From 8458b4ee399769376ff95442282e90a35109cde9 Mon Sep 17 00:00:00 2001 From: SChernykh Date: Tue, 15 Jun 2021 15:51:29 +0200 Subject: [PATCH] Added signature functions --- src/base/base.cmake | 5 + src/base/tools/cryptonote/BlobReader.h | 1 + src/base/tools/cryptonote/BlockTemplate.cpp | 6 +- src/base/tools/cryptonote/BlockTemplate.h | 1 + src/base/tools/cryptonote/Signatures.cpp | 144 + src/base/tools/cryptonote/Signatures.h | 37 + src/base/tools/cryptonote/WalletAddress.cpp | 4 +- src/base/tools/cryptonote/WalletAddress.h | 1 + src/base/tools/cryptonote/crypto-ops-data.c | 879 +++++ src/base/tools/cryptonote/crypto-ops.c | 3845 +++++++++++++++++++ src/base/tools/cryptonote/crypto-ops.h | 173 + 11 files changed, 5089 insertions(+), 7 deletions(-) create mode 100644 src/base/tools/cryptonote/Signatures.cpp create mode 100644 src/base/tools/cryptonote/Signatures.h create mode 100644 src/base/tools/cryptonote/crypto-ops-data.c create mode 100644 src/base/tools/cryptonote/crypto-ops.c create mode 100644 src/base/tools/cryptonote/crypto-ops.h diff --git a/src/base/base.cmake b/src/base/base.cmake index c947f4b13..e33d787d6 100644 --- a/src/base/base.cmake +++ b/src/base/base.cmake @@ -78,7 +78,9 @@ set(HEADERS_BASE src/base/tools/Timer.h src/base/tools/cryptonote/BlobReader.h src/base/tools/cryptonote/BlockTemplate.h + src/base/tools/cryptonote/Signatures.h src/base/tools/cryptonote/WalletAddress.h + src/base/tools/cryptonote/crypto-ops.h ) set(SOURCES_BASE @@ -130,7 +132,10 @@ set(SOURCES_BASE src/base/tools/String.cpp src/base/tools/Timer.cpp src/base/tools/cryptonote/BlockTemplate.cpp + src/base/tools/cryptonote/Signatures.cpp src/base/tools/cryptonote/WalletAddress.cpp + src/base/tools/cryptonote/crypto-ops.c + src/base/tools/cryptonote/crypto-ops-data.c ) diff --git a/src/base/tools/cryptonote/BlobReader.h b/src/base/tools/cryptonote/BlobReader.h index 90815299b..58f81e2dd 100644 --- a/src/base/tools/cryptonote/BlobReader.h +++ b/src/base/tools/cryptonote/BlobReader.h @@ -1,4 +1,5 @@ /* XMRig + * Copyright 2012-2013 The Cryptonote developers * Copyright 2014-2021 The Monero Project * Copyright 2018-2021 SChernykh * Copyright 2016-2021 XMRig , diff --git a/src/base/tools/cryptonote/BlockTemplate.cpp b/src/base/tools/cryptonote/BlockTemplate.cpp index 8b7845ab4..207bff81b 100644 --- a/src/base/tools/cryptonote/BlockTemplate.cpp +++ b/src/base/tools/cryptonote/BlockTemplate.cpp @@ -1,4 +1,5 @@ /* XMRig + * Copyright 2012-2013 The Cryptonote developers * Copyright 2014-2021 The Monero Project * Copyright 2018-2021 SChernykh * Copyright 2016-2021 XMRig , @@ -24,9 +25,6 @@ #include "base/tools/cryptonote/BlockTemplate.h" -#pragma optimize("", off) - - namespace xmrig { @@ -170,7 +168,7 @@ void CBlockTemplate::CalculateMerkleTreeHash(const uint8_t* hashes, size_t count size_t cnt = count; while (cnt & (cnt - 1)) cnt &= cnt - 1; - Buffer ints(HASH_SIZE); + Buffer ints(cnt * HASH_SIZE); memcpy(ints.data(), hashes, (cnt * 2 - count) * HASH_SIZE); for (i = cnt * 2 - count, j = cnt * 2 - count; j < cnt; i += 2, ++j) { diff --git a/src/base/tools/cryptonote/BlockTemplate.h b/src/base/tools/cryptonote/BlockTemplate.h index 5c242395f..bf87b5d6d 100644 --- a/src/base/tools/cryptonote/BlockTemplate.h +++ b/src/base/tools/cryptonote/BlockTemplate.h @@ -1,4 +1,5 @@ /* XMRig + * Copyright 2012-2013 The Cryptonote developers * Copyright 2014-2021 The Monero Project * Copyright 2018-2021 SChernykh * Copyright 2016-2021 XMRig , diff --git a/src/base/tools/cryptonote/Signatures.cpp b/src/base/tools/cryptonote/Signatures.cpp new file mode 100644 index 000000000..ced225616 --- /dev/null +++ b/src/base/tools/cryptonote/Signatures.cpp @@ -0,0 +1,144 @@ +/* XMRig + * Copyright 2012-2013 The Cryptonote developers + * Copyright 2014-2021 The Monero Project + * Copyright 2018-2021 SChernykh + * Copyright 2016-2021 XMRig , + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see . + */ + + +#include "base/crypto/keccak.h" +#include "base/tools/cryptonote/Signatures.h" +#include "base/tools/cryptonote/crypto-ops.h" +#include "base/tools/Cvt.h" + + +struct ec_scalar { char data[32]; }; +struct hash { char data[32]; }; +struct ec_point { char data[32]; }; +struct signature { ec_scalar c, r; }; +struct s_comm { hash h; ec_point key; ec_point comm; }; + + +static bool less32(const uint8_t* k0, const uint8_t* k1) +{ + for (int n = 31; n >= 0; --n) + { + if (k0[n] < k1[n]) + return true; + if (k0[n] > k1[n]) + return false; + } + return false; +} + + +static void random32_unbiased(uint8_t* bytes) +{ + // l = 2^252 + 27742317777372353535851937790883648493. + // l fits 15 times in 32 bytes (iow, 15 l is the highest multiple of l that fits in 32 bytes) + static const uint8_t limit[32] = { 0xe3, 0x6a, 0x67, 0x72, 0x8b, 0xce, 0x13, 0x29, 0x8f, 0x30, 0x82, 0x8c, 0x0b, 0xa4, 0x10, 0x39, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf0 }; + + do { + xmrig::Cvt::randomBytes(bytes, 32); + if (!less32(bytes, limit)) { + continue; + } + sc_reduce32(bytes); + } while (!sc_isnonzero(bytes)); +} + + +/* generate a random 32-byte (256-bit) integer and copy it to res */ +static void random_scalar(ec_scalar& res) +{ + random32_unbiased((uint8_t*) res.data); +} + + +static void hash_to_scalar(const void* data, size_t length, ec_scalar& res) +{ + uint8_t md[200]; + xmrig::keccak((const char*) data, length, md); + memcpy(&res, md, sizeof(res)); + sc_reduce32((uint8_t*) &res); +} + + +namespace xmrig { + + +void generate_signature(const uint8_t* prefix_hash, const uint8_t* pub, const uint8_t* sec, uint8_t* sig_bytes) +{ + ge_p3 tmp3; + ec_scalar k; + s_comm buf; + + memcpy(buf.h.data, prefix_hash, sizeof(buf.h.data)); + memcpy(buf.key.data, pub, sizeof(buf.key.data)); + + signature& sig = *reinterpret_cast(sig_bytes); + + do { + random_scalar(k); + ge_scalarmult_base(&tmp3, (unsigned char*)&k); + ge_p3_tobytes((unsigned char*)&buf.comm, &tmp3); + hash_to_scalar(&buf, sizeof(s_comm), sig.c); + + if (!sc_isnonzero((const unsigned char*)sig.c.data)) { + continue; + } + + sc_mulsub((unsigned char*)&sig.r, (unsigned char*)&sig.c, sec, (unsigned char*)&k); + } while (!sc_isnonzero((const unsigned char*)sig.r.data)); +} + + +bool check_signature(const uint8_t* prefix_hash, const uint8_t* pub, const uint8_t* sig_bytes) +{ + ge_p2 tmp2; + ge_p3 tmp3; + ec_scalar c; + s_comm buf; + + memcpy(buf.h.data, prefix_hash, sizeof(buf.h.data)); + memcpy(buf.key.data, pub, sizeof(buf.key.data)); + + if (ge_frombytes_vartime(&tmp3, pub) != 0) { + return false; + } + + const signature& sig = *reinterpret_cast(sig_bytes); + + if (sc_check((const uint8_t*)&sig.c) != 0 || sc_check((const uint8_t*)&sig.r) != 0 || !sc_isnonzero((const uint8_t*)&sig.c)) { + return false; + } + + ge_double_scalarmult_base_vartime(&tmp2, (const uint8_t*)&sig.c, &tmp3, (const uint8_t*)&sig.r); + ge_tobytes((uint8_t*)&buf.comm, &tmp2); + + static const ec_point infinity = { { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} }; + if (memcmp(&buf.comm, &infinity, 32) == 0) + return false; + + hash_to_scalar(&buf, sizeof(s_comm), c); + sc_sub((uint8_t*)&c, (uint8_t*)&c, (const uint8_t*)&sig.c); + + return sc_isnonzero((uint8_t*)&c) == 0; +} + + + +} /* namespace xmrig */ diff --git a/src/base/tools/cryptonote/Signatures.h b/src/base/tools/cryptonote/Signatures.h new file mode 100644 index 000000000..a9db90462 --- /dev/null +++ b/src/base/tools/cryptonote/Signatures.h @@ -0,0 +1,37 @@ +/* XMRig + * Copyright 2012-2013 The Cryptonote developers + * Copyright 2014-2021 The Monero Project + * Copyright 2018-2021 SChernykh + * Copyright 2016-2021 XMRig , + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see . + */ + +#ifndef XMRIG_SIGNATURES_H +#define XMRIG_SIGNATURES_H + + +#include + + +namespace xmrig { + + +void generate_signature(const uint8_t* prefix_hash, const uint8_t* pub, const uint8_t* sec, uint8_t* sig); +bool check_signature(const uint8_t* prefix_hash, const uint8_t* pub, const uint8_t* sig); + +} /* namespace xmrig */ + + +#endif /* XMRIG_SIGNATURES_H */ diff --git a/src/base/tools/cryptonote/WalletAddress.cpp b/src/base/tools/cryptonote/WalletAddress.cpp index 2ee2e7a38..0445626ee 100644 --- a/src/base/tools/cryptonote/WalletAddress.cpp +++ b/src/base/tools/cryptonote/WalletAddress.cpp @@ -1,4 +1,5 @@ /* XMRig + * Copyright 2012-2013 The Cryptonote developers * Copyright 2014-2021 The Monero Project * Copyright 2018-2021 SChernykh * Copyright 2016-2021 XMRig , @@ -26,9 +27,6 @@ #include -#pragma optimize("", off) - - namespace xmrig { diff --git a/src/base/tools/cryptonote/WalletAddress.h b/src/base/tools/cryptonote/WalletAddress.h index 166b99c24..cc3c2ec42 100644 --- a/src/base/tools/cryptonote/WalletAddress.h +++ b/src/base/tools/cryptonote/WalletAddress.h @@ -1,4 +1,5 @@ /* XMRig + * Copyright 2012-2013 The Cryptonote developers * Copyright 2014-2021 The Monero Project * Copyright 2018-2021 SChernykh * Copyright 2016-2021 XMRig , diff --git a/src/base/tools/cryptonote/crypto-ops-data.c b/src/base/tools/cryptonote/crypto-ops-data.c new file mode 100644 index 000000000..d16fd9429 --- /dev/null +++ b/src/base/tools/cryptonote/crypto-ops-data.c @@ -0,0 +1,879 @@ +// Copyright (c) 2014-2020, The Monero Project +// +// All rights reserved. +// +// Redistribution and use in source and binary forms, with or without modification, are +// permitted provided that the following conditions are met: +// +// 1. Redistributions of source code must retain the above copyright notice, this list of +// conditions and the following disclaimer. +// +// 2. Redistributions in binary form must reproduce the above copyright notice, this list +// of conditions and the following disclaimer in the documentation and/or other +// materials provided with the distribution. +// +// 3. Neither the name of the copyright holder nor the names of its contributors may be +// used to endorse or promote products derived from this software without specific +// prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY +// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF +// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL +// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, +// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF +// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers + +#include + +#include "crypto-ops.h" + +/* sqrt(x) is such an integer y that 0 <= y <= p - 1, y % 2 = 0, and y^2 = x (mod p). */ +/* d = -121665 / 121666 */ +const fe fe_d = {-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116}; /* d */ +const fe fe_sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482}; /* sqrt(-1) */ +const fe fe_d2 = {-21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199}; /* 2 * d */ + +/* base[i][j] = (j+1)*256^i*B */ +const ge_precomp ge_base[32][8] = { + { + {{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605}, + {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378}, + {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}}, + {{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303}, + {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081}, + {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697}}, + {{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024}, + {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574}, + {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}}, + {{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540}, + {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397}, + {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325}}, + {{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380}, + {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306}, + {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}}, + {{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777}, + {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737}, + {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652}}, + {{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766}, + {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701}, + {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}}, + {{14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726}, + {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955}, + {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425}} + }, { + {{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171}, + {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510}, + {17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660}}, + {{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639}, + {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963}, + {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950}}, + {{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568}, + {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335}, + {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628}}, + {{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007}, + {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772}, + {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653}}, + {{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567}, + {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686}, + {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372}}, + {{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887}, + {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954}, + {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953}}, + {{24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833}, + {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532}, + {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876}}, + {{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268}, + {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214}, + {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038}} + }, { + {{6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800}, + {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645}, + {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664}}, + {{1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933}, + {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182}, + {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222}}, + {{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991}, + {20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880}, + {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092}}, + {{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295}, + {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788}, + {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553}}, + {{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026}, + {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347}, + {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033}}, + {{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395}, + {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278}, + {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890}}, + {{32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995}, + {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596}, + {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891}}, + {{31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060}, + {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608}, + {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606}} + }, { + {{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389}, + {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 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-10498527, -16307831, -23479533, -9371869, -21393143, 2465074}, + {20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140}}, + {{-16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717}, + {-1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101}, + {24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127}} + }, { + {{-12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632}, + {-26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415}, + {-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160}}, + {{31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876}, + {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625}, + {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478}}, + {{27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164}, + {26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595}, + {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248}}, + {{-16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858}, + {15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193}, + {8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184}}, + {{-18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942}, + {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635}, + {21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948}}, + {{11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935}, + {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415}, + {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416}}, + {{-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018}, + {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778}, + {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659}}, + {{-24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385}, + {18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503}, + {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329}} + }, { + {{20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056}, + {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838}, + {24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948}}, + {{-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691}, + {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118}, + {-23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517}}, + {{-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269}, + {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904}, + {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589}}, + {{-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193}, + {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910}, + {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930}}, + {{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667}, + {25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481}, + {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876}}, + {{22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640}, + {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278}, + {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112}}, + {{26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272}, + {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012}, + {-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221}}, + {{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046}, + {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345}, + {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310}} + }, { + {{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937}, + {31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636}, + {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008}}, + {{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429}, + {-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576}, + {31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066}}, + {{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490}, + {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104}, + {33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053}}, + {{31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275}, + {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511}, + {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095}}, + {{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439}, + {23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939}, + {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424}}, + {{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310}, + {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608}, + {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079}}, + {{-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101}, + {21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418}, + {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576}}, + {{30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356}, + {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996}, + {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099}} + }, { + {{-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728}, + {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658}, + {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242}}, + {{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001}, + {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766}, + {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373}}, + {{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458}, + {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628}, + {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657}}, + {{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062}, + {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616}, + {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014}}, + {{24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383}, + {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814}, + {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718}}, + {{30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417}, + {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222}, + {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444}}, + {{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597}, + {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970}, + {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799}}, + {{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647}, + {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511}, + {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032}} + }, { + {{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834}, + {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461}, + {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062}}, + {{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516}, + {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547}, + {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240}}, + {{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038}, + {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741}, + {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103}}, + {{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747}, + {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323}, + {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016}}, + {{-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373}, + {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228}, + {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141}}, + {{16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399}, + {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831}, + {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376}}, + {{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313}, + {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958}, + {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577}}, + {{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743}, + {29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684}, + {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476}} + } +}; + +const ge_precomp ge_Bi[8] = { + {{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605}, + {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378}, + {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}}, {{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024}, + {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574}, + {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}}, {{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380}, + {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306}, + {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}}, {{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766}, + {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701}, + {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}}, {{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877}, + {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951}, + {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784}}, {{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436}, + {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918}, + {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877}}, {{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800}, + {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305}, + {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300}}, {{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876}, + {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619}, + {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683}} +}; + +/* A = 2 * (1 - d) / (1 + d) = 486662 */ +const fe fe_ma2 = {-12721188, -3529, 0, 0, 0, 0, 0, 0, 0, 0}; /* -A^2 */ +const fe fe_ma = {-486662, 0, 0, 0, 0, 0, 0, 0, 0, 0}; /* -A */ +const fe fe_fffb1 = {-31702527, -2466483, -26106795, -12203692, -12169197, -321052, 14850977, -10296299, -16929438, -407568}; /* sqrt(-2 * A * (A + 2)) */ +const fe fe_fffb2 = {8166131, -6741800, -17040804, 3154616, 21461005, 1466302, -30876704, -6368709, 10503587, -13363080}; /* sqrt(2 * A * (A + 2)) */ +const fe fe_fffb3 = {-13620103, 14639558, 4532995, 7679154, 16815101, -15883539, -22863840, -14813421, 13716513, -6477756}; /* sqrt(-sqrt(-1) * A * (A + 2)) */ +const fe fe_fffb4 = {-21786234, -12173074, 21573800, 4524538, -4645904, 16204591, 8012863, -8444712, 3212926, 6885324}; /* sqrt(sqrt(-1) * A * (A + 2)) */ +const ge_p3 ge_p3_identity = { {0}, {1, 0}, {1, 0}, {0} }; +const ge_p3 ge_p3_H = { + {7329926, -15101362, 31411471, 7614783, 27996851, -3197071, -11157635, -6878293, 466949, -7986503}, + {5858699, 5096796, 21321203, -7536921, -5553480, -11439507, -5627669, 15045946, 19977121, 5275251}, + {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {23443568, -5110398, -8776029, -4345135, 6889568, -14710814, 7474843, 3279062, 14550766, -7453428} +}; diff --git a/src/base/tools/cryptonote/crypto-ops.c b/src/base/tools/cryptonote/crypto-ops.c new file mode 100644 index 000000000..40bac7351 --- /dev/null +++ b/src/base/tools/cryptonote/crypto-ops.c @@ -0,0 +1,3845 @@ +// Copyright (c) 2014-2020, The Monero Project +// +// All rights reserved. +// +// Redistribution and use in source and binary forms, with or without modification, are +// permitted provided that the following conditions are met: +// +// 1. Redistributions of source code must retain the above copyright notice, this list of +// conditions and the following disclaimer. +// +// 2. Redistributions in binary form must reproduce the above copyright notice, this list +// of conditions and the following disclaimer in the documentation and/or other +// materials provided with the distribution. +// +// 3. Neither the name of the copyright holder nor the names of its contributors may be +// used to endorse or promote products derived from this software without specific +// prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY +// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF +// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL +// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, +// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF +// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers + +#include +#include + +#include "crypto-ops.h" + +#ifdef _MSC_VER +#pragma warning(disable: 4146 4244) +#endif + +/* Predeclarations */ + +static void fe_mul(fe, const fe, const fe); +static void fe_sq(fe, const fe); +static void ge_madd(ge_p1p1 *, const ge_p3 *, const ge_precomp *); +static void ge_msub(ge_p1p1 *, const ge_p3 *, const ge_precomp *); +static void ge_p2_0(ge_p2 *); +static void ge_p3_dbl(ge_p1p1 *, const ge_p3 *); +static void fe_divpowm1(fe, const fe, const fe); + +/* Common functions */ + +uint64_t load_3(const unsigned char *in) { + uint64_t result; + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + return result; +} + +uint64_t load_4(const unsigned char *in) +{ + uint64_t result; + result = (uint64_t) in[0]; + result |= ((uint64_t) in[1]) << 8; + result |= ((uint64_t) in[2]) << 16; + result |= ((uint64_t) in[3]) << 24; + return result; +} + +/* From fe_0.c */ + +/* +h = 0 +*/ + +static void fe_0(fe h) { + h[0] = 0; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; + h[5] = 0; + h[6] = 0; + h[7] = 0; + h[8] = 0; + h[9] = 0; +} + +/* From fe_1.c */ + +/* +h = 1 +*/ + +static void fe_1(fe h) { + h[0] = 1; + h[1] = 0; + h[2] = 0; + h[3] = 0; + h[4] = 0; + h[5] = 0; + h[6] = 0; + h[7] = 0; + h[8] = 0; + h[9] = 0; +} + +/* From fe_add.c */ + +/* +h = f + g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +void fe_add(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t h0 = f0 + g0; + int32_t h1 = f1 + g1; + int32_t h2 = f2 + g2; + int32_t h3 = f3 + g3; + int32_t h4 = f4 + g4; + int32_t h5 = f5 + g5; + int32_t h6 = f6 + g6; + int32_t h7 = f7 + g7; + int32_t h8 = f8 + g8; + int32_t h9 = f9 + g9; + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* From fe_cmov.c */ + +/* +Replace (f,g) with (g,g) if b == 1; +replace (f,g) with (f,g) if b == 0. + +Preconditions: b in {0,1}. +*/ + +static void fe_cmov(fe f, const fe g, unsigned int b) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t x0 = f0 ^ g0; + int32_t x1 = f1 ^ g1; + int32_t x2 = f2 ^ g2; + int32_t x3 = f3 ^ g3; + int32_t x4 = f4 ^ g4; + int32_t x5 = f5 ^ g5; + int32_t x6 = f6 ^ g6; + int32_t x7 = f7 ^ g7; + int32_t x8 = f8 ^ g8; + int32_t x9 = f9 ^ g9; + assert((((b - 1) & ~b) | ((b - 2) & ~(b - 1))) == (unsigned int) -1); + b = -b; + x0 &= b; + x1 &= b; + x2 &= b; + x3 &= b; + x4 &= b; + x5 &= b; + x6 &= b; + x7 &= b; + x8 &= b; + x9 &= b; + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + f[5] = f5 ^ x5; + f[6] = f6 ^ x6; + f[7] = f7 ^ x7; + f[8] = f8 ^ x8; + f[9] = f9 ^ x9; +} + +/* From fe_copy.c */ + +/* +h = f +*/ + +static void fe_copy(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + h[0] = f0; + h[1] = f1; + h[2] = f2; + h[3] = f3; + h[4] = f4; + h[5] = f5; + h[6] = f6; + h[7] = f7; + h[8] = f8; + h[9] = f9; +} + +/* From fe_invert.c */ + +void fe_invert(fe out, const fe z) { + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + fe_sq(t0, z); + fe_sq(t1, t0); + fe_sq(t1, t1); + fe_mul(t1, z, t1); + fe_mul(t0, t0, t1); + fe_sq(t2, t0); + fe_mul(t1, t1, t2); + fe_sq(t2, t1); + for (i = 0; i < 4; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); + fe_sq(t2, t1); + for (i = 0; i < 9; ++i) { + fe_sq(t2, t2); + } + fe_mul(t2, t2, t1); + fe_sq(t3, t2); + for (i = 0; i < 19; ++i) { + fe_sq(t3, t3); + } + fe_mul(t2, t3, t2); + fe_sq(t2, t2); + for (i = 0; i < 9; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); + fe_sq(t2, t1); + for (i = 0; i < 49; ++i) { + fe_sq(t2, t2); + } + fe_mul(t2, t2, t1); + fe_sq(t3, t2); + for (i = 0; i < 99; ++i) { + fe_sq(t3, t3); + } + fe_mul(t2, t3, t2); + fe_sq(t2, t2); + for (i = 0; i < 49; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); + fe_sq(t1, t1); + for (i = 0; i < 4; ++i) { + fe_sq(t1, t1); + } + fe_mul(out, t1, t0); + + return; +} + +/* From fe_isnegative.c */ + +/* +return 1 if f is in {1,3,5,...,q-2} +return 0 if f is in {0,2,4,...,q-1} + +Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +static int fe_isnegative(const fe f) { + unsigned char s[32]; + fe_tobytes(s, f); + return s[0] & 1; +} + +/* From fe_isnonzero.c, modified */ + +static int fe_isnonzero(const fe f) { + unsigned char s[32]; + fe_tobytes(s, f); + return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] | + s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] | + s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] | + s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1; +} + +/* From fe_mul.c */ + +/* +h = f * g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + +Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +*/ + +/* +Notes on implementation strategy: + +Using schoolbook multiplication. +Karatsuba would save a little in some cost models. + +Most multiplications by 2 and 19 are 32-bit precomputations; +cheaper than 64-bit postcomputations. + +There is one remaining multiplication by 19 in the carry chain; +one *19 precomputation can be merged into this, +but the resulting data flow is considerably less clean. + +There are 12 carries below. +10 of them are 2-way parallelizable and vectorizable. +Can get away with 11 carries, but then data flow is much deeper. + +With tighter constraints on inputs can squeeze carries into int32. +*/ + +static void fe_mul(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ + int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + int32_t g3_19 = 19 * g3; + int32_t g4_19 = 19 * g4; + int32_t g5_19 = 19 * g5; + int32_t g6_19 = 19 * g6; + int32_t g7_19 = 19 * g7; + int32_t g8_19 = 19 * g8; + int32_t g9_19 = 19 * g9; + int32_t f1_2 = 2 * f1; + int32_t f3_2 = 2 * f3; + int32_t f5_2 = 2 * f5; + int32_t f7_2 = 2 * f7; + int32_t f9_2 = 2 * f9; + int64_t f0g0 = f0 * (int64_t) g0; + int64_t f0g1 = f0 * (int64_t) g1; + int64_t f0g2 = f0 * (int64_t) g2; + int64_t f0g3 = f0 * (int64_t) g3; + int64_t f0g4 = f0 * (int64_t) g4; + int64_t f0g5 = f0 * (int64_t) g5; + int64_t f0g6 = f0 * (int64_t) g6; + int64_t f0g7 = f0 * (int64_t) g7; + int64_t f0g8 = f0 * (int64_t) g8; + int64_t f0g9 = f0 * (int64_t) g9; + int64_t f1g0 = f1 * (int64_t) g0; + int64_t f1g1_2 = f1_2 * (int64_t) g1; + int64_t f1g2 = f1 * (int64_t) g2; + int64_t f1g3_2 = f1_2 * (int64_t) g3; + int64_t f1g4 = f1 * (int64_t) g4; + int64_t f1g5_2 = f1_2 * (int64_t) g5; + int64_t f1g6 = f1 * (int64_t) g6; + int64_t f1g7_2 = f1_2 * (int64_t) g7; + int64_t f1g8 = f1 * (int64_t) g8; + int64_t f1g9_38 = f1_2 * (int64_t) g9_19; + int64_t f2g0 = f2 * (int64_t) g0; + int64_t f2g1 = f2 * (int64_t) g1; + int64_t f2g2 = f2 * (int64_t) g2; + int64_t f2g3 = f2 * (int64_t) g3; + int64_t f2g4 = f2 * (int64_t) g4; + int64_t f2g5 = f2 * (int64_t) g5; + int64_t f2g6 = f2 * (int64_t) g6; + int64_t f2g7 = f2 * (int64_t) g7; + int64_t f2g8_19 = f2 * (int64_t) g8_19; + int64_t f2g9_19 = f2 * (int64_t) g9_19; + int64_t f3g0 = f3 * (int64_t) g0; + int64_t f3g1_2 = f3_2 * (int64_t) g1; + int64_t f3g2 = f3 * (int64_t) g2; + int64_t f3g3_2 = f3_2 * (int64_t) g3; + int64_t f3g4 = f3 * (int64_t) g4; + int64_t f3g5_2 = f3_2 * (int64_t) g5; + int64_t f3g6 = f3 * (int64_t) g6; + int64_t f3g7_38 = f3_2 * (int64_t) g7_19; + int64_t f3g8_19 = f3 * (int64_t) g8_19; + int64_t f3g9_38 = f3_2 * (int64_t) g9_19; + int64_t f4g0 = f4 * (int64_t) g0; + int64_t f4g1 = f4 * (int64_t) g1; + int64_t f4g2 = f4 * (int64_t) g2; + int64_t f4g3 = f4 * (int64_t) g3; + int64_t f4g4 = f4 * (int64_t) g4; + int64_t f4g5 = f4 * (int64_t) g5; + int64_t f4g6_19 = f4 * (int64_t) g6_19; + int64_t f4g7_19 = f4 * (int64_t) g7_19; + int64_t f4g8_19 = f4 * (int64_t) g8_19; + int64_t f4g9_19 = f4 * (int64_t) g9_19; + int64_t f5g0 = f5 * (int64_t) g0; + int64_t f5g1_2 = f5_2 * (int64_t) g1; + int64_t f5g2 = f5 * (int64_t) g2; + int64_t f5g3_2 = f5_2 * (int64_t) g3; + int64_t f5g4 = f5 * (int64_t) g4; + int64_t f5g5_38 = f5_2 * (int64_t) g5_19; + int64_t f5g6_19 = f5 * (int64_t) g6_19; + int64_t f5g7_38 = f5_2 * (int64_t) g7_19; + int64_t f5g8_19 = f5 * (int64_t) g8_19; + int64_t f5g9_38 = f5_2 * (int64_t) g9_19; + int64_t f6g0 = f6 * (int64_t) g0; + int64_t f6g1 = f6 * (int64_t) g1; + int64_t f6g2 = f6 * (int64_t) g2; + int64_t f6g3 = f6 * (int64_t) g3; + int64_t f6g4_19 = f6 * (int64_t) g4_19; + int64_t f6g5_19 = f6 * (int64_t) g5_19; + int64_t f6g6_19 = f6 * (int64_t) g6_19; + int64_t f6g7_19 = f6 * (int64_t) g7_19; + int64_t f6g8_19 = f6 * (int64_t) g8_19; + int64_t f6g9_19 = f6 * (int64_t) g9_19; + int64_t f7g0 = f7 * (int64_t) g0; + int64_t f7g1_2 = f7_2 * (int64_t) g1; + int64_t f7g2 = f7 * (int64_t) g2; + int64_t f7g3_38 = f7_2 * (int64_t) g3_19; + int64_t f7g4_19 = f7 * (int64_t) g4_19; + int64_t f7g5_38 = f7_2 * (int64_t) g5_19; + int64_t f7g6_19 = f7 * (int64_t) g6_19; + int64_t f7g7_38 = f7_2 * (int64_t) g7_19; + int64_t f7g8_19 = f7 * (int64_t) g8_19; + int64_t f7g9_38 = f7_2 * (int64_t) g9_19; + int64_t f8g0 = f8 * (int64_t) g0; + int64_t f8g1 = f8 * (int64_t) g1; + int64_t f8g2_19 = f8 * (int64_t) g2_19; + int64_t f8g3_19 = f8 * (int64_t) g3_19; + int64_t f8g4_19 = f8 * (int64_t) g4_19; + int64_t f8g5_19 = f8 * (int64_t) g5_19; + int64_t f8g6_19 = f8 * (int64_t) g6_19; + int64_t f8g7_19 = f8 * (int64_t) g7_19; + int64_t f8g8_19 = f8 * (int64_t) g8_19; + int64_t f8g9_19 = f8 * (int64_t) g9_19; + int64_t f9g0 = f9 * (int64_t) g0; + int64_t f9g1_38 = f9_2 * (int64_t) g1_19; + int64_t f9g2_19 = f9 * (int64_t) g2_19; + int64_t f9g3_38 = f9_2 * (int64_t) g3_19; + int64_t f9g4_19 = f9 * (int64_t) g4_19; + int64_t f9g5_38 = f9_2 * (int64_t) g5_19; + int64_t f9g6_19 = f9 * (int64_t) g6_19; + int64_t f9g7_38 = f9_2 * (int64_t) g7_19; + int64_t f9g8_19 = f9 * (int64_t) g8_19; + int64_t f9g9_38 = f9_2 * (int64_t) g9_19; + int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; + int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; + int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; + int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; + int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; + int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; + int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; + int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; + int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; + int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + /* + |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 + */ + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ + + carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ + + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ + + carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* From fe_neg.c */ + +/* +h = -f + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. +*/ + +static void fe_neg(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t h0 = -f0; + int32_t h1 = -f1; + int32_t h2 = -f2; + int32_t h3 = -f3; + int32_t h4 = -f4; + int32_t h5 = -f5; + int32_t h6 = -f6; + int32_t h7 = -f7; + int32_t h8 = -f8; + int32_t h9 = -f9; + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* From fe_sq.c */ + +/* +h = f * f +Can overlap h with f. + +Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + +Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +static void fe_sq(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + + carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + + carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + + carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* From fe_sq2.c */ + +/* +h = 2 * f * f +Can overlap h with f. + +Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + +Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +static void fe_sq2(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + + carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + + carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + + carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* From fe_sub.c */ + +/* +h = f - g +Can overlap h with f or g. + +Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + +Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. +*/ + +static void fe_sub(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t h0 = f0 - g0; + int32_t h1 = f1 - g1; + int32_t h2 = f2 - g2; + int32_t h3 = f3 - g3; + int32_t h4 = f4 - g4; + int32_t h5 = f5 - g5; + int32_t h6 = f6 - g6; + int32_t h7 = f7 - g7; + int32_t h8 = f8 - g8; + int32_t h9 = f9 - g9; + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* From fe_tobytes.c */ + +/* +Preconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + +Write p=2^255-19; q=floor(h/p). +Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + +Proof: + Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. + + Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + Then 0> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + + carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; + carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; + carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; + carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; + carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; + carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; + carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; + carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; + carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; + carry9 = h9 >> 25; h9 -= carry9 << 25; + /* h10 = carry9 */ + + /* + Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + Have h0+...+2^230 h9 between 0 and 2^255-1; + evidently 2^255 h10-2^255 q = 0. + Goal: Output h0+...+2^230 h9. + */ + + s[0] = h0 >> 0; + s[1] = h0 >> 8; + s[2] = h0 >> 16; + s[3] = (h0 >> 24) | (h1 << 2); + s[4] = h1 >> 6; + s[5] = h1 >> 14; + s[6] = (h1 >> 22) | (h2 << 3); + s[7] = h2 >> 5; + s[8] = h2 >> 13; + s[9] = (h2 >> 21) | (h3 << 5); + s[10] = h3 >> 3; + s[11] = h3 >> 11; + s[12] = (h3 >> 19) | (h4 << 6); + s[13] = h4 >> 2; + s[14] = h4 >> 10; + s[15] = h4 >> 18; + s[16] = h5 >> 0; + s[17] = h5 >> 8; + s[18] = h5 >> 16; + s[19] = (h5 >> 24) | (h6 << 1); + s[20] = h6 >> 7; + s[21] = h6 >> 15; + s[22] = (h6 >> 23) | (h7 << 3); + s[23] = h7 >> 5; + s[24] = h7 >> 13; + s[25] = (h7 >> 21) | (h8 << 4); + s[26] = h8 >> 4; + s[27] = h8 >> 12; + s[28] = (h8 >> 20) | (h9 << 6); + s[29] = h9 >> 2; + s[30] = h9 >> 10; + s[31] = h9 >> 18; +} + +/* From ge_add.c */ + +void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { + fe t0; + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->YplusX); + fe_mul(r->Y, r->Y, q->YminusX); + fe_mul(r->T, q->T2d, p->T); + fe_mul(r->X, p->Z, q->Z); + fe_add(t0, r->X, r->X); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); +} + +/* From ge_double_scalarmult.c, modified */ + +static void slide(signed char *r, const unsigned char *a) { + int i; + int b; + int k; + + for (i = 0; i < 256; ++i) { + r[i] = 1 & (a[i >> 3] >> (i & 7)); + } + + for (i = 0; i < 256; ++i) { + if (r[i]) { + for (b = 1; b <= 6 && i + b < 256; ++b) { + if (r[i + b]) { + if (r[i] + (r[i + b] << b) <= 15) { + r[i] += r[i + b] << b; r[i + b] = 0; + } else if (r[i] - (r[i + b] << b) >= -15) { + r[i] -= r[i + b] << b; + for (k = i + b; k < 256; ++k) { + if (!r[k]) { + r[k] = 1; + break; + } + r[k] = 0; + } + } else + break; + } + } + } + } +} + +void ge_dsm_precomp(ge_dsmp r, const ge_p3 *s) { + ge_p1p1 t; + ge_p3 s2, u; + ge_p3_to_cached(&r[0], s); + ge_p3_dbl(&t, s); ge_p1p1_to_p3(&s2, &t); + ge_add(&t, &s2, &r[0]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[1], &u); + ge_add(&t, &s2, &r[1]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[2], &u); + ge_add(&t, &s2, &r[2]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[3], &u); + ge_add(&t, &s2, &r[3]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[4], &u); + ge_add(&t, &s2, &r[4]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[5], &u); + ge_add(&t, &s2, &r[5]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[6], &u); + ge_add(&t, &s2, &r[6]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[7], &u); +} + +/* +r = a * A + b * B +where a = a[0]+256*a[1]+...+256^31 a[31]. +and b = b[0]+256*b[1]+...+256^31 b[31]. +B is the Ed25519 base point (x,4/5) with x positive. +*/ + +void ge_double_scalarmult_base_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) { + signed char aslide[256]; + signed char bslide[256]; + ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ + ge_p1p1 t; + ge_p3 u; + int i; + + slide(aslide, a); + slide(bslide, b); + ge_dsm_precomp(Ai, A); + + ge_p2_0(r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i]) break; + } + + for (; i >= 0; --i) { + ge_p2_dbl(&t, r); + + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ai[aslide[i]/2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ai[(-aslide[i])/2]); + } + + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_madd(&t, &u, &ge_Bi[bslide[i]/2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_msub(&t, &u, &ge_Bi[(-bslide[i])/2]); + } + + ge_p1p1_to_p2(r, &t); + } +} + +// Computes aG + bB + cC (G is the fixed basepoint) +void ge_triple_scalarmult_base_vartime(ge_p2 *r, const unsigned char *a, const unsigned char *b, const ge_dsmp Bi, const unsigned char *c, const ge_dsmp Ci) { + signed char aslide[256]; + signed char bslide[256]; + signed char cslide[256]; + ge_p1p1 t; + ge_p3 u; + int i; + + slide(aslide, a); + slide(bslide, b); + slide(cslide, c); + + ge_p2_0(r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i] || cslide[i]) break; + } + + for (; i >= 0; --i) { + ge_p2_dbl(&t, r); + + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_madd(&t, &u, &ge_Bi[aslide[i]/2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_msub(&t, &u, &ge_Bi[(-aslide[i])/2]); + } + + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Bi[bslide[i]/2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Bi[(-bslide[i])/2]); + } + + if (cslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ci[cslide[i]/2]); + } else if (cslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ci[(-cslide[i])/2]); + } + + ge_p1p1_to_p2(r, &t); + } +} + +void ge_double_scalarmult_base_vartime_p3(ge_p3 *r3, const unsigned char *a, const ge_p3 *A, const unsigned char *b) { + signed char aslide[256]; + signed char bslide[256]; + ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ + ge_p1p1 t; + ge_p3 u; + ge_p2 r; + int i; + + slide(aslide, a); + slide(bslide, b); + ge_dsm_precomp(Ai, A); + + ge_p2_0(&r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i]) break; + } + + for (; i >= 0; --i) { + ge_p2_dbl(&t, &r); + + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ai[aslide[i]/2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ai[(-aslide[i])/2]); + } + + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_madd(&t, &u, &ge_Bi[bslide[i]/2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_msub(&t, &u, &ge_Bi[(-bslide[i])/2]); + } + + if (i == 0) + ge_p1p1_to_p3(r3, &t); + else + ge_p1p1_to_p2(&r, &t); + } +} + +/* From ge_frombytes.c, modified */ + +int ge_frombytes_vartime(ge_p3 *h, const unsigned char *s) { + fe u; + fe v; + fe vxx; + fe check; + + /* From fe_frombytes.c */ + + int64_t h0 = load_4(s); + int64_t h1 = load_3(s + 4) << 6; + int64_t h2 = load_3(s + 7) << 5; + int64_t h3 = load_3(s + 10) << 3; + int64_t h4 = load_3(s + 13) << 2; + int64_t h5 = load_4(s + 16); + int64_t h6 = load_3(s + 20) << 7; + int64_t h7 = load_3(s + 23) << 5; + int64_t h8 = load_3(s + 26) << 4; + int64_t h9 = (load_3(s + 29) & 8388607) << 2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + /* Validate the number to be canonical */ + if (h9 == 33554428 && h8 == 268435440 && h7 == 536870880 && h6 == 2147483520 && + h5 == 4294967295 && h4 == 67108860 && h3 == 134217720 && h2 == 536870880 && + h1 == 1073741760 && h0 >= 4294967277) { + return -1; + } + + carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + h->Y[0] = h0; + h->Y[1] = h1; + h->Y[2] = h2; + h->Y[3] = h3; + h->Y[4] = h4; + h->Y[5] = h5; + h->Y[6] = h6; + h->Y[7] = h7; + h->Y[8] = h8; + h->Y[9] = h9; + + /* End fe_frombytes.c */ + + fe_1(h->Z); + fe_sq(u, h->Y); + fe_mul(v, u, fe_d); + fe_sub(u, u, h->Z); /* u = y^2-1 */ + fe_add(v, v, h->Z); /* v = dy^2+1 */ + + fe_divpowm1(h->X, u, v); /* x = uv^3(uv^7)^((q-5)/8) */ + + fe_sq(vxx, h->X); + fe_mul(vxx, vxx, v); + fe_sub(check, vxx, u); /* vx^2-u */ + if (fe_isnonzero(check)) { + fe_add(check, vxx, u); /* vx^2+u */ + if (fe_isnonzero(check)) { + return -1; + } + fe_mul(h->X, h->X, fe_sqrtm1); + } + + if (fe_isnegative(h->X) != (s[31] >> 7)) { + /* If x = 0, the sign must be positive */ + if (!fe_isnonzero(h->X)) { + return -1; + } + fe_neg(h->X, h->X); + } + + fe_mul(h->T, h->X, h->Y); + return 0; +} + +/* From ge_madd.c */ + +/* +r = p + q +*/ + +static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { + fe t0; + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->yplusx); + fe_mul(r->Y, r->Y, q->yminusx); + fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); +} + +/* From ge_msub.c */ + +/* +r = p - q +*/ + +static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { + fe t0; + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->yminusx); + fe_mul(r->Y, r->Y, q->yplusx); + fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_sub(r->Z, t0, r->T); + fe_add(r->T, t0, r->T); +} + +/* From ge_p1p1_to_p2.c */ + +/* +r = p +*/ + +void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { + fe_mul(r->X, p->X, p->T); + fe_mul(r->Y, p->Y, p->Z); + fe_mul(r->Z, p->Z, p->T); +} + +/* From ge_p1p1_to_p3.c */ + +/* +r = p +*/ + +void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { + fe_mul(r->X, p->X, p->T); + fe_mul(r->Y, p->Y, p->Z); + fe_mul(r->Z, p->Z, p->T); + fe_mul(r->T, p->X, p->Y); +} + +/* From ge_p2_0.c */ + +static void ge_p2_0(ge_p2 *h) { + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); +} + +/* From ge_p2_dbl.c */ + +/* +r = 2 * p +*/ + +void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { + fe t0; + fe_sq(r->X, p->X); + fe_sq(r->Z, p->Y); + fe_sq2(r->T, p->Z); + fe_add(r->Y, p->X, p->Y); + fe_sq(t0, r->Y); + fe_add(r->Y, r->Z, r->X); + fe_sub(r->Z, r->Z, r->X); + fe_sub(r->X, t0, r->Y); + fe_sub(r->T, r->T, r->Z); +} + +/* From ge_p3_0.c */ + +static void ge_p3_0(ge_p3 *h) { + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); + fe_0(h->T); +} + +/* From ge_p3_dbl.c */ + +/* +r = 2 * p +*/ + +static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { + ge_p2 q; + ge_p3_to_p2(&q, p); + ge_p2_dbl(r, &q); +} + +/* From ge_p3_to_cached.c */ + +/* +r = p +*/ + +void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { + fe_add(r->YplusX, p->Y, p->X); + fe_sub(r->YminusX, p->Y, p->X); + fe_copy(r->Z, p->Z); + fe_mul(r->T2d, p->T, fe_d2); +} + +/* From ge_p3_to_p2.c */ + +/* +r = p +*/ + +void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { + fe_copy(r->X, p->X); + fe_copy(r->Y, p->Y); + fe_copy(r->Z, p->Z); +} + +/* From ge_p3_tobytes.c */ + +void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) { + fe recip; + fe x; + fe y; + + fe_invert(recip, h->Z); + fe_mul(x, h->X, recip); + fe_mul(y, h->Y, recip); + fe_tobytes(s, y); + s[31] ^= fe_isnegative(x) << 7; +} + +/* From ge_precomp_0.c */ + +static void ge_precomp_0(ge_precomp *h) { + fe_1(h->yplusx); + fe_1(h->yminusx); + fe_0(h->xy2d); +} + +/* From ge_scalarmult_base.c */ + +static unsigned char equal(signed char b, signed char c) { + unsigned char ub = b; + unsigned char uc = c; + unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ + uint32_t y = x; /* 0: yes; 1..255: no */ + y -= 1; /* 4294967295: yes; 0..254: no */ + y >>= 31; /* 1: yes; 0: no */ + return y; +} + +static unsigned char negative(signed char b) { + unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ + x >>= 63; /* 1: yes; 0: no */ + return x; +} + +static void ge_precomp_cmov(ge_precomp *t, const ge_precomp *u, unsigned char b) { + fe_cmov(t->yplusx, u->yplusx, b); + fe_cmov(t->yminusx, u->yminusx, b); + fe_cmov(t->xy2d, u->xy2d, b); +} + +static void select(ge_precomp *t, int pos, signed char b) { + ge_precomp minust; + unsigned char bnegative = negative(b); + unsigned char babs = b - (((-bnegative) & b) << 1); + + ge_precomp_0(t); + ge_precomp_cmov(t, &ge_base[pos][0], equal(babs, 1)); + ge_precomp_cmov(t, &ge_base[pos][1], equal(babs, 2)); + ge_precomp_cmov(t, &ge_base[pos][2], equal(babs, 3)); + ge_precomp_cmov(t, &ge_base[pos][3], equal(babs, 4)); + ge_precomp_cmov(t, &ge_base[pos][4], equal(babs, 5)); + ge_precomp_cmov(t, &ge_base[pos][5], equal(babs, 6)); + ge_precomp_cmov(t, &ge_base[pos][6], equal(babs, 7)); + ge_precomp_cmov(t, &ge_base[pos][7], equal(babs, 8)); + fe_copy(minust.yplusx, t->yminusx); + fe_copy(minust.yminusx, t->yplusx); + fe_neg(minust.xy2d, t->xy2d); + ge_precomp_cmov(t, &minust, bnegative); +} + +/* +h = a * B +where a = a[0]+256*a[1]+...+256^31 a[31] +B is the Ed25519 base point (x,4/5) with x positive. + +Preconditions: + a[31] <= 127 +*/ + +void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) { + signed char e[64]; + signed char carry; + ge_p1p1 r; + ge_p2 s; + ge_precomp t; + int i; + + for (i = 0; i < 32; ++i) { + e[2 * i + 0] = (a[i] >> 0) & 15; + e[2 * i + 1] = (a[i] >> 4) & 15; + } + /* each e[i] is between 0 and 15 */ + /* e[63] is between 0 and 7 */ + + carry = 0; + for (i = 0; i < 63; ++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry << 4; + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ + + ge_p3_0(h); + for (i = 1; i < 64; i += 2) { + select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r); + } + + ge_p3_dbl(&r, h); ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); ge_p1p1_to_p3(h, &r); + + for (i = 0; i < 64; i += 2) { + select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r); + } +} + +/* From ge_sub.c */ + +/* +r = p - q +*/ + +void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { + fe t0; + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->YminusX); + fe_mul(r->Y, r->Y, q->YplusX); + fe_mul(r->T, q->T2d, p->T); + fe_mul(r->X, p->Z, q->Z); + fe_add(t0, r->X, r->X); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_sub(r->Z, t0, r->T); + fe_add(r->T, t0, r->T); +} + +/* From ge_tobytes.c */ + +void ge_tobytes(unsigned char *s, const ge_p2 *h) { + fe recip; + fe x; + fe y; + + fe_invert(recip, h->Z); + fe_mul(x, h->X, recip); + fe_mul(y, h->Y, recip); + fe_tobytes(s, y); + s[31] ^= fe_isnegative(x) << 7; +} + +/* From sc_reduce.c */ + +/* +Input: + s[0]+256*s[1]+...+256^63*s[63] = s + +Output: + s[0]+256*s[1]+...+256^31*s[31] = s mod l + where l = 2^252 + 27742317777372353535851937790883648493. + Overwrites s in place. +*/ + +void sc_reduce(unsigned char *s) { + int64_t s0 = 2097151 & load_3(s); + int64_t s1 = 2097151 & (load_4(s + 2) >> 5); + int64_t s2 = 2097151 & (load_3(s + 5) >> 2); + int64_t s3 = 2097151 & (load_4(s + 7) >> 7); + int64_t s4 = 2097151 & (load_4(s + 10) >> 4); + int64_t s5 = 2097151 & (load_3(s + 13) >> 1); + int64_t s6 = 2097151 & (load_4(s + 15) >> 6); + int64_t s7 = 2097151 & (load_3(s + 18) >> 3); + int64_t s8 = 2097151 & load_3(s + 21); + int64_t s9 = 2097151 & (load_4(s + 23) >> 5); + int64_t s10 = 2097151 & (load_3(s + 26) >> 2); + int64_t s11 = 2097151 & (load_4(s + 28) >> 7); + int64_t s12 = 2097151 & (load_4(s + 31) >> 4); + int64_t s13 = 2097151 & (load_3(s + 34) >> 1); + int64_t s14 = 2097151 & (load_4(s + 36) >> 6); + int64_t s15 = 2097151 & (load_3(s + 39) >> 3); + int64_t s16 = 2097151 & load_3(s + 42); + int64_t s17 = 2097151 & (load_4(s + 44) >> 5); + int64_t s18 = 2097151 & (load_3(s + 47) >> 2); + int64_t s19 = 2097151 & (load_4(s + 49) >> 7); + int64_t s20 = 2097151 & (load_4(s + 52) >> 4); + int64_t s21 = 2097151 & (load_3(s + 55) >> 1); + int64_t s22 = 2097151 & (load_4(s + 57) >> 6); + int64_t s23 = (load_4(s + 60) >> 3); + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +/* New code */ + +static void fe_divpowm1(fe r, const fe u, const fe v) { + fe v3, uv7, t0, t1, t2; + int i; + + fe_sq(v3, v); + fe_mul(v3, v3, v); /* v3 = v^3 */ + fe_sq(uv7, v3); + fe_mul(uv7, uv7, v); + fe_mul(uv7, uv7, u); /* uv7 = uv^7 */ + + /*fe_pow22523(uv7, uv7);*/ + + /* From fe_pow22523.c */ + + fe_sq(t0, uv7); + fe_sq(t1, t0); + fe_sq(t1, t1); + fe_mul(t1, uv7, t1); + fe_mul(t0, t0, t1); + fe_sq(t0, t0); + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 0; i < 4; ++i) { + fe_sq(t1, t1); + } + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 0; i < 9; ++i) { + fe_sq(t1, t1); + } + fe_mul(t1, t1, t0); + fe_sq(t2, t1); + for (i = 0; i < 19; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); + for (i = 0; i < 10; ++i) { + fe_sq(t1, t1); + } + fe_mul(t0, t1, t0); + fe_sq(t1, t0); + for (i = 0; i < 49; ++i) { + fe_sq(t1, t1); + } + fe_mul(t1, t1, t0); + fe_sq(t2, t1); + for (i = 0; i < 99; ++i) { + fe_sq(t2, t2); + } + fe_mul(t1, t2, t1); + for (i = 0; i < 50; ++i) { + fe_sq(t1, t1); + } + fe_mul(t0, t1, t0); + fe_sq(t0, t0); + fe_sq(t0, t0); + fe_mul(t0, t0, uv7); + + /* End fe_pow22523.c */ + /* t0 = (uv^7)^((q-5)/8) */ + fe_mul(t0, t0, v3); + fe_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */ +} + +static void ge_cached_0(ge_cached *r) { + fe_1(r->YplusX); + fe_1(r->YminusX); + fe_1(r->Z); + fe_0(r->T2d); +} + +static void ge_cached_cmov(ge_cached *t, const ge_cached *u, unsigned char b) { + fe_cmov(t->YplusX, u->YplusX, b); + fe_cmov(t->YminusX, u->YminusX, b); + fe_cmov(t->Z, u->Z, b); + fe_cmov(t->T2d, u->T2d, b); +} + +/* Assumes that a[31] <= 127 */ +void ge_scalarmult(ge_p2 *r, const unsigned char *a, const ge_p3 *A) { + signed char e[64]; + int carry, carry2, i; + ge_cached Ai[8]; /* 1 * A, 2 * A, ..., 8 * A */ + ge_p1p1 t; + ge_p3 u; + + carry = 0; /* 0..1 */ + for (i = 0; i < 31; i++) { + carry += a[i]; /* 0..256 */ + carry2 = (carry + 8) >> 4; /* 0..16 */ + e[2 * i] = carry - (carry2 << 4); /* -8..7 */ + carry = (carry2 + 8) >> 4; /* 0..1 */ + e[2 * i + 1] = carry2 - (carry << 4); /* -8..7 */ + } + carry += a[31]; /* 0..128 */ + carry2 = (carry + 8) >> 4; /* 0..8 */ + e[62] = carry - (carry2 << 4); /* -8..7 */ + e[63] = carry2; /* 0..8 */ + + ge_p3_to_cached(&Ai[0], A); + for (i = 0; i < 7; i++) { + ge_add(&t, A, &Ai[i]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[i + 1], &u); + } + + ge_p2_0(r); + for (i = 63; i >= 0; i--) { + signed char b = e[i]; + unsigned char bnegative = negative(b); + unsigned char babs = b - (((-bnegative) & b) << 1); + ge_cached cur, minuscur; + ge_p2_dbl(&t, r); + ge_p1p1_to_p2(r, &t); + ge_p2_dbl(&t, r); + ge_p1p1_to_p2(r, &t); + ge_p2_dbl(&t, r); + ge_p1p1_to_p2(r, &t); + ge_p2_dbl(&t, r); + ge_p1p1_to_p3(&u, &t); + ge_cached_0(&cur); + ge_cached_cmov(&cur, &Ai[0], equal(babs, 1)); + ge_cached_cmov(&cur, &Ai[1], equal(babs, 2)); + ge_cached_cmov(&cur, &Ai[2], equal(babs, 3)); + ge_cached_cmov(&cur, &Ai[3], equal(babs, 4)); + ge_cached_cmov(&cur, &Ai[4], equal(babs, 5)); + ge_cached_cmov(&cur, &Ai[5], equal(babs, 6)); + ge_cached_cmov(&cur, &Ai[6], equal(babs, 7)); + ge_cached_cmov(&cur, &Ai[7], equal(babs, 8)); + fe_copy(minuscur.YplusX, cur.YminusX); + fe_copy(minuscur.YminusX, cur.YplusX); + fe_copy(minuscur.Z, cur.Z); + fe_neg(minuscur.T2d, cur.T2d); + ge_cached_cmov(&cur, &minuscur, bnegative); + ge_add(&t, &u, &cur); + ge_p1p1_to_p2(r, &t); + } +} + +void ge_scalarmult_p3(ge_p3 *r3, const unsigned char *a, const ge_p3 *A) { + signed char e[64]; + int carry, carry2, i; + ge_cached Ai[8]; /* 1 * A, 2 * A, ..., 8 * A */ + ge_p1p1 t; + ge_p3 u; + ge_p2 r; + + carry = 0; /* 0..1 */ + for (i = 0; i < 31; i++) { + carry += a[i]; /* 0..256 */ + carry2 = (carry + 8) >> 4; /* 0..16 */ + e[2 * i] = carry - (carry2 << 4); /* -8..7 */ + carry = (carry2 + 8) >> 4; /* 0..1 */ + e[2 * i + 1] = carry2 - (carry << 4); /* -8..7 */ + } + carry += a[31]; /* 0..128 */ + carry2 = (carry + 8) >> 4; /* 0..8 */ + e[62] = carry - (carry2 << 4); /* -8..7 */ + e[63] = carry2; /* 0..8 */ + + ge_p3_to_cached(&Ai[0], A); + for (i = 0; i < 7; i++) { + ge_add(&t, A, &Ai[i]); + ge_p1p1_to_p3(&u, &t); + ge_p3_to_cached(&Ai[i + 1], &u); + } + + ge_p2_0(&r); + for (i = 63; i >= 0; i--) { + signed char b = e[i]; + unsigned char bnegative = negative(b); + unsigned char babs = b - (((-bnegative) & b) << 1); + ge_cached cur, minuscur; + ge_p2_dbl(&t, &r); + ge_p1p1_to_p2(&r, &t); + ge_p2_dbl(&t, &r); + ge_p1p1_to_p2(&r, &t); + ge_p2_dbl(&t, &r); + ge_p1p1_to_p2(&r, &t); + ge_p2_dbl(&t, &r); + ge_p1p1_to_p3(&u, &t); + ge_cached_0(&cur); + ge_cached_cmov(&cur, &Ai[0], equal(babs, 1)); + ge_cached_cmov(&cur, &Ai[1], equal(babs, 2)); + ge_cached_cmov(&cur, &Ai[2], equal(babs, 3)); + ge_cached_cmov(&cur, &Ai[3], equal(babs, 4)); + ge_cached_cmov(&cur, &Ai[4], equal(babs, 5)); + ge_cached_cmov(&cur, &Ai[5], equal(babs, 6)); + ge_cached_cmov(&cur, &Ai[6], equal(babs, 7)); + ge_cached_cmov(&cur, &Ai[7], equal(babs, 8)); + fe_copy(minuscur.YplusX, cur.YminusX); + fe_copy(minuscur.YminusX, cur.YplusX); + fe_copy(minuscur.Z, cur.Z); + fe_neg(minuscur.T2d, cur.T2d); + ge_cached_cmov(&cur, &minuscur, bnegative); + ge_add(&t, &u, &cur); + if (i == 0) + ge_p1p1_to_p3(r3, &t); + else + ge_p1p1_to_p2(&r, &t); + } +} + +void ge_double_scalarmult_precomp_vartime2(ge_p2 *r, const unsigned char *a, const ge_dsmp Ai, const unsigned char *b, const ge_dsmp Bi) { + signed char aslide[256]; + signed char bslide[256]; + ge_p1p1 t; + ge_p3 u; + int i; + + slide(aslide, a); + slide(bslide, b); + + ge_p2_0(r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i]) break; + } + + for (; i >= 0; --i) { + ge_p2_dbl(&t, r); + + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ai[aslide[i]/2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ai[(-aslide[i])/2]); + } + + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Bi[bslide[i]/2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Bi[(-bslide[i])/2]); + } + + ge_p1p1_to_p2(r, &t); + } +} + +// Computes aA + bB + cC (all points require precomputation) +void ge_triple_scalarmult_precomp_vartime(ge_p2 *r, const unsigned char *a, const ge_dsmp Ai, const unsigned char *b, const ge_dsmp Bi, const unsigned char *c, const ge_dsmp Ci) { + signed char aslide[256]; + signed char bslide[256]; + signed char cslide[256]; + ge_p1p1 t; + ge_p3 u; + int i; + + slide(aslide, a); + slide(bslide, b); + slide(cslide, c); + + ge_p2_0(r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i] || cslide[i]) break; + } + + for (; i >= 0; --i) { + ge_p2_dbl(&t, r); + + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ai[aslide[i]/2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ai[(-aslide[i])/2]); + } + + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Bi[bslide[i]/2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Bi[(-bslide[i])/2]); + } + + if (cslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ci[cslide[i]/2]); + } else if (cslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ci[(-cslide[i])/2]); + } + + ge_p1p1_to_p2(r, &t); + } +} + +void ge_double_scalarmult_precomp_vartime2_p3(ge_p3 *r3, const unsigned char *a, const ge_dsmp Ai, const unsigned char *b, const ge_dsmp Bi) { + signed char aslide[256]; + signed char bslide[256]; + ge_p1p1 t; + ge_p3 u; + ge_p2 r; + int i; + + slide(aslide, a); + slide(bslide, b); + + ge_p2_0(&r); + + for (i = 255; i >= 0; --i) { + if (aslide[i] || bslide[i]) break; + } + + for (; i >= 0; --i) { + ge_p2_dbl(&t, &r); + + if (aslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Ai[aslide[i]/2]); + } else if (aslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Ai[(-aslide[i])/2]); + } + + if (bslide[i] > 0) { + ge_p1p1_to_p3(&u, &t); + ge_add(&t, &u, &Bi[bslide[i]/2]); + } else if (bslide[i] < 0) { + ge_p1p1_to_p3(&u, &t); + ge_sub(&t, &u, &Bi[(-bslide[i])/2]); + } + + if (i == 0) + ge_p1p1_to_p3(r3, &t); + else + ge_p1p1_to_p2(&r, &t); + } +} + +void ge_double_scalarmult_precomp_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b, const ge_dsmp Bi) { + ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ + + ge_dsm_precomp(Ai, A); + ge_double_scalarmult_precomp_vartime2(r, a, Ai, b, Bi); +} + +void ge_mul8(ge_p1p1 *r, const ge_p2 *t) { + ge_p2 u; + ge_p2_dbl(r, t); + ge_p1p1_to_p2(&u, r); + ge_p2_dbl(r, &u); + ge_p1p1_to_p2(&u, r); + ge_p2_dbl(r, &u); +} + +void ge_fromfe_frombytes_vartime(ge_p2 *r, const unsigned char *s) { + fe u, v, w, x, y, z; + unsigned char sign; + + /* From fe_frombytes.c */ + + int64_t h0 = load_4(s); + int64_t h1 = load_3(s + 4) << 6; + int64_t h2 = load_3(s + 7) << 5; + int64_t h3 = load_3(s + 10) << 3; + int64_t h4 = load_3(s + 13) << 2; + int64_t h5 = load_4(s + 16); + int64_t h6 = load_3(s + 20) << 7; + int64_t h7 = load_3(s + 23) << 5; + int64_t h8 = load_3(s + 26) << 4; + int64_t h9 = load_3(s + 29) << 2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; + carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; + carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; + carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; + carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; + + carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; + carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; + carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; + carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; + carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; + + u[0] = h0; + u[1] = h1; + u[2] = h2; + u[3] = h3; + u[4] = h4; + u[5] = h5; + u[6] = h6; + u[7] = h7; + u[8] = h8; + u[9] = h9; + + /* End fe_frombytes.c */ + + fe_sq2(v, u); /* 2 * u^2 */ + fe_1(w); + fe_add(w, v, w); /* w = 2 * u^2 + 1 */ + fe_sq(x, w); /* w^2 */ + fe_mul(y, fe_ma2, v); /* -2 * A^2 * u^2 */ + fe_add(x, x, y); /* x = w^2 - 2 * A^2 * u^2 */ + fe_divpowm1(r->X, w, x); /* (w / x)^(m + 1) */ + fe_sq(y, r->X); + fe_mul(x, y, x); + fe_sub(y, w, x); + fe_copy(z, fe_ma); + if (fe_isnonzero(y)) { + fe_add(y, w, x); + if (fe_isnonzero(y)) { + goto negative; + } else { + fe_mul(r->X, r->X, fe_fffb1); + } + } else { + fe_mul(r->X, r->X, fe_fffb2); + } + fe_mul(r->X, r->X, u); /* u * sqrt(2 * A * (A + 2) * w / x) */ + fe_mul(z, z, v); /* -2 * A * u^2 */ + sign = 0; + goto setsign; +negative: + fe_mul(x, x, fe_sqrtm1); + fe_sub(y, w, x); + if (fe_isnonzero(y)) { + assert((fe_add(y, w, x), !fe_isnonzero(y))); + fe_mul(r->X, r->X, fe_fffb3); + } else { + fe_mul(r->X, r->X, fe_fffb4); + } + /* r->X = sqrt(A * (A + 2) * w / x) */ + /* z = -A */ + sign = 1; +setsign: + if (fe_isnegative(r->X) != sign) { + assert(fe_isnonzero(r->X)); + fe_neg(r->X, r->X); + } + fe_add(r->Z, z, w); + fe_sub(r->Y, z, w); + fe_mul(r->X, r->X, r->Z); +#if !defined(NDEBUG) + { + fe check_x, check_y, check_iz, check_v; + fe_invert(check_iz, r->Z); + fe_mul(check_x, r->X, check_iz); + fe_mul(check_y, r->Y, check_iz); + fe_sq(check_x, check_x); + fe_sq(check_y, check_y); + fe_mul(check_v, check_x, check_y); + fe_mul(check_v, fe_d, check_v); + fe_add(check_v, check_v, check_x); + fe_sub(check_v, check_v, check_y); + fe_1(check_x); + fe_add(check_v, check_v, check_x); + assert(!fe_isnonzero(check_v)); + } +#endif +} + +void sc_0(unsigned char *s) { + int i; + for (i = 0; i < 32; i++) { + s[i] = 0; + } +} + +void sc_reduce32(unsigned char *s) { + int64_t s0 = 2097151 & load_3(s); + int64_t s1 = 2097151 & (load_4(s + 2) >> 5); + int64_t s2 = 2097151 & (load_3(s + 5) >> 2); + int64_t s3 = 2097151 & (load_4(s + 7) >> 7); + int64_t s4 = 2097151 & (load_4(s + 10) >> 4); + int64_t s5 = 2097151 & (load_3(s + 13) >> 1); + int64_t s6 = 2097151 & (load_4(s + 15) >> 6); + int64_t s7 = 2097151 & (load_3(s + 18) >> 3); + int64_t s8 = 2097151 & load_3(s + 21); + int64_t s9 = 2097151 & (load_4(s + 23) >> 5); + int64_t s10 = 2097151 & (load_3(s + 26) >> 2); + int64_t s11 = (load_4(s + 28) >> 7); + int64_t s12 = 0; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +void sc_add(unsigned char *s, const unsigned char *a, const unsigned char *b) { + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + int64_t s0 = a0 + b0; + int64_t s1 = a1 + b1; + int64_t s2 = a2 + b2; + int64_t s3 = a3 + b3; + int64_t s4 = a4 + b4; + int64_t s5 = a5 + b5; + int64_t s6 = a6 + b6; + int64_t s7 = a7 + b7; + int64_t s8 = a8 + b8; + int64_t s9 = a9 + b9; + int64_t s10 = a10 + b10; + int64_t s11 = a11 + b11; + int64_t s12 = 0; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +void sc_sub(unsigned char *s, const unsigned char *a, const unsigned char *b) { + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + int64_t s0 = a0 - b0; + int64_t s1 = a1 - b1; + int64_t s2 = a2 - b2; + int64_t s3 = a3 - b3; + int64_t s4 = a4 - b4; + int64_t s5 = a5 - b5; + int64_t s6 = a6 - b6; + int64_t s7 = a7 - b7; + int64_t s8 = a8 - b8; + int64_t s9 = a9 - b9; + int64_t s10 = a10 - b10; + int64_t s11 = a11 - b11; + int64_t s12 = 0; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +/* +Input: + a[0]+256*a[1]+...+256^31*a[31] = a + b[0]+256*b[1]+...+256^31*b[31] = b + c[0]+256*c[1]+...+256^31*c[31] = c + +Output: + s[0]+256*s[1]+...+256^31*s[31] = (c-ab) mod l + where l = 2^252 + 27742317777372353535851937790883648493. +*/ + +void sc_mulsub(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) { + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + int64_t c0 = 2097151 & load_3(c); + int64_t c1 = 2097151 & (load_4(c + 2) >> 5); + int64_t c2 = 2097151 & (load_3(c + 5) >> 2); + int64_t c3 = 2097151 & (load_4(c + 7) >> 7); + int64_t c4 = 2097151 & (load_4(c + 10) >> 4); + int64_t c5 = 2097151 & (load_3(c + 13) >> 1); + int64_t c6 = 2097151 & (load_4(c + 15) >> 6); + int64_t c7 = 2097151 & (load_3(c + 18) >> 3); + int64_t c8 = 2097151 & load_3(c + 21); + int64_t c9 = 2097151 & (load_4(c + 23) >> 5); + int64_t c10 = 2097151 & (load_3(c + 26) >> 2); + int64_t c11 = (load_4(c + 28) >> 7); + int64_t s0; + int64_t s1; + int64_t s2; + int64_t s3; + int64_t s4; + int64_t s5; + int64_t s6; + int64_t s7; + int64_t s8; + int64_t s9; + int64_t s10; + int64_t s11; + int64_t s12; + int64_t s13; + int64_t s14; + int64_t s15; + int64_t s16; + int64_t s17; + int64_t s18; + int64_t s19; + int64_t s20; + int64_t s21; + int64_t s22; + int64_t s23; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + int64_t carry17; + int64_t carry18; + int64_t carry19; + int64_t carry20; + int64_t carry21; + int64_t carry22; + + s0 = c0 - a0*b0; + s1 = c1 - (a0*b1 + a1*b0); + s2 = c2 - (a0*b2 + a1*b1 + a2*b0); + s3 = c3 - (a0*b3 + a1*b2 + a2*b1 + a3*b0); + s4 = c4 - (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0); + s5 = c5 - (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0); + s6 = c6 - (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0); + s7 = c7 - (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0); + s8 = c8 - (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0); + s9 = c9 - (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0); + s10 = c10 - (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0); + s11 = c11 - (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0); + s12 = -(a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1); + s13 = -(a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2); + s14 = -(a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3); + s15 = -(a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4); + s16 = -(a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5); + s17 = -(a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6); + s18 = -(a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7); + s19 = -(a8*b11 + a9*b10 + a10*b9 + a11*b8); + s20 = -(a9*b11 + a10*b10 + a11*b9); + s21 = -(a10*b11 + a11*b10); + s22 = -a11*b11; + s23 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; + carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; + carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; + carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; + carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +//copied from above and modified +/* +Input: + a[0]+256*a[1]+...+256^31*a[31] = a + b[0]+256*b[1]+...+256^31*b[31] = b + +Output: + s[0]+256*s[1]+...+256^31*s[31] = (ab) mod l + where l = 2^252 + 27742317777372353535851937790883648493. +*/ +void sc_mul(unsigned char *s, const unsigned char *a, const unsigned char *b) { + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + int64_t s0; + int64_t s1; + int64_t s2; + int64_t s3; + int64_t s4; + int64_t s5; + int64_t s6; + int64_t s7; + int64_t s8; + int64_t s9; + int64_t s10; + int64_t s11; + int64_t s12; + int64_t s13; + int64_t s14; + int64_t s15; + int64_t s16; + int64_t s17; + int64_t s18; + int64_t s19; + int64_t s20; + int64_t s21; + int64_t s22; + int64_t s23; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + int64_t carry17; + int64_t carry18; + int64_t carry19; + int64_t carry20; + int64_t carry21; + int64_t carry22; + + s0 = a0*b0; + s1 = (a0*b1 + a1*b0); + s2 = (a0*b2 + a1*b1 + a2*b0); + s3 = (a0*b3 + a1*b2 + a2*b1 + a3*b0); + s4 = (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0); + s5 = (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0); + s6 = (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0); + s7 = (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0); + s8 = (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0); + s9 = (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0); + s10 = (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0); + s11 = (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0); + s12 = (a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1); + s13 = (a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2); + s14 = (a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3); + s15 = (a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4); + s16 = (a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5); + s17 = (a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6); + s18 = (a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7); + s19 = (a8*b11 + a9*b10 + a10*b9 + a11*b8); + s20 = (a9*b11 + a10*b10 + a11*b9); + s21 = (a10*b11 + a11*b10); + s22 = a11*b11; + s23 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; + carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; + carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; + carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; + carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +//copied from above and modified +/* +Input: + a[0]+256*a[1]+...+256^31*a[31] = a + b[0]+256*b[1]+...+256^31*b[31] = b + c[0]+256*c[1]+...+256^31*c[31] = c + +Output: + s[0]+256*s[1]+...+256^31*s[31] = (c+ab) mod l + where l = 2^252 + 27742317777372353535851937790883648493. +*/ + +void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) { + int64_t a0 = 2097151 & load_3(a); + int64_t a1 = 2097151 & (load_4(a + 2) >> 5); + int64_t a2 = 2097151 & (load_3(a + 5) >> 2); + int64_t a3 = 2097151 & (load_4(a + 7) >> 7); + int64_t a4 = 2097151 & (load_4(a + 10) >> 4); + int64_t a5 = 2097151 & (load_3(a + 13) >> 1); + int64_t a6 = 2097151 & (load_4(a + 15) >> 6); + int64_t a7 = 2097151 & (load_3(a + 18) >> 3); + int64_t a8 = 2097151 & load_3(a + 21); + int64_t a9 = 2097151 & (load_4(a + 23) >> 5); + int64_t a10 = 2097151 & (load_3(a + 26) >> 2); + int64_t a11 = (load_4(a + 28) >> 7); + int64_t b0 = 2097151 & load_3(b); + int64_t b1 = 2097151 & (load_4(b + 2) >> 5); + int64_t b2 = 2097151 & (load_3(b + 5) >> 2); + int64_t b3 = 2097151 & (load_4(b + 7) >> 7); + int64_t b4 = 2097151 & (load_4(b + 10) >> 4); + int64_t b5 = 2097151 & (load_3(b + 13) >> 1); + int64_t b6 = 2097151 & (load_4(b + 15) >> 6); + int64_t b7 = 2097151 & (load_3(b + 18) >> 3); + int64_t b8 = 2097151 & load_3(b + 21); + int64_t b9 = 2097151 & (load_4(b + 23) >> 5); + int64_t b10 = 2097151 & (load_3(b + 26) >> 2); + int64_t b11 = (load_4(b + 28) >> 7); + int64_t c0 = 2097151 & load_3(c); + int64_t c1 = 2097151 & (load_4(c + 2) >> 5); + int64_t c2 = 2097151 & (load_3(c + 5) >> 2); + int64_t c3 = 2097151 & (load_4(c + 7) >> 7); + int64_t c4 = 2097151 & (load_4(c + 10) >> 4); + int64_t c5 = 2097151 & (load_3(c + 13) >> 1); + int64_t c6 = 2097151 & (load_4(c + 15) >> 6); + int64_t c7 = 2097151 & (load_3(c + 18) >> 3); + int64_t c8 = 2097151 & load_3(c + 21); + int64_t c9 = 2097151 & (load_4(c + 23) >> 5); + int64_t c10 = 2097151 & (load_3(c + 26) >> 2); + int64_t c11 = (load_4(c + 28) >> 7); + int64_t s0; + int64_t s1; + int64_t s2; + int64_t s3; + int64_t s4; + int64_t s5; + int64_t s6; + int64_t s7; + int64_t s8; + int64_t s9; + int64_t s10; + int64_t s11; + int64_t s12; + int64_t s13; + int64_t s14; + int64_t s15; + int64_t s16; + int64_t s17; + int64_t s18; + int64_t s19; + int64_t s20; + int64_t s21; + int64_t s22; + int64_t s23; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + int64_t carry10; + int64_t carry11; + int64_t carry12; + int64_t carry13; + int64_t carry14; + int64_t carry15; + int64_t carry16; + int64_t carry17; + int64_t carry18; + int64_t carry19; + int64_t carry20; + int64_t carry21; + int64_t carry22; + + s0 = c0 + a0*b0; + s1 = c1 + (a0*b1 + a1*b0); + s2 = c2 + (a0*b2 + a1*b1 + a2*b0); + s3 = c3 + (a0*b3 + a1*b2 + a2*b1 + a3*b0); + s4 = c4 + (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0); + s5 = c5 + (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0); + s6 = c6 + (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0); + s7 = c7 + (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0); + s8 = c8 + (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0); + s9 = c9 + (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0); + s10 = c10 + (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0); + s11 = c11 + (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0); + s12 = (a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1); + s13 = (a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2); + s14 = (a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3); + s15 = (a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4); + s16 = (a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5); + s17 = (a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6); + s18 = (a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7); + s19 = (a8*b11 + a9*b10 + a10*b9 + a11*b8); + s20 = (a9*b11 + a10*b10 + a11*b9); + s21 = (a10*b11 + a11*b10); + s22 = a11*b11; + s23 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; + carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; + carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; + carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; + carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; + + s11 += s23 * 666643; + s12 += s23 * 470296; + s13 += s23 * 654183; + s14 -= s23 * 997805; + s15 += s23 * 136657; + s16 -= s23 * 683901; + + s10 += s22 * 666643; + s11 += s22 * 470296; + s12 += s22 * 654183; + s13 -= s22 * 997805; + s14 += s22 * 136657; + s15 -= s22 * 683901; + + s9 += s21 * 666643; + s10 += s21 * 470296; + s11 += s21 * 654183; + s12 -= s21 * 997805; + s13 += s21 * 136657; + s14 -= s21 * 683901; + + s8 += s20 * 666643; + s9 += s20 * 470296; + s10 += s20 * 654183; + s11 -= s20 * 997805; + s12 += s20 * 136657; + s13 -= s20 * 683901; + + s7 += s19 * 666643; + s8 += s19 * 470296; + s9 += s19 * 654183; + s10 -= s19 * 997805; + s11 += s19 * 136657; + s12 -= s19 * 683901; + + s6 += s18 * 666643; + s7 += s18 * 470296; + s8 += s18 * 654183; + s9 -= s18 * 997805; + s10 += s18 * 136657; + s11 -= s18 * 683901; + + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; + carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; + carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; + + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; + carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; + + s5 += s17 * 666643; + s6 += s17 * 470296; + s7 += s17 * 654183; + s8 -= s17 * 997805; + s9 += s17 * 136657; + s10 -= s17 * 683901; + + s4 += s16 * 666643; + s5 += s16 * 470296; + s6 += s16 * 654183; + s7 -= s16 * 997805; + s8 += s16 * 136657; + s9 -= s16 * 683901; + + s3 += s15 * 666643; + s4 += s15 * 470296; + s5 += s15 * 654183; + s6 -= s15 * 997805; + s7 += s15 * 136657; + s8 -= s15 * 683901; + + s2 += s14 * 666643; + s3 += s14 * 470296; + s4 += s14 * 654183; + s5 -= s14 * 997805; + s6 += s14 * 136657; + s7 -= s14 * 683901; + + s1 += s13 * 666643; + s2 += s13 * 470296; + s3 += s13 * 654183; + s4 -= s13 * 997805; + s5 += s13 * 136657; + s6 -= s13 * 683901; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; + carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; + carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; + carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; + carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; + carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; + + carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; + carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; + carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; + carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; + carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; + carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + s12 = 0; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; + + s0 += s12 * 666643; + s1 += s12 * 470296; + s2 += s12 * 654183; + s3 -= s12 * 997805; + s4 += s12 * 136657; + s5 -= s12 * 683901; + + carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; + carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; + carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; + carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; + carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; + carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; + carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; + carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; + carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; + carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; + carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; + + s[0] = s0 >> 0; + s[1] = s0 >> 8; + s[2] = (s0 >> 16) | (s1 << 5); + s[3] = s1 >> 3; + s[4] = s1 >> 11; + s[5] = (s1 >> 19) | (s2 << 2); + s[6] = s2 >> 6; + s[7] = (s2 >> 14) | (s3 << 7); + s[8] = s3 >> 1; + s[9] = s3 >> 9; + s[10] = (s3 >> 17) | (s4 << 4); + s[11] = s4 >> 4; + s[12] = s4 >> 12; + s[13] = (s4 >> 20) | (s5 << 1); + s[14] = s5 >> 7; + s[15] = (s5 >> 15) | (s6 << 6); + s[16] = s6 >> 2; + s[17] = s6 >> 10; + s[18] = (s6 >> 18) | (s7 << 3); + s[19] = s7 >> 5; + s[20] = s7 >> 13; + s[21] = s8 >> 0; + s[22] = s8 >> 8; + s[23] = (s8 >> 16) | (s9 << 5); + s[24] = s9 >> 3; + s[25] = s9 >> 11; + s[26] = (s9 >> 19) | (s10 << 2); + s[27] = s10 >> 6; + s[28] = (s10 >> 14) | (s11 << 7); + s[29] = s11 >> 1; + s[30] = s11 >> 9; + s[31] = s11 >> 17; +} + +static int64_t signum(int64_t a) { + return a > 0 ? 1 : a < 0 ? -1 : 0; +} + +int sc_check(const unsigned char *s) { + int64_t s0 = load_4(s); + int64_t s1 = load_4(s + 4); + int64_t s2 = load_4(s + 8); + int64_t s3 = load_4(s + 12); + int64_t s4 = load_4(s + 16); + int64_t s5 = load_4(s + 20); + int64_t s6 = load_4(s + 24); + int64_t s7 = load_4(s + 28); + return (signum(1559614444 - s0) + (signum(1477600026 - s1) << 1) + (signum(2734136534 - s2) << 2) + (signum(350157278 - s3) << 3) + (signum(-s4) << 4) + (signum(-s5) << 5) + (signum(-s6) << 6) + (signum(268435456 - s7) << 7)) >> 8; +} + +int sc_isnonzero(const unsigned char *s) { + return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] | + s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] | + s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] | + s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1; +} + +int ge_p3_is_point_at_infinity(const ge_p3 *p) { + // X = 0 and Y == Z + int n; + for (n = 0; n < 10; ++n) + { + if (p->X[n] | p->T[n]) + return 0; + if (p->Y[n] != p->Z[n]) + return 0; + } + return 1; +} diff --git a/src/base/tools/cryptonote/crypto-ops.h b/src/base/tools/cryptonote/crypto-ops.h new file mode 100644 index 000000000..8d68e41c9 --- /dev/null +++ b/src/base/tools/cryptonote/crypto-ops.h @@ -0,0 +1,173 @@ +// Copyright (c) 2014-2020, The Monero Project +// +// All rights reserved. +// +// Redistribution and use in source and binary forms, with or without modification, are +// permitted provided that the following conditions are met: +// +// 1. Redistributions of source code must retain the above copyright notice, this list of +// conditions and the following disclaimer. +// +// 2. Redistributions in binary form must reproduce the above copyright notice, this list +// of conditions and the following disclaimer in the documentation and/or other +// materials provided with the distribution. +// +// 3. Neither the name of the copyright holder nor the names of its contributors may be +// used to endorse or promote products derived from this software without specific +// prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY +// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF +// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL +// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, +// STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF +// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers + +#pragma once + +#ifdef __cplusplus +extern "C" { +#endif + +/* From fe.h */ + +typedef int32_t fe[10]; + +/* From ge.h */ + +typedef struct { + fe X; + fe Y; + fe Z; +} ge_p2; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p3; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p1p1; + +typedef struct { + fe yplusx; + fe yminusx; + fe xy2d; +} ge_precomp; + +typedef struct { + fe YplusX; + fe YminusX; + fe Z; + fe T2d; +} ge_cached; + +/* From ge_add.c */ + +void ge_add(ge_p1p1 *, const ge_p3 *, const ge_cached *); + +/* From ge_double_scalarmult.c, modified */ + +typedef ge_cached ge_dsmp[8]; +extern const ge_precomp ge_Bi[8]; +void ge_dsm_precomp(ge_dsmp r, const ge_p3 *s); +void ge_double_scalarmult_base_vartime(ge_p2 *, const unsigned char *, const ge_p3 *, const unsigned char *); +void ge_triple_scalarmult_base_vartime(ge_p2 *, const unsigned char *, const unsigned char *, const ge_dsmp, const unsigned char *, const ge_dsmp); +void ge_double_scalarmult_base_vartime_p3(ge_p3 *, const unsigned char *, const ge_p3 *, const unsigned char *); + +/* From ge_frombytes.c, modified */ + +extern const fe fe_sqrtm1; +extern const fe fe_d; +int ge_frombytes_vartime(ge_p3 *, const unsigned char *); + +/* From ge_p1p1_to_p2.c */ + +void ge_p1p1_to_p2(ge_p2 *, const ge_p1p1 *); + +/* From ge_p1p1_to_p3.c */ + +void ge_p1p1_to_p3(ge_p3 *, const ge_p1p1 *); + +/* From ge_p2_dbl.c */ + +void ge_p2_dbl(ge_p1p1 *, const ge_p2 *); + +/* From ge_p3_to_cached.c */ + +extern const fe fe_d2; +void ge_p3_to_cached(ge_cached *, const ge_p3 *); + +/* From ge_p3_to_p2.c */ + +void ge_p3_to_p2(ge_p2 *, const ge_p3 *); + +/* From ge_p3_tobytes.c */ + +void ge_p3_tobytes(unsigned char *, const ge_p3 *); + +/* From ge_scalarmult_base.c */ + +extern const ge_precomp ge_base[32][8]; +void ge_scalarmult_base(ge_p3 *, const unsigned char *); + +/* From ge_tobytes.c */ + +void ge_tobytes(unsigned char *, const ge_p2 *); + +/* From sc_reduce.c */ + +void sc_reduce(unsigned char *); + +/* New code */ + +void ge_scalarmult(ge_p2 *, const unsigned char *, const ge_p3 *); +void ge_scalarmult_p3(ge_p3 *, const unsigned char *, const ge_p3 *); +void ge_double_scalarmult_precomp_vartime(ge_p2 *, const unsigned char *, const ge_p3 *, const unsigned char *, const ge_dsmp); +void ge_triple_scalarmult_precomp_vartime(ge_p2 *, const unsigned char *, const ge_dsmp, const unsigned char *, const ge_dsmp, const unsigned char *, const ge_dsmp); +void ge_double_scalarmult_precomp_vartime2(ge_p2 *, const unsigned char *, const ge_dsmp, const unsigned char *, const ge_dsmp); +void ge_double_scalarmult_precomp_vartime2_p3(ge_p3 *, const unsigned char *, const ge_dsmp, const unsigned char *, const ge_dsmp); +void ge_mul8(ge_p1p1 *, const ge_p2 *); +extern const fe fe_ma2; +extern const fe fe_ma; +extern const fe fe_fffb1; +extern const fe fe_fffb2; +extern const fe fe_fffb3; +extern const fe fe_fffb4; +extern const ge_p3 ge_p3_identity; +extern const ge_p3 ge_p3_H; +void ge_fromfe_frombytes_vartime(ge_p2 *, const unsigned char *); +void sc_0(unsigned char *); +void sc_reduce32(unsigned char *); +void sc_add(unsigned char *, const unsigned char *, const unsigned char *); +void sc_sub(unsigned char *, const unsigned char *, const unsigned char *); +void sc_mulsub(unsigned char *, const unsigned char *, const unsigned char *, const unsigned char *); +void sc_mul(unsigned char *, const unsigned char *, const unsigned char *); +void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c); +int sc_check(const unsigned char *); +int sc_isnonzero(const unsigned char *); /* Doesn't normalize */ + +// internal +uint64_t load_3(const unsigned char *in); +uint64_t load_4(const unsigned char *in); +void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q); +void fe_add(fe h, const fe f, const fe g); +void fe_tobytes(unsigned char *, const fe); +void fe_invert(fe out, const fe z); + +int ge_p3_is_point_at_infinity(const ge_p3 *p); + +#ifdef __cplusplus +} +#endif