0x19192B32, 0x737395E6, - 0x6060A0C0, 0x81819819, 0x4F4FD19E, 0xDCDC7FA3, 0x22226644, 0x2A2A7E54, - 0x9090AB3B, 0x8888830B, 0x4646CA8C, 0xEEEE29C7, 0xB8B8D36B, 0x14143C28, - 0xDEDE79A7, 0x5E5EE2BC, 0x0B0B1D16, 0xDBDB76AD, 0xE0E03BDB, 0x32325664, - 0x3A3A4E74, 0x0A0A1E14, 0x4949DB92, 0x06060A0C, 0x24246C48, 0x5C5CE4B8, - 0xC2C25D9F, 0xD3D36EBD, 0xACACEF43, 0x6262A6C4, 0x9191A839, 0x9595A431, - 0xE4E437D3, 0x79798BF2, 0xE7E732D5, 0xC8C8438B, 0x3737596E, 0x6D6DB7DA, - 0x8D8D8C01, 0xD5D564B1, 0x4E4ED29C, 0xA9A9E049, 0x6C6CB4D8, 0x5656FAAC, - 0xF4F407F3, 0xEAEA25CF, 0x6565AFCA, 0x7A7A8EF4, 0xAEAEE947, 0x08081810, - 0xBABAD56F, 0x787888F0, 0x25256F4A, 0x2E2E725C, 0x1C1C2438, 0xA6A6F157, - 0xB4B4C773, 0xC6C65197, 0xE8E823CB, 0xDDDD7CA1, 0x74749CE8, 0x1F1F213E, - 0x4B4BDD96, 0xBDBDDC61, 0x8B8B860D, 0x8A8A850F, 0x707090E0, 0x3E3E427C, - 0xB5B5C471, 0x6666AACC, 0x4848D890, 0x03030506, 0xF6F601F7, 0x0E0E121C, - 0x6161A3C2, 0x35355F6A, 0x5757F9AE, 0xB9B9D069, 0x86869117, 0xC1C15899, - 0x1D1D273A, 0x9E9EB927, 0xE1E138D9, 0xF8F813EB, 0x9898B32B, 0x11113322, - 0x6969BBD2, 0xD9D970A9, 0x8E8E8907, 0x9494A733, 0x9B9BB62D, 0x1E1E223C, - 0x87879215, 0xE9E920C9, 0xCECE4987, 0x5555FFAA, 0x28287850, 0xDFDF7AA5, - 0x8C8C8F03, 0xA1A1F859, 0x89898009, 0x0D0D171A, 0xBFBFDA65, 0xE6E631D7, - 0x4242C684, 0x6868B8D0, 0x4141C382, 0x9999B029, 0x2D2D775A, 0x0F0F111E, - 0xB0B0CB7B, 0x5454FCA8, 0xBBBBD66D, 0x16163A2C }; - -const u32bit TD[1024] = { - 0x51F4A750, 0x7E416553, 0x1A17A4C3, 0x3A275E96, 0x3BAB6BCB, 0x1F9D45F1, - 0xACFA58AB, 0x4BE30393, 0x2030FA55, 0xAD766DF6, 0x88CC7691, 0xF5024C25, - 0x4FE5D7FC, 0xC52ACBD7, 0x26354480, 0xB562A38F, 0xDEB15A49, 0x25BA1B67, - 0x45EA0E98, 0x5DFEC0E1, 0xC32F7502, 0x814CF012, 0x8D4697A3, 0x6BD3F9C6, - 0x038F5FE7, 0x15929C95, 0xBF6D7AEB, 0x955259DA, 0xD4BE832D, 0x587421D3, - 0x49E06929, 0x8EC9C844, 0x75C2896A, 0xF48E7978, 0x99583E6B, 0x27B971DD, - 0xBEE14FB6, 0xF088AD17, 0xC920AC66, 0x7DCE3AB4, 0x63DF4A18, 0xE51A3182, - 0x97513360, 0x62537F45, 0xB16477E0, 0xBB6BAE84, 0xFE81A01C, 0xF9082B94, - 0x70486858, 0x8F45FD19, 0x94DE6C87, 0x527BF8B7, 0xAB73D323, 0x724B02E2, - 0xE31F8F57, 0x6655AB2A, 0xB2EB2807, 0x2FB5C203, 0x86C57B9A, 0xD33708A5, - 0x302887F2, 0x23BFA5B2, 0x02036ABA, 0xED16825C, 0x8ACF1C2B, 0xA779B492, - 0xF307F2F0, 0x4E69E2A1, 0x65DAF4CD, 0x0605BED5, 0xD134621F, 0xC4A6FE8A, - 0x342E539D, 0xA2F355A0, 0x058AE132, 0xA4F6EB75, 0x0B83EC39, 0x4060EFAA, - 0x5E719F06, 0xBD6E1051, 0x3E218AF9, 0x96DD063D, 0xDD3E05AE, 0x4DE6BD46, - 0x91548DB5, 0x71C45D05, 0x0406D46F, 0x605015FF, 0x1998FB24, 0xD6BDE997, - 0x894043CC, 0x67D99E77, 0xB0E842BD, 0x07898B88, 0xE7195B38, 0x79C8EEDB, - 0xA17C0A47, 0x7C420FE9, 0xF8841EC9, 0x00000000, 0x09808683, 0x322BED48, - 0x1E1170AC, 0x6C5A724E, 0xFD0EFFFB, 0x0F853856, 0x3DAED51E, 0x362D3927, - 0x0A0FD964, 0x685CA621, 0x9B5B54D1, 0x24362E3A, 0x0C0A67B1, 0x9357E70F, - 0xB4EE96D2, 0x1B9B919E, 0x80C0C54F, 0x61DC20A2, 0x5A774B69, 0x1C121A16, - 0xE293BA0A, 0xC0A02AE5, 0x3C22E043, 0x121B171D, 0x0E090D0B, 0xF28BC7AD, - 0x2DB6A8B9, 0x141EA9C8, 0x57F11985, 0xAF75074C, 0xEE99DDBB, 0xA37F60FD, - 0xF701269F, 0x5C72F5BC, 0x44663BC5, 0x5BFB7E34, 0x8B432976, 0xCB23C6DC, - 0xB6EDFC68, 0xB8E4F163, 0xD731DCCA, 0x42638510, 0x13972240, 0x84C61120, - 0x854A247D, 0xD2BB3DF8, 0xAEF93211, 0xC729A16D, 0x1D9E2F4B, 0xDCB230F3, - 0x0D8652EC, 0x77C1E3D0, 0x2BB3166C, 0xA970B999, 0x119448FA, 0x47E96422, - 0xA8FC8CC4, 0xA0F03F1A, 0x567D2CD8, 0x223390EF, 0x87494EC7, 0xD938D1C1, - 0x8CCAA2FE, 0x98D40B36, 0xA6F581CF, 0xA57ADE28, 0xDAB78E26, 0x3FADBFA4, - 0x2C3A9DE4, 0x5078920D, 0x6A5FCC9B, 0x547E4662, 0xF68D13C2, 0x90D8B8E8, - 0x2E39F75E, 0x82C3AFF5, 0x9F5D80BE, 0x69D0937C, 0x6FD52DA9, 0xCF2512B3, - 0xC8AC993B, 0x10187DA7, 0xE89C636E, 0xDB3BBB7B, 0xCD267809, 0x6E5918F4, - 0xEC9AB701, 0x834F9AA8, 0xE6956E65, 0xAAFFE67E, 0x21BCCF08, 0xEF15E8E6, - 0xBAE79BD9, 0x4A6F36CE, 0xEA9F09D4, 0x29B07CD6, 0x31A4B2AF, 0x2A3F2331, - 0xC6A59430, 0x35A266C0, 0x744EBC37, 0xFC82CAA6, 0xE090D0B0, 0x33A7D815, - 0xF104984A, 0x41ECDAF7, 0x7FCD500E, 0x1791F62F, 0x764DD68D, 0x43EFB04D, - 0xCCAA4D54, 0xE49604DF, 0x9ED1B5E3, 0x4C6A881B, 0xC12C1FB8, 0x4665517F, - 0x9D5EEA04, 0x018C355D, 0xFA877473, 0xFB0B412E, 0xB3671D5A, 0x92DBD252, - 0xE9105633, 0x6DD64713, 0x9AD7618C, 0x37A10C7A, 0x59F8148E, 0xEB133C89, - 0xCEA927EE, 0xB761C935, 0xE11CE5ED, 0x7A47B13C, 0x9CD2DF59, 0x55F2733F, - 0x1814CE79, 0x73C737BF, 0x53F7CDEA, 0x5FFDAA5B, 0xDF3D6F14, 0x7844DB86, - 0xCAAFF381, 0xB968C43E, 0x3824342C, 0xC2A3405F, 0x161DC372, 0xBCE2250C, - 0x283C498B, 0xFF0D9541, 0x39A80171, 0x080CB3DE, 0xD8B4E49C, 0x6456C190, - 0x7BCB8461, 0xD532B670, 0x486C5C74, 0xD0B85742, 0x5051F4A7, 0x537E4165, - 0xC31A17A4, 0x963A275E, 0xCB3BAB6B, 0xF11F9D45, 0xABACFA58, 0x934BE303, - 0x552030FA, 0xF6AD766D, 0x9188CC76, 0x25F5024C, 0xFC4FE5D7, 0xD7C52ACB, - 0x80263544, 0x8FB562A3, 0x49DEB15A, 0x6725BA1B, 0x9845EA0E, 0xE15DFEC0, - 0x02C32F75, 0x12814CF0, 0xA38D4697, 0xC66BD3F9, 0xE7038F5F, 0x9515929C, - 0xEBBF6D7A, 0xDA955259, 0x2DD4BE83, 0xD3587421, 0x2949E069, 0x448EC9C8, - 0x6A75C289, 0x78F48E79, 0x6B99583E, 0xDD27B971, 0xB6BEE14F, 0x17F088AD, - 0x66C920AC, 0xB47DCE3A, 0x1863DF4A, 0x82E51A31, 0x60975133, 0x4562537F, - 0xE0B16477, 0x84BB6BAE, 0x1CFE81A0, 0x94F9082B, 0x58704868, 0x198F45FD, - 0x8794DE6C, 0xB7527BF8, 0x23AB73D3, 0xE2724B02, 0x57E31F8F, 0x2A6655AB, - 0x07B2EB28, 0x032FB5C2, 0x9A86C57B, 0xA5D33708, 0xF2302887, 0xB223BFA5, - 0xBA02036A, 0x5CED1682, 0x2B8ACF1C, 0x92A779B4, 0xF0F307F2, 0xA14E69E2, - 0xCD65DAF4, 0xD50605BE, 0x1FD13462, 0x8AC4A6FE, 0x9D342E53, 0xA0A2F355, - 0x32058AE1, 0x75A4F6EB, 0x390B83EC, 0xAA4060EF, 0x065E719F, 0x51BD6E10, - 0xF93E218A, 0x3D96DD06, 0xAEDD3E05, 0x464DE6BD, 0xB591548D, 0x0571C45D, - 0x6F0406D4, 0xFF605015, 0x241998FB, 0x97D6BDE9, 0xCC894043, 0x7767D99E, - 0xBDB0E842, 0x8807898B, 0x38E7195B, 0xDB79C8EE, 0x47A17C0A, 0xE97C420F, - 0xC9F8841E, 0x00000000, 0x83098086, 0x48322BED, 0xAC1E1170, 0x4E6C5A72, - 0xFBFD0EFF, 0x560F8538, 0x1E3DAED5, 0x27362D39, 0x640A0FD9, 0x21685CA6, - 0xD19B5B54, 0x3A24362E, 0xB10C0A67, 0x0F9357E7, 0xD2B4EE96, 0x9E1B9B91, - 0x4F80C0C5, 0xA261DC20, 0x695A774B, 0x161C121A, 0x0AE293BA, 0xE5C0A02A, - 0x433C22E0, 0x1D121B17, 0x0B0E090D, 0xADF28BC7, 0xB92DB6A8, 0xC8141EA9, - 0x8557F119, 0x4CAF7507, 0xBBEE99DD, 0xFDA37F60, 0x9FF70126, 0xBC5C72F5, - 0xC544663B, 0x345BFB7E, 0x768B4329, 0xDCCB23C6, 0x68B6EDFC, 0x63B8E4F1, - 0xCAD731DC, 0x10426385, 0x40139722, 0x2084C611, 0x7D854A24, 0xF8D2BB3D, - 0x11AEF932, 0x6DC729A1, 0x4B1D9E2F, 0xF3DCB230, 0xEC0D8652, 0xD077C1E3, - 0x6C2BB316, 0x99A970B9, 0xFA119448, 0x2247E964, 0xC4A8FC8C, 0x1AA0F03F, - 0xD8567D2C, 0xEF223390, 0xC787494E, 0xC1D938D1, 0xFE8CCAA2, 0x3698D40B, - 0xCFA6F581, 0x28A57ADE, 0x26DAB78E, 0xA43FADBF, 0xE42C3A9D, 0x0D507892, - 0x9B6A5FCC, 0x62547E46, 0xC2F68D13, 0xE890D8B8, 0x5E2E39F7, 0xF582C3AF, - 0xBE9F5D80, 0x7C69D093, 0xA96FD52D, 0xB3CF2512, 0x3BC8AC99, 0xA710187D, - 0x6EE89C63, 0x7BDB3BBB, 0x09CD2678, 0xF46E5918, 0x01EC9AB7, 0xA8834F9A, - 0x65E6956E, 0x7EAAFFE6, 0x0821BCCF, 0xE6EF15E8, 0xD9BAE79B, 0xCE4A6F36, - 0xD4EA9F09, 0xD629B07C, 0xAF31A4B2, 0x312A3F23, 0x30C6A594, 0xC035A266, - 0x37744EBC, 0xA6FC82CA, 0xB0E090D0, 0x1533A7D8, 0x4AF10498, 0xF741ECDA, - 0x0E7FCD50, 0x2F1791F6, 0x8D764DD6, 0x4D43EFB0, 0x54CCAA4D, 0xDFE49604, - 0xE39ED1B5, 0x1B4C6A88, 0xB8C12C1F, 0x7F466551, 0x049D5EEA, 0x5D018C35, - 0x73FA8774, 0x2EFB0B41, 0x5AB3671D, 0x5292DBD2, 0x33E91056, 0x136DD647, - 0x8C9AD761, 0x7A37A10C, 0x8E59F814, 0x89EB133C, 0xEECEA927, 0x35B761C9, - 0xEDE11CE5, 0x3C7A47B1, 0x599CD2DF, 0x3F55F273, 0x791814CE, 0xBF73C737, - 0xEA53F7CD, 0x5B5FFDAA, 0x14DF3D6F, 0x867844DB, 0x81CAAFF3, 0x3EB968C4, - 0x2C382434, 0x5FC2A340, 0x72161DC3, 0x0CBCE225, 0x8B283C49, 0x41FF0D95, - 0x7139A801, 0xDE080CB3, 0x9CD8B4E4, 0x906456C1, 0x617BCB84, 0x70D532B6, - 0x74486C5C, 0x42D0B857, 0xA75051F4, 0x65537E41, 0xA4C31A17, 0x5E963A27, - 0x6BCB3BAB, 0x45F11F9D, 0x58ABACFA, 0x03934BE3, 0xFA552030, 0x6DF6AD76, - 0x769188CC, 0x4C25F502, 0xD7FC4FE5, 0xCBD7C52A, 0x44802635, 0xA38FB562, - 0x5A49DEB1, 0x1B6725BA, 0x0E9845EA, 0xC0E15DFE, 0x7502C32F, 0xF012814C, - 0x97A38D46, 0xF9C66BD3, 0x5FE7038F, 0x9C951592, 0x7AEBBF6D, 0x59DA9552, - 0x832DD4BE, 0x21D35874, 0x692949E0, 0xC8448EC9, 0x896A75C2, 0x7978F48E, - 0x3E6B9958, 0x71DD27B9, 0x4FB6BEE1, 0xAD17F088, 0xAC66C920, 0x3AB47DCE, - 0x4A1863DF, 0x3182E51A, 0x33609751, 0x7F456253, 0x77E0B164, 0xAE84BB6B, - 0xA01CFE81, 0x2B94F908, 0x68587048, 0xFD198F45, 0x6C8794DE, 0xF8B7527B, - 0xD323AB73, 0x02E2724B, 0x8F57E31F, 0xAB2A6655, 0x2807B2EB, 0xC2032FB5, - 0x7B9A86C5, 0x08A5D337, 0x87F23028, 0xA5B223BF, 0x6ABA0203, 0x825CED16, - 0x1C2B8ACF, 0xB492A779, 0xF2F0F307, 0xE2A14E69, 0xF4CD65DA, 0xBED50605, - 0x621FD134, 0xFE8AC4A6, 0x539D342E, 0x55A0A2F3, 0xE132058A, 0xEB75A4F6, - 0xEC390B83, 0xEFAA4060, 0x9F065E71, 0x1051BD6E, 0x8AF93E21, 0x063D96DD, - 0x05AEDD3E, 0xBD464DE6, 0x8DB59154, 0x5D0571C4, 0xD46F0406, 0x15FF6050, - 0xFB241998, 0xE997D6BD, 0x43CC8940, 0x9E7767D9, 0x42BDB0E8, 0x8B880789, - 0x5B38E719, 0xEEDB79C8, 0x0A47A17C, 0x0FE97C42, 0x1EC9F884, 0x00000000, - 0x86830980, 0xED48322B, 0x70AC1E11, 0x724E6C5A, 0xFFFBFD0E, 0x38560F85, - 0xD51E3DAE, 0x3927362D, 0xD9640A0F, 0xA621685C, 0x54D19B5B, 0x2E3A2436, - 0x67B10C0A, 0xE70F9357, 0x96D2B4EE, 0x919E1B9B, 0xC54F80C0, 0x20A261DC, - 0x4B695A77, 0x1A161C12, 0xBA0AE293, 0x2AE5C0A0, 0xE0433C22, 0x171D121B, - 0x0D0B0E09, 0xC7ADF28B, 0xA8B92DB6, 0xA9C8141E, 0x198557F1, 0x074CAF75, - 0xDDBBEE99, 0x60FDA37F, 0x269FF701, 0xF5BC5C72, 0x3BC54466, 0x7E345BFB, - 0x29768B43, 0xC6DCCB23, 0xFC68B6ED, 0xF163B8E4, 0xDCCAD731, 0x85104263, - 0x22401397, 0x112084C6, 0x247D854A, 0x3DF8D2BB, 0x3211AEF9, 0xA16DC729, - 0x2F4B1D9E, 0x30F3DCB2, 0x52EC0D86, 0xE3D077C1, 0x166C2BB3, 0xB999A970, - 0x48FA1194, 0x642247E9, 0x8CC4A8FC, 0x3F1AA0F0, 0x2CD8567D, 0x90EF2233, - 0x4EC78749, 0xD1C1D938, 0xA2FE8CCA, 0x0B3698D4, 0x81CFA6F5, 0xDE28A57A, - 0x8E26DAB7, 0xBFA43FAD, 0x9DE42C3A, 0x920D5078, 0xCC9B6A5F, 0x4662547E, - 0x13C2F68D, 0xB8E890D8, 0xF75E2E39, 0xAFF582C3, 0x80BE9F5D, 0x937C69D0, - 0x2DA96FD5, 0x12B3CF25, 0x993BC8AC, 0x7DA71018, 0x636EE89C, 0xBB7BDB3B, - 0x7809CD26, 0x18F46E59, 0xB701EC9A, 0x9AA8834F, 0x6E65E695, 0xE67EAAFF, - 0xCF0821BC, 0xE8E6EF15, 0x9BD9BAE7, 0x36CE4A6F, 0x09D4EA9F, 0x7CD629B0, - 0xB2AF31A4, 0x23312A3F, 0x9430C6A5, 0x66C035A2, 0xBC37744E, 0xCAA6FC82, - 0xD0B0E090, 0xD81533A7, 0x984AF104, 0xDAF741EC, 0x500E7FCD, 0xF62F1791, - 0xD68D764D, 0xB04D43EF, 0x4D54CCAA, 0x04DFE496, 0xB5E39ED1, 0x881B4C6A, - 0x1FB8C12C, 0x517F4665, 0xEA049D5E, 0x355D018C, 0x7473FA87, 0x412EFB0B, - 0x1D5AB367, 0xD25292DB, 0x5633E910, 0x47136DD6, 0x618C9AD7, 0x0C7A37A1, - 0x148E59F8, 0x3C89EB13, 0x27EECEA9, 0xC935B761, 0xE5EDE11C, 0xB13C7A47, - 0xDF599CD2, 0x733F55F2, 0xCE791814, 0x37BF73C7, 0xCDEA53F7, 0xAA5B5FFD, - 0x6F14DF3D, 0xDB867844, 0xF381CAAF, 0xC43EB968, 0x342C3824, 0x405FC2A3, - 0xC372161D, 0x250CBCE2, 0x498B283C, 0x9541FF0D, 0x017139A8, 0xB3DE080C, - 0xE49CD8B4, 0xC1906456, 0x84617BCB, 0xB670D532, 0x5C74486C, 0x5742D0B8, - 0xF4A75051, 0x4165537E, 0x17A4C31A, 0x275E963A, 0xAB6BCB3B, 0x9D45F11F, - 0xFA58ABAC, 0xE303934B, 0x30FA5520, 0x766DF6AD, 0xCC769188, 0x024C25F5, - 0xE5D7FC4F, 0x2ACBD7C5, 0x35448026, 0x62A38FB5, 0xB15A49DE, 0xBA1B6725, - 0xEA0E9845, 0xFEC0E15D, 0x2F7502C3, 0x4CF01281, 0x4697A38D, 0xD3F9C66B, - 0x8F5FE703, 0x929C9515, 0x6D7AEBBF, 0x5259DA95, 0xBE832DD4, 0x7421D358, - 0xE0692949, 0xC9C8448E, 0xC2896A75, 0x8E7978F4, 0x583E6B99, 0xB971DD27, - 0xE14FB6BE, 0x88AD17F0, 0x20AC66C9, 0xCE3AB47D, 0xDF4A1863, 0x1A3182E5, - 0x51336097, 0x537F4562, 0x6477E0B1, 0x6BAE84BB, 0x81A01CFE, 0x082B94F9, - 0x48685870, 0x45FD198F, 0xDE6C8794, 0x7BF8B752, 0x73D323AB, 0x4B02E272, - 0x1F8F57E3, 0x55AB2A66, 0xEB2807B2, 0xB5C2032F, 0xC57B9A86, 0x3708A5D3, - 0x2887F230, 0xBFA5B223, 0x036ABA02, 0x16825CED, 0xCF1C2B8A, 0x79B492A7, - 0x07F2F0F3, 0x69E2A14E, 0xDAF4CD65, 0x05BED506, 0x34621FD1, 0xA6FE8AC4, - 0x2E539D34, 0xF355A0A2, 0x8AE13205, 0xF6EB75A4, 0x83EC390B, 0x60EFAA40, - 0x719F065E, 0x6E1051BD, 0x218AF93E, 0xDD063D96, 0x3E05AEDD, 0xE6BD464D, - 0x548DB591, 0xC45D0571, 0x06D46F04, 0x5015FF60, 0x98FB2419, 0xBDE997D6, - 0x4043CC89, 0xD99E7767, 0xE842BDB0, 0x898B8807, 0x195B38E7, 0xC8EEDB79, - 0x7C0A47A1, 0x420FE97C, 0x841EC9F8, 0x00000000, 0x80868309, 0x2BED4832, - 0x1170AC1E, 0x5A724E6C, 0x0EFFFBFD, 0x8538560F, 0xAED51E3D, 0x2D392736, - 0x0FD9640A, 0x5CA62168, 0x5B54D19B, 0x362E3A24, 0x0A67B10C, 0x57E70F93, - 0xEE96D2B4, 0x9B919E1B, 0xC0C54F80, 0xDC20A261, 0x774B695A, 0x121A161C, - 0x93BA0AE2, 0xA02AE5C0, 0x22E0433C, 0x1B171D12, 0x090D0B0E, 0x8BC7ADF2, - 0xB6A8B92D, 0x1EA9C814, 0xF1198557, 0x75074CAF, 0x99DDBBEE, 0x7F60FDA3, - 0x01269FF7, 0x72F5BC5C, 0x663BC544, 0xFB7E345B, 0x4329768B, 0x23C6DCCB, - 0xEDFC68B6, 0xE4F163B8, 0x31DCCAD7, 0x63851042, 0x97224013, 0xC6112084, - 0x4A247D85, 0xBB3DF8D2, 0xF93211AE, 0x29A16DC7, 0x9E2F4B1D, 0xB230F3DC, - 0x8652EC0D, 0xC1E3D077, 0xB3166C2B, 0x70B999A9, 0x9448FA11, 0xE9642247, - 0xFC8CC4A8, 0xF03F1AA0, 0x7D2CD856, 0x3390EF22, 0x494EC787, 0x38D1C1D9, - 0xCAA2FE8C, 0xD40B3698, 0xF581CFA6, 0x7ADE28A5, 0xB78E26DA, 0xADBFA43F, - 0x3A9DE42C, 0x78920D50, 0x5FCC9B6A, 0x7E466254, 0x8D13C2F6, 0xD8B8E890, - 0x39F75E2E, 0xC3AFF582, 0x5D80BE9F, 0xD0937C69, 0xD52DA96F, 0x2512B3CF, - 0xAC993BC8, 0x187DA710, 0x9C636EE8, 0x3BBB7BDB, 0x267809CD, 0x5918F46E, - 0x9AB701EC, 0x4F9AA883, 0x956E65E6, 0xFFE67EAA, 0xBCCF0821, 0x15E8E6EF, - 0xE79BD9BA, 0x6F36CE4A, 0x9F09D4EA, 0xB07CD629, 0xA4B2AF31, 0x3F23312A, - 0xA59430C6, 0xA266C035, 0x4EBC3774, 0x82CAA6FC, 0x90D0B0E0, 0xA7D81533, - 0x04984AF1, 0xECDAF741, 0xCD500E7F, 0x91F62F17, 0x4DD68D76, 0xEFB04D43, - 0xAA4D54CC, 0x9604DFE4, 0xD1B5E39E, 0x6A881B4C, 0x2C1FB8C1, 0x65517F46, - 0x5EEA049D, 0x8C355D01, 0x877473FA, 0x0B412EFB, 0x671D5AB3, 0xDBD25292, - 0x105633E9, 0xD647136D, 0xD7618C9A, 0xA10C7A37, 0xF8148E59, 0x133C89EB, - 0xA927EECE, 0x61C935B7, 0x1CE5EDE1, 0x47B13C7A, 0xD2DF599C, 0xF2733F55, - 0x14CE7918, 0xC737BF73, 0xF7CDEA53, 0xFDAA5B5F, 0x3D6F14DF, 0x44DB8678, - 0xAFF381CA, 0x68C43EB9, 0x24342C38, 0xA3405FC2, 0x1DC37216, 0xE2250CBC, - 0x3C498B28, 0x0D9541FF, 0xA8017139, 0x0CB3DE08, 0xB4E49CD8, 0x56C19064, - 0xCB84617B, 0x32B670D5, 0x6C5C7448, 0xB85742D0 }; +inline byte xtime(byte s) { return (s << 1) ^ ((s >> 7) * 0x1B); } +inline byte xtime4(byte s) { return xtime(xtime(s)); } +inline byte xtime8(byte s) { return xtime(xtime(xtime(s))); } + +inline byte xtime3(byte s) { return xtime(s) ^ s; } +inline byte xtime9(byte s) { return xtime8(s) ^ s; } +inline byte xtime11(byte s) { return xtime8(s) ^ xtime(s) ^ s; } +inline byte xtime13(byte s) { return xtime8(s) ^ xtime4(s) ^ s; } +inline byte xtime14(byte s) { return xtime8(s) ^ xtime4(s) ^ xtime(s); } + +const std::vector<u32bit>& AES_TE() + { + auto compute_TE = []() { + std::vector<u32bit> TE(1024); + for(size_t i = 0; i != 256; ++i) + { + const byte s = SE[i]; + const u32bit x = make_u32bit(xtime(s), s, s, xtime3(s)); + + TE[i] = x; + TE[i+256] = rotate_right(x, 8); + TE[i+512] = rotate_right(x, 16); + TE[i+768] = rotate_right(x, 24); + } + return TE; + }; + + static std::vector<u32bit> TE = compute_TE(); + return TE; + } + +const std::vector<u32bit>& AES_TD() + { + auto compute_TD = []() { + std::vector<u32bit> TD(1024); + for(size_t i = 0; i != 256; ++i) + { + const byte s = SD[i]; + const u32bit x = make_u32bit(xtime14(s), xtime9(s), xtime13(s), xtime11(s)); + + TD[i] = x; + TD[i+256] = rotate_right(x, 8); + TD[i+512] = rotate_right(x, 16); + TD[i+768] = rotate_right(x, 24); + } + return TD; + }; + static std::vector<u32bit> TD = compute_TD(); + return TD; + } /* * AES Encryption @@ -418,12 +156,17 @@ void aes_encrypt_n(const byte in[], byte out[], { BOTAN_ASSERT(EK.size() && ME.size() == 16, "Key was set"); - const size_t BLOCK_SIZE = 16; + const size_t cache_line_size = CPUID::cache_line_size(); - const u32bit* TE0 = TE; - const u32bit* TE1 = TE + 256; - const u32bit* TE2 = TE + 512; - const u32bit* TE3 = TE + 768; + const std::vector<u32bit>& TE = AES_TE(); + + // Hit every cache line of TE + u32bit Z = 0; + for(size_t i = 0; i < TE.size(); i += cache_line_size / sizeof(u32bit)) + { + Z |= TE[i]; + } + Z &= TE[82]; // this is zero, which hopefully the compiler cannot deduce for(size_t i = 0; i != blocks; ++i) { @@ -432,6 +175,8 @@ void aes_encrypt_n(const byte in[], byte out[], u32bit T2 = load_be<u32bit>(in, 2) ^ EK[2]; u32bit T3 = load_be<u32bit>(in, 3) ^ EK[3]; + T0 ^= Z; + /* Use only the first 256 entries of the TE table and do the * rotations directly in the code. This reduces the number of * cache lines potentially used in the first round from 64 to 16 @@ -462,44 +207,25 @@ void aes_encrypt_n(const byte in[], byte out[], for(size_t r = 2*4; r < EK.size(); r += 2*4) { - T0 = TE0[get_byte(0, B0)] ^ TE1[get_byte(1, B1)] ^ - TE2[get_byte(2, B2)] ^ TE3[get_byte(3, B3)] ^ EK[r]; - T1 = TE0[get_byte(0, B1)] ^ TE1[get_byte(1, B2)] ^ - TE2[get_byte(2, B3)] ^ TE3[get_byte(3, B0)] ^ EK[r+1]; - T2 = TE0[get_byte(0, B2)] ^ TE1[get_byte(1, B3)] ^ - TE2[get_byte(2, B0)] ^ TE3[get_byte(3, B1)] ^ EK[r+2]; - T3 = TE0[get_byte(0, B3)] ^ TE1[get_byte(1, B0)] ^ - TE2[get_byte(2, B1)] ^ TE3[get_byte(3, B2)] ^ EK[r+3]; - - B0 = TE0[get_byte(0, T0)] ^ TE1[get_byte(1, T1)] ^ - TE2[get_byte(2, T2)] ^ TE3[get_byte(3, T3)] ^ EK[r+4]; - B1 = TE0[get_byte(0, T1)] ^ TE1[get_byte(1, T2)] ^ - TE2[get_byte(2, T3)] ^ TE3[get_byte(3, T0)] ^ EK[r+5]; - B2 = TE0[get_byte(0, T2)] ^ TE1[get_byte(1, T3)] ^ - TE2[get_byte(2, T0)] ^ TE3[get_byte(3, T1)] ^ EK[r+6]; - B3 = TE0[get_byte(0, T3)] ^ TE1[get_byte(1, T0)] ^ - TE2[get_byte(2, T1)] ^ TE3[get_byte(3, T2)] ^ EK[r+7]; + T0 = EK[r ] ^ TE[get_byte(0, B0) ] ^ TE[get_byte(1, B1) + 256] ^ + TE[get_byte(2, B2) + 512] ^ TE[get_byte(3, B3) + 768]; + T1 = EK[r+1] ^ TE[get_byte(0, B1) ] ^ TE[get_byte(1, B2) + 256] ^ + TE[get_byte(2, B3) + 512] ^ TE[get_byte(3, B0) + 768]; + T2 = EK[r+2] ^ TE[get_byte(0, B2) ] ^ TE[get_byte(1, B3) + 256] ^ + TE[get_byte(2, B0) + 512] ^ TE[get_byte(3, B1) + 768]; + T3 = EK[r+3] ^ TE[get_byte(0, B3) ] ^ TE[get_byte(1, B0) + 256] ^ + TE[get_byte(2, B1) + 512] ^ TE[get_byte(3, B2) + 768]; + + B0 = EK[r+4] ^ TE[get_byte(0, T0) ] ^ TE[get_byte(1, T1) + 256] ^ + TE[get_byte(2, T2) + 512] ^ TE[get_byte(3, T3) + 768]; + B1 = EK[r+5] ^ TE[get_byte(0, T1) ] ^ TE[get_byte(1, T2) + 256] ^ + TE[get_byte(2, T3) + 512] ^ TE[get_byte(3, T0) + 768]; + B2 = EK[r+6] ^ TE[get_byte(0, T2) ] ^ TE[get_byte(1, T3) + 256] ^ + TE[get_byte(2, T0) + 512] ^ TE[get_byte(3, T1) + 768]; + B3 = EK[r+7] ^ TE[get_byte(0, T3) ] ^ TE[get_byte(1, T0) + 256] ^ + TE[get_byte(2, T1) + 512] ^ TE[get_byte(3, T2) + 768]; } - /* - Joseph Bonneau and Ilya Mironov's paper "Cache-Collision Timing - Attacks Against AES" describes an attack that can recover AES - keys with as few as 2**13 samples. - - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.4753 - - They recommend using a byte-wide table, which still allows an attack - but increases the samples required from 2**13 to 2**25: - - """In addition to OpenSSL v. 0.9.8.(a), which was used in our - experiments, the AES implementations of Crypto++ 5.2.1 and - LibTomCrypt 1.09 use the original Rijndael C implementation with - very few changes and are highly vulnerable. The AES implementations - in libgcrypt v. 1.2.2 and Botan v. 1.4.2 are also vulnerable, but - use a smaller byte-wide final table which lessens the effectiveness - of the attacks.""" - */ - out[ 0] = SE[get_byte(0, B0)] ^ ME[0]; out[ 1] = SE[get_byte(1, B1)] ^ ME[1]; out[ 2] = SE[get_byte(2, B2)] ^ ME[2]; @@ -517,8 +243,8 @@ void aes_encrypt_n(const byte in[], byte out[], out[14] = SE[get_byte(2, B1)] ^ ME[14]; out[15] = SE[get_byte(3, B2)] ^ ME[15]; - in += BLOCK_SIZE; - out += BLOCK_SIZE; + in += 16; + out += 16; } } @@ -531,12 +257,15 @@ void aes_decrypt_n(const byte in[], byte out[], size_t blocks, { BOTAN_ASSERT(DK.size() && MD.size() == 16, "Key was set"); - const size_t BLOCK_SIZE = 16; + const size_t cache_line_size = CPUID::cache_line_size(); + const std::vector<u32bit>& TD = AES_TD(); - const u32bit* TD0 = TD; - const u32bit* TD1 = TD + 256; - const u32bit* TD2 = TD + 512; - const u32bit* TD3 = TD + 768; + u32bit Z = 0; + for(size_t i = 0; i < TD.size(); i += cache_line_size / sizeof(u32bit)) + { + Z |= TD[i]; + } + Z &= TD[99]; // this is zero, which hopefully the compiler cannot deduce for(size_t i = 0; i != blocks; ++i) { @@ -545,6 +274,8 @@ void aes_decrypt_n(const byte in[], byte out[], size_t blocks, u32bit T2 = load_be<u32bit>(in, 2) ^ DK[2]; u32bit T3 = load_be<u32bit>(in, 3) ^ DK[3]; + T0 ^= Z; + u32bit B0 = TD[get_byte(0, T0)] ^ rotate_right(TD[get_byte(1, T3)], 8) ^ rotate_right(TD[get_byte(2, T2)], 16) ^ @@ -567,23 +298,23 @@ void aes_decrypt_n(const byte in[], byte out[], size_t blocks, for(size_t r = 2*4; r < DK.size(); r += 2*4) { - T0 = TD0[get_byte(0, B0)] ^ TD1[get_byte(1, B3)] ^ - TD2[get_byte(2, B2)] ^ TD3[get_byte(3, B1)] ^ DK[r]; - T1 = TD0[get_byte(0, B1)] ^ TD1[get_byte(1, B0)] ^ - TD2[get_byte(2, B3)] ^ TD3[get_byte(3, B2)] ^ DK[r+1]; - T2 = TD0[get_byte(0, B2)] ^ TD1[get_byte(1, B1)] ^ - TD2[get_byte(2, B0)] ^ TD3[get_byte(3, B3)] ^ DK[r+2]; - T3 = TD0[get_byte(0, B3)] ^ TD1[get_byte(1, B2)] ^ - TD2[get_byte(2, B1)] ^ TD3[get_byte(3, B0)] ^ DK[r+3]; - - B0 = TD0[get_byte(0, T0)] ^ TD1[get_byte(1, T3)] ^ - TD2[get_byte(2, T2)] ^ TD3[get_byte(3, T1)] ^ DK[r+4]; - B1 = TD0[get_byte(0, T1)] ^ TD1[get_byte(1, T0)] ^ - TD2[get_byte(2, T3)] ^ TD3[get_byte(3, T2)] ^ DK[r+5]; - B2 = TD0[get_byte(0, T2)] ^ TD1[get_byte(1, T1)] ^ - TD2[get_byte(2, T0)] ^ TD3[get_byte(3, T3)] ^ DK[r+6]; - B3 = TD0[get_byte(0, T3)] ^ TD1[get_byte(1, T2)] ^ - TD2[get_byte(2, T1)] ^ TD3[get_byte(3, T0)] ^ DK[r+7]; + T0 = DK[r ] ^ TD[get_byte(0, B0) ] ^ TD[get_byte(1, B3) + 256] ^ + TD[get_byte(2, B2) + 512] ^ TD[get_byte(3, B1) + 768]; + T1 = DK[r+1] ^ TD[get_byte(0, B1) ] ^ TD[get_byte(1, B0) + 256] ^ + TD[get_byte(2, B3) + 512] ^ TD[get_byte(3, B2) + 768]; + T2 = DK[r+2] ^ TD[get_byte(0, B2) ] ^ TD[get_byte(1, B1) + 256] ^ + TD[get_byte(2, B0) + 512] ^ TD[get_byte(3, B3) + 768]; + T3 = DK[r+3] ^ TD[get_byte(0, B3) ] ^ TD[get_byte(1, B2) + 256] ^ + TD[get_byte(2, B1) + 512] ^ TD[get_byte(3, B0) + 768]; + + B0 = DK[r+4] ^ TD[get_byte(0, T0) ] ^ TD[get_byte(1, T3) + 256] ^ + TD[get_byte(2, T2) + 512] ^ TD[get_byte(3, T1) + 768]; + B1 = DK[r+5] ^ TD[get_byte(0, T1) ] ^ TD[get_byte(1, T0) + 256] ^ + TD[get_byte(2, T3) + 512] ^ TD[get_byte(3, T2) + 768]; + B2 = DK[r+6] ^ TD[get_byte(0, T2) ] ^ TD[get_byte(1, T1) + 256] ^ + TD[get_byte(2, T0) + 512] ^ TD[get_byte(3, T3) + 768]; + B3 = DK[r+7] ^ TD[get_byte(0, T3) ] ^ TD[get_byte(1, T2) + 256] ^ + TD[get_byte(2, T1) + 512] ^ TD[get_byte(3, T0) + 768]; } out[ 0] = SD[get_byte(0, B0)] ^ MD[0]; @@ -603,8 +334,8 @@ void aes_decrypt_n(const byte in[], byte out[], size_t blocks, out[14] = SD[get_byte(2, B1)] ^ MD[14]; out[15] = SD[get_byte(3, B0)] ^ MD[15]; - in += BLOCK_SIZE; - out += BLOCK_SIZE; + in += 16; + out += 16; } } @@ -648,6 +379,8 @@ void aes_key_schedule(const byte key[], size_t length, } } + const std::vector<u32bit>& TD = AES_TD(); + for(size_t i = 0; i != 4*(rounds+1); i += 4) { XDK[i ] = XEK[4*rounds-i ]; |