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abseil-cpp/absl/random/internal/randen_slow.cc

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// Copyright 2017 The Abseil Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "absl/random/internal/randen_slow.h"
#include <cstddef>
#include <cstdint>
#include <cstring>
#include "absl/random/internal/platform.h"
namespace {
// AES portions based on rijndael-alg-fst.c,
// https://fastcrypto.org/front/misc/rijndael-alg-fst.c
//
// Implementation of
// http://www.csrc.nist.gov/publications/fips/fips197/fips-197.pdf
constexpr uint32_t te0[256] = {
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,
};
constexpr uint32_t te1[256] = {
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,
};
constexpr uint32_t te2[256] = {
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,
};
constexpr uint32_t te3[256] = {
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,
};
struct alignas(16) u64x2 {
constexpr u64x2() : v{0, 0} {};
constexpr u64x2(uint64_t hi, uint64_t lo) : v{lo, hi} {}
uint64_t v[2];
};
// Software implementation of the Vector128 class, using uint32_t
// as an underlying vector register.
//
struct Vector128 {
inline ABSL_ATTRIBUTE_ALWAYS_INLINE Vector128& operator^=(
const Vector128& other) {
s[0] ^= other.s[0];
s[1] ^= other.s[1];
s[2] ^= other.s[2];
s[3] ^= other.s[3];
return *this;
}
uint32_t s[4];
};
inline ABSL_ATTRIBUTE_ALWAYS_INLINE Vector128
Vector128Load(const void* ABSL_RANDOM_INTERNAL_RESTRICT from) {
Vector128 result;
const uint8_t* ABSL_RANDOM_INTERNAL_RESTRICT src =
reinterpret_cast<const uint8_t*>(from);
result.s[0] = static_cast<uint32_t>(src[0]) << 24 |
static_cast<uint32_t>(src[1]) << 16 |
static_cast<uint32_t>(src[2]) << 8 |
static_cast<uint32_t>(src[3]);
result.s[1] = static_cast<uint32_t>(src[4]) << 24 |
static_cast<uint32_t>(src[5]) << 16 |
static_cast<uint32_t>(src[6]) << 8 |
static_cast<uint32_t>(src[7]);
result.s[2] = static_cast<uint32_t>(src[8]) << 24 |
static_cast<uint32_t>(src[9]) << 16 |
static_cast<uint32_t>(src[10]) << 8 |
static_cast<uint32_t>(src[11]);
result.s[3] = static_cast<uint32_t>(src[12]) << 24 |
static_cast<uint32_t>(src[13]) << 16 |
static_cast<uint32_t>(src[14]) << 8 |
static_cast<uint32_t>(src[15]);
return result;
}
inline ABSL_ATTRIBUTE_ALWAYS_INLINE void Vector128Store(
const Vector128& v, void* ABSL_RANDOM_INTERNAL_RESTRICT to) {
uint8_t* dst = reinterpret_cast<uint8_t*>(to);
dst[0] = static_cast<uint8_t>(v.s[0] >> 24);
dst[1] = static_cast<uint8_t>(v.s[0] >> 16);
dst[2] = static_cast<uint8_t>(v.s[0] >> 8);
dst[3] = static_cast<uint8_t>(v.s[0]);
dst[4] = static_cast<uint8_t>(v.s[1] >> 24);
dst[5] = static_cast<uint8_t>(v.s[1] >> 16);
dst[6] = static_cast<uint8_t>(v.s[1] >> 8);
dst[7] = static_cast<uint8_t>(v.s[1]);
dst[8] = static_cast<uint8_t>(v.s[2] >> 24);
dst[9] = static_cast<uint8_t>(v.s[2] >> 16);
dst[10] = static_cast<uint8_t>(v.s[2] >> 8);
dst[11] = static_cast<uint8_t>(v.s[2]);
dst[12] = static_cast<uint8_t>(v.s[3] >> 24);
dst[13] = static_cast<uint8_t>(v.s[3] >> 16);
dst[14] = static_cast<uint8_t>(v.s[3] >> 8);
dst[15] = static_cast<uint8_t>(v.s[3]);
}
// One round of AES. "round_key" is a public constant for breaking the
// symmetry of AES (ensures previously equal columns differ afterwards).
inline ABSL_ATTRIBUTE_ALWAYS_INLINE Vector128
AesRound(const Vector128& state, const Vector128& round_key) {
// clang-format off
Vector128 result;
result.s[0] = round_key.s[0] ^
te0[uint8_t(state.s[0] >> 24)] ^
te1[uint8_t(state.s[1] >> 16)] ^
te2[uint8_t(state.s[2] >> 8)] ^
te3[uint8_t(state.s[3])];
result.s[1] = round_key.s[1] ^
te0[uint8_t(state.s[1] >> 24)] ^
te1[uint8_t(state.s[2] >> 16)] ^
te2[uint8_t(state.s[3] >> 8)] ^
te3[uint8_t(state.s[0])];
result.s[2] = round_key.s[2] ^
te0[uint8_t(state.s[2] >> 24)] ^
te1[uint8_t(state.s[3] >> 16)] ^
te2[uint8_t(state.s[0] >> 8)] ^
te3[uint8_t(state.s[1])];
result.s[3] = round_key.s[3] ^
te0[uint8_t(state.s[3] >> 24)] ^
te1[uint8_t(state.s[0] >> 16)] ^
te2[uint8_t(state.s[1] >> 8)] ^
te3[uint8_t(state.s[2])];
return result;
// clang-format on
}
// RANDen = RANDom generator or beetroots in Swiss German.
// 'Strong' (well-distributed, unpredictable, backtracking-resistant) random
// generator, faster in some benchmarks than std::mt19937_64 and pcg64_c32.
//
// High-level summary:
// 1) Reverie (see "A Robust and Sponge-Like PRNG with Improved Efficiency") is
// a sponge-like random generator that requires a cryptographic permutation.
// It improves upon "Provably Robust Sponge-Based PRNGs and KDFs" by
// achieving backtracking resistance with only one Permute() per buffer.
//
// 2) "Simpira v2: A Family of Efficient Permutations Using the AES Round
// Function" constructs up to 1024-bit permutations using an improved
// Generalized Feistel network with 2-round AES-128 functions. This Feistel
// block shuffle achieves diffusion faster and is less vulnerable to
// sliced-biclique attacks than the Type-2 cyclic shuffle.
//
// 3) "Improving the Generalized Feistel" and "New criterion for diffusion
// property" extends the same kind of improved Feistel block shuffle to 16
// branches, which enables a 2048-bit permutation.
//
// Combine these three ideas and also change Simpira's subround keys from
// structured/low-entropy counters to digits of Pi.
// Randen constants.
constexpr size_t kFeistelBlocks = 16;
constexpr size_t kFeistelFunctions = kFeistelBlocks / 2; // = 8
constexpr size_t kFeistelRounds = 16 + 1; // > 4 * log2(kFeistelBlocks)
constexpr size_t kKeys = kFeistelRounds * kFeistelFunctions;
// INCLUDE keys.
#include "absl/random/internal/randen-keys.inc"
static_assert(kKeys == kRoundKeys, "kKeys and kRoundKeys must be equal");
// 2 uint64_t lanes per Vector128
static constexpr size_t kLanes = 2;
// The improved Feistel block shuffle function for 16 blocks.
inline ABSL_ATTRIBUTE_ALWAYS_INLINE void BlockShuffle(
uint64_t* ABSL_RANDOM_INTERNAL_RESTRICT state_u64) {
static_assert(kFeistelBlocks == 16,
"Feistel block shuffle only works for 16 blocks.");
constexpr size_t shuffle[kFeistelBlocks] = {7, 2, 13, 4, 11, 8, 3, 6,
15, 0, 9, 10, 1, 14, 5, 12};
u64x2* ABSL_RANDOM_INTERNAL_RESTRICT state =
reinterpret_cast<u64x2*>(state_u64);
// The fully unrolled loop without the memcpy improves the speed by about
// 30% over the equivalent (leaving code here as a comment):
if (false) {
u64x2 source[kFeistelBlocks];
std::memcpy(source, state, sizeof(source));
for (size_t i = 0; i < kFeistelBlocks; i++) {
const u64x2 v0 = source[shuffle[i]];
state[i] = v0;
}
}
const u64x2 v0 = state[shuffle[0]];
const u64x2 v1 = state[shuffle[1]];
const u64x2 v2 = state[shuffle[2]];
const u64x2 v3 = state[shuffle[3]];
const u64x2 v4 = state[shuffle[4]];
const u64x2 v5 = state[shuffle[5]];
const u64x2 v6 = state[shuffle[6]];
const u64x2 v7 = state[shuffle[7]];
const u64x2 w0 = state[shuffle[8]];
const u64x2 w1 = state[shuffle[9]];
const u64x2 w2 = state[shuffle[10]];
const u64x2 w3 = state[shuffle[11]];
const u64x2 w4 = state[shuffle[12]];
const u64x2 w5 = state[shuffle[13]];
const u64x2 w6 = state[shuffle[14]];
const u64x2 w7 = state[shuffle[15]];
state[0] = v0;
state[1] = v1;
state[2] = v2;
state[3] = v3;
state[4] = v4;
state[5] = v5;
state[6] = v6;
state[7] = v7;
state[8] = w0;
state[9] = w1;
state[10] = w2;
state[11] = w3;
state[12] = w4;
state[13] = w5;
state[14] = w6;
state[15] = w7;
}
// Feistel round function using two AES subrounds. Very similar to F()
// from Simpira v2, but with independent subround keys. Uses 17 AES rounds
// per 16 bytes (vs. 10 for AES-CTR). Computing eight round functions in
// parallel hides the 7-cycle AESNI latency on HSW. Note that the Feistel
// XORs are 'free' (included in the second AES instruction).
inline ABSL_ATTRIBUTE_ALWAYS_INLINE const u64x2* FeistelRound(
uint64_t* ABSL_RANDOM_INTERNAL_RESTRICT state,
const u64x2* ABSL_RANDOM_INTERNAL_RESTRICT keys) {
for (size_t branch = 0; branch < kFeistelBlocks; branch += 4) {
const Vector128 s0 = Vector128Load(state + kLanes * branch);
const Vector128 s1 = Vector128Load(state + kLanes * (branch + 1));
const Vector128 f0 = AesRound(s0, Vector128Load(keys));
keys++;
const Vector128 o1 = AesRound(f0, s1);
Vector128Store(o1, state + kLanes * (branch + 1));
// Manually unroll this loop once. about 10% better than not unrolled.
const Vector128 s2 = Vector128Load(state + kLanes * (branch + 2));
const Vector128 s3 = Vector128Load(state + kLanes * (branch + 3));
const Vector128 f2 = AesRound(s2, Vector128Load(keys));
keys++;
const Vector128 o3 = AesRound(f2, s3);
Vector128Store(o3, state + kLanes * (branch + 3));
}
return keys;
}
// Cryptographic permutation based via type-2 Generalized Feistel Network.
// Indistinguishable from ideal by chosen-ciphertext adversaries using less than
// 2^64 queries if the round function is a PRF. This is similar to the b=8 case
// of Simpira v2, but more efficient than its generic construction for b=16.
inline ABSL_ATTRIBUTE_ALWAYS_INLINE void Permute(
const void* keys, uint64_t* ABSL_RANDOM_INTERNAL_RESTRICT state) {
const u64x2* ABSL_RANDOM_INTERNAL_RESTRICT keys128 =
static_cast<const u64x2*>(keys);
for (size_t round = 0; round < kFeistelRounds; ++round) {
keys128 = FeistelRound(state, keys128);
BlockShuffle(state);
}
}
} // namespace
namespace absl {
namespace random_internal {
const void* RandenSlow::GetKeys() {
// Round keys for one AES per Feistel round and branch.
// The canonical implementation uses first digits of Pi.
return round_keys;
}
void RandenSlow::Absorb(const void* seed_void, void* state_void) {
uint64_t* ABSL_RANDOM_INTERNAL_RESTRICT state =
reinterpret_cast<uint64_t*>(state_void);
const uint64_t* ABSL_RANDOM_INTERNAL_RESTRICT seed =
reinterpret_cast<const uint64_t*>(seed_void);
constexpr size_t kCapacityBlocks = kCapacityBytes / sizeof(uint64_t);
static_assert(kCapacityBlocks * sizeof(uint64_t) == kCapacityBytes,
"Not i*V");
for (size_t i = kCapacityBlocks; i < kStateBytes / sizeof(uint64_t); ++i) {
state[i] ^= seed[i - kCapacityBlocks];
}
}
void RandenSlow::Generate(const void* keys, void* state_void) {
static_assert(kCapacityBytes == sizeof(Vector128), "Capacity mismatch");
uint64_t* ABSL_RANDOM_INTERNAL_RESTRICT state =
reinterpret_cast<uint64_t*>(state_void);
const Vector128 prev_inner = Vector128Load(state);
Permute(keys, state);
// Ensure backtracking resistance.
Vector128 inner = Vector128Load(state);
inner ^= prev_inner;
Vector128Store(inner, state);
}
} // namespace random_internal
} // namespace absl