rottenwheel/monero
1
0
Fork 0
mirror of https://codeberg.org/anoncontributorxmr/monero.git synced 2024-11-30 14:53:27 +01:00
Code Issues Actions Packages Projects Releases Wiki Activity

Added ref10 shen_ed25519_ref code, which includes code that can replace crypto-ops with a version straight from Bernstein's ref 10

Browse Source
This commit is contained in:
ShenNoether 2015-08-23 14:48:50 -06:00
parent 0d70fdca8c
commit 0a4bc84b2f
174 changed files with 23117 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

10
src/crypto/shen_ed25519_ref/Makefile Executable file
View File

@ -0,0 +1,10 @@
CC=gcc
CFLAGS=-O2 -Wall
OBJS= fe25519.o ge25519.o sc25519.o sha512-blocks.o sha512-hash.o ed25519.o randombytes.o verify.o
test: test.o $(OBJS)
gcc -o $@ $^
clean:
rm -f *.o test

2
src/crypto/shen_ed25519_ref/api.h Executable file
View File

@ -0,0 +1,2 @@
#define CRYPTO_BYTES 32
#define CRYPTO_SCALARBYTES 32

872
src/crypto/shen_ed25519_ref/crypto-ops-data.c Normal file
View File

@ -0,0 +1,872 @@
// Copyright (c) 2014-2015, 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 <stdint.h>
#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, 8754525, 7446702, -5676054, 5797016},
{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341}},
{{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505},
{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553},
{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655}},
{{15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220},
{12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631},
{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099}},
{{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556},
{14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749},
{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930}},
{{1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391},
{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253},
{20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066}},
{{24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958},
{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082},
{-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383}},
{{-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521},
{-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807},
{23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948}},
{{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134},
{-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455},
{27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629}}
}, {
{{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069},
{-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746},
{24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919}},
{{11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837},
{8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906},
{-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771}},
{{-25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817},
{10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098},
{10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409}},
{{-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504},
{-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727},
{28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420}},
{{-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003},
{-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605},
{-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384}},
{{-26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701},
{-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683},
{29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708}},
{{-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563},
{-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260},
{-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387}},
{{-19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -27444329, -15000531, -5996870, 15664672},
{23294591, -16632613, -22650781, -8470978, 27844204, 11461195, 13099750, -2460356, 18151676, 13417686},
{-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, 1661597, -12551441, 15271676, -15452665}}
}, {
{{11433042, -13228665, 8239631, -5279517, -1985436, -725718, -18698764, 2167544, -6921301, -13440182},
{-31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -9917708, -8638997, 12215110, 12028277},
{14098400, 6555944, 23007258, 5757252, -15427832, -12950502, 30123440, 4617780, -16900089, -655628}},
{{-4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -15819999, 10154009, 23973261, -12684474},
{-26531820, -3695990, -1908898, 2534301, -31870557, -16550355, 18341390, -11419951, 32013174, -10103539},
{-25479301, 10876443, -11771086, -14625140, -12369567, 1838104, 21911214, 6354752, 4425632, -837822}},
{{-10433389, -14612966, 22229858, -3091047, -13191166, 776729, -17415375, -12020462, 4725005, 14044970},
{19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -1411784, -19522291, -16109756},
{-24864089, 12986008, -10898878, -5558584, -11312371, -148526, 19541418, 8180106, 9282262, 10282508}},
{{-26205082, 4428547, -8661196, -13194263, 4098402, -14165257, 15522535, 8372215, 5542595, -10702683},
{-10562541, 14895633, 26814552, -16673850, -17480754, -2489360, -2781891, 6993761, -18093885, 10114655},
{-20107055, -929418, 31422704, 10427861, -7110749, 6150669, -29091755, -11529146, 25953725, -106158}},
{{-4234397, -8039292, -9119125, 3046000, 2101609, -12607294, 19390020, 6094296, -3315279, 12831125},
{-15998678, 7578152, 5310217, 14408357, -33548620, -224739, 31575954, 6326196, 7381791, -2421839},
{-20902779, 3296811, 24736065, -16328389, 18374254, 7318640, 6295303, 8082724, -15362489, 12339664}},
{{27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, 15768922, 25091167, 14856294},
{-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, -12695493, -22182473, -9012899},
{-11423429, -5421590, 11632845, 3405020, 30536730, -11674039, -27260765, 13866390, 30146206, 9142070}},
{{3924129, -15307516, -13817122, -10054960, 12291820, -668366, -27702774, 9326384, -8237858, 4171294},
{-15921940, 16037937, 6713787, 16606682, -21612135, 2790944, 26396185, 3731949, 345228, -5462949},
{-21327538, 13448259, 25284571, 1143661, 20614966, -8849387, 2031539, -12391231, -16253183, -13582083}},
{{31016211, -16722429, 26371392, -14451233, -5027349, 14854137, 17477601, 3842657, 28012650, -16405420},
{-5075835, 9368966, -8562079, -4600902, -15249953, 6970560, -9189873, 16292057, -8867157, 3507940},
{29439664, 3537914, 23333589, 6997794, -17555561, -11018068, -15209202, -15051267, -9164929, 6580396}}
}, {
{{-12185861, -7679788, 16438269, 10826160, -8696817, -6235611, 17860444, -9273846, -2095802, 9304567},
{20714564, -4336911, 29088195, 7406487, 11426967, -5095705, 14792667, -14608617, 5289421, -477127},
{-16665533, -10650790, -6160345, -13305760, 9192020, -1802462, 17271490, 12349094, 26939669, -3752294}},
{{-12889898, 9373458, 31595848, 16374215, 21471720, 13221525, -27283495, -12348559, -3698806, 117887},
{22263325, -6560050, 3984570, -11174646, -15114008, -566785, 28311253, 5358056, -23319780, 541964},
{16259219, 3261970, 2309254, -15534474, -16885711, -4581916, 24134070, -16705829, -13337066, -13552195}},
{{9378160, -13140186, -22845982, -12745264, 28198281, -7244098, -2399684, -717351, 690426, 14876244},
{24977353, -314384, -8223969, -13465086, 28432343, -1176353, -13068804, -12297348, -22380984, 6618999},
{-1538174, 11685646, 12944378, 13682314, -24389511, -14413193, 8044829, -13817328, 32239829, -5652762}},
{{-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, -10350059, 32779359, 5095274},
{-33008130, -5214506, -32264887, -3685216, 9460461, -9327423, -24601656, 14506724, 21639561, -2630236},
{-16400943, -13112215, 25239338, 15531969, 3987758, -4499318, -1289502, -6863535, 17874574, 558605}},
{{-13600129, 10240081, 9171883, 16131053, -20869254, 9599700, 33499487, 5080151, 2085892, 5119761},
{-22205145, -2519528, -16381601, 414691, -25019550, 2170430, 30634760, -8363614, -31999993, -5759884},
{-6845704, 15791202, 8550074, -1312654, 29928809, -12092256, 27534430, -7192145, -22351378, 12961482}},
{{-24492060, -9570771, 10368194, 11582341, -23397293, -2245287, 16533930, 8206996, -30194652, -5159638},
{-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, 7031275, 7589640, 8945490},
{-32152748, 8917967, 6661220, -11677616, -1192060, -15793393, 7251489, -11182180, 24099109, -14456170}},
{{5019558, -7907470, 4244127, -14714356, -26933272, 6453165, -19118182, -13289025, -6231896, -10280736},
{10853594, 10721687, 26480089, 5861829, -22995819, 1972175, -1866647, -10557898, -3363451, -6441124},
{-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, -2008168, -13866408, 7421392}},
{{8139927, -6546497, 32257646, -5890546, 30375719, 1886181, -21175108, 15441252, 28826358, -4123029},
{6267086, 9695052, 7709135, -16603597, -32869068, -1886135, 14795160, -7840124, 13746021, -1742048},
{28584902, 7787108, -6732942, -15050729, 22846041, -7571236, -3181936, -363524, 4771362, -8419958}}
}, {
{{24949256, 6376279, -27466481, -8174608, -18646154, -9930606, 33543569, -12141695, 3569627, 11342593},
{26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, 4608608, 7325975, -14801071},
{-11618399, -14554430, -24321212, 7655128, -1369274, 5214312, -27400540, 10258390, -17646694, -8186692}},
{{11431204, 15823007, 26570245, 14329124, 18029990, 4796082, -31446179, 15580664, 9280358, -3973687},
{-160783, -10326257, -22855316, -4304997, -20861367, -13621002, -32810901, -11181622, -15545091, 4387441},
{-20799378, 12194512, 3937617, -5805892, -27154820, 9340370, -24513992, 8548137, 20617071, -7482001}},
{{-938825, -3930586, -8714311, 16124718, 24603125, -6225393, -13775352, -11875822, 24345683, 10325460},
{-19855277, -1568885, -22202708, 8714034, 14007766, 6928528, 16318175, -1010689, 4766743, 3552007},
{-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, 14481909, 10988822, -3994762}},
{{15564307, -14311570, 3101243, 5684148, 30446780, -8051356, 12677127, -6505343, -8295852, 13296005},
{-9442290, 6624296, -30298964, -11913677, -4670981, -2057379, 31521204, 9614054, -30000824, 12074674},
{4771191, -135239, 14290749, -13089852, 27992298, 14998318, -1413936, -1556716, 29832613, -16391035}},
{{7064884, -7541174, -19161962, -5067537, -18891269, -2912736, 25825242, 5293297, -27122660, 13101590},
{-2298563, 2439670, -7466610, 1719965, -27267541, -16328445, 32512469, -5317593, -30356070, -4190957},
{-30006540, 10162316, -33180176, 3981723, -16482138, -13070044, 14413974, 9515896, 19568978, 9628812}},
{{33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, -6106839, -6291786, 3437740},
{-18978877, 3884493, 19469877, 12726490, 15913552, 13614290, -22961733, 70104, 7463304, 4176122},
{-27124001, 10659917, 11482427, -16070381, 12771467, -6635117, -32719404, -5322751, 24216882, 5944158}},
{{8894125, 7450974, -2664149, -9765752, -28080517, -12389115, 19345746, 14680796, 11632993, 5847885},
{26942781, -2315317, 9129564, -4906607, 26024105, 11769399, -11518837, 6367194, -9727230, 4782140},
{19916461, -4828410, -22910704, -11414391, 25606324, -5972441, 33253853, 8220911, 6358847, -1873857}},
{{801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, -4480480, -13538503, 1387155},
{19646058, 5720633, -11416706, 12814209, 11607948, 12749789, 14147075, 15156355, -21866831, 11835260},
{19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, 15467869, -26560550, 5052483}}
}, {
{{-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, -12618185, 12228557, -7003677},
{32944382, 14922211, -22844894, 5188528, 21913450, -8719943, 4001465, 13238564, -6114803, 8653815},
{22865569, -4652735, 27603668, -12545395, 14348958, 8234005, 24808405, 5719875, 28483275, 2841751}},
{{-16420968, -1113305, -327719, -12107856, 21886282, -15552774, -1887966, -315658, 19932058, -12739203},
{-11656086, 10087521, -8864888, -5536143, -19278573, -3055912, 3999228, 13239134, -4777469, -13910208},
{1382174, -11694719, 17266790, 9194690, -13324356, 9720081, 20403944, 11284705, -14013818, 3093230}},
{{16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, 16271225, -24049421, -6691850},
{-21911077, -5927941, -4611316, -5560156, -31744103, -10785293, 24123614, 15193618, -21652117, -16739389},
{-9935934, -4289447, -25279823, 4372842, 2087473, 10399484, 31870908, 14690798, 17361620, 11864968}},
{{-11307610, 6210372, 13206574, 5806320, -29017692, -13967200, -12331205, -7486601, -25578460, -16240689},
{14668462, -12270235, 26039039, 15305210, 25515617, 4542480, 10453892, 6577524, 9145645, -6443880},
{5974874, 3053895, -9433049, -10385191, -31865124, 3225009, -7972642, 3936128, -5652273, -3050304}},
{{30625386, -4729400, -25555961, -12792866, -20484575, 7695099, 17097188, -16303496, -27999779, 1803632},
{-3553091, 9865099, -5228566, 4272701, -5673832, -16689700, 14911344, 12196514, -21405489, 7047412},
{20093277, 9920966, -11138194, -5343857, 13161587, 12044805, -32856851, 4124601, -32343828, -10257566}},
{{-20788824, 14084654, -13531713, 7842147, 19119038, -13822605, 4752377, -8714640, -21679658, 2288038},
{-26819236, -3283715, 29965059, 3039786, -14473765, 2540457, 29457502, 14625692, -24819617, 12570232},
{-1063558, -11551823, 16920318, 12494842, 1278292, -5869109, -21159943, -3498680, -11974704, 4724943}},
{{17960970, -11775534, -4140968, -9702530, -8876562, -1410617, -12907383, -8659932, -29576300, 1903856},
{23134274, -14279132, -10681997, -1611936, 20684485, 15770816, -12989750, 3190296, 26955097, 14109738},
{15308788, 5320727, -30113809, -14318877, 22902008, 7767164, 29425325, -11277562, 31960942, 11934971}},
{{-27395711, 8435796, 4109644, 12222639, -24627868, 14818669, 20638173, 4875028, 10491392, 1379718},
{-13159415, 9197841, 3875503, -8936108, -1383712, -5879801, 33518459, 16176658, 21432314, 12180697},
{-11787308, 11500838, 13787581, -13832590, -22430679, 10140205, 1465425, 12689540, -10301319, -13872883}}
}, {
{{5414091, -15386041, -21007664, 9643570, 12834970, 1186149, -2622916, -1342231, 26128231, 6032912},
{-26337395, -13766162, 32496025, -13653919, 17847801, -12669156, 3604025, 8316894, -25875034, -10437358},
{3296484, 6223048, 24680646, -12246460, -23052020, 5903205, -8862297, -4639164, 12376617, 3188849}},
{{29190488, -14659046, 27549113, -1183516, 3520066, -10697301, 32049515, -7309113, -16109234, -9852307},
{-14744486, -9309156, 735818, -598978, -20407687, -5057904, 25246078, -15795669, 18640741, -960977},
{-6928835, -16430795, 10361374, 5642961, 4910474, 12345252, -31638386, -494430, 10530747, 1053335}},
{{-29265967, -14186805, -13538216, -12117373, -19457059, -10655384, -31462369, -2948985, 24018831, 15026644},
{-22592535, -3145277, -2289276, 5953843, -13440189, 9425631, 25310643, 13003497, -2314791, -15145616},
{-27419985, -603321, -8043984, -1669117, -26092265, 13987819, -27297622, 187899, -23166419, -2531735}},
{{-21744398, -13810475, 1844840, 5021428, -10434399, -15911473, 9716667, 16266922, -5070217, 726099},
{29370922, -6053998, 7334071, -15342259, 9385287, 2247707, -13661962, -4839461, 30007388, -15823341},
{-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, 730663, 9835848, 4555336}},
{{-23376435, 1410446, -22253753, -12899614, 30867635, 15826977, 17693930, 544696, -11985298, 12422646},
{31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -5118685, -4096706, 29120153, 13924425},
{-17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -9383939, -11317700, 7240931, -237388}},
{{-31361739, -11346780, -15007447, -5856218, -22453340, -12152771, 1222336, 4389483, 3293637, -15551743},
{-16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -24319580, 7733547, 12796905, -6335822},
{-8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -28253339, 3647836, 3222231, -11160462}},
{{18606113, 1693100, -25448386, -15170272, 4112353, 10045021, 23603893, -2048234, -7550776, 2484985},
{9255317, -3131197, -12156162, -1004256, 13098013, -9214866, 16377220, -2102812, -19802075, -3034702},
{-22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -31718148, 9936966, -30097688, -10618797}},
{{21878590, -5001297, 4338336, 13643897, -3036865, 13160960, 19708896, 5415497, -7360503, -4109293},
{27736861, 10103576, 12500508, 8502413, -3413016, -9633558, 10436918, -1550276, -23659143, -8132100},
{19492550, -12104365, -29681976, -852630, -3208171, 12403437, 30066266, 8367329, 13243957, 8709688}}
}, {
{{12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -11194191, -5645734, 5150968, 7274186},
{2831366, -12492146, 1478975, 6122054, 23825128, -12733586, 31097299, 6083058, 31021603, -9793610},
{-2529932, -2229646, 445613, 10720828, -13849527, -11505937, -23507731, 16354465, 15067285, -14147707}},
{{7840942, 14037873, -33364863, 15934016, -728213, -3642706, 21403988, 1057586, -19379462, -12403220},
{915865, -16469274, 15608285, -8789130, -24357026, 6060030, -17371319, 8410997, -7220461, 16527025},
{32922597, -556987, 20336074, -16184568, 10903705, -5384487, 16957574, 52992, 23834301, 6588044}},
{{32752030, 11232950, 3381995, -8714866, 22652988, -10744103, 17159699, 16689107, -20314580, -1305992},
{-4689649, 9166776, -25710296, -10847306, 11576752, 12733943, 7924251, -2752281, 1976123, -7249027},
{21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -3371252, 12331345, -8237197}},
{{8651614, -4477032, -16085636, -4996994, 13002507, 2950805, 29054427, -5106970, 10008136, -4667901},
{31486080, 15114593, -14261250, 12951354, 14369431, -7387845, 16347321, -13662089, 8684155, -10532952},
{19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -26263207, -6086921, 31316348, 14219878}},
{{-28594490, 1193785, 32245219, 11392485, 31092169, 15722801, 27146014, 6992409, 29126555, 9207390},
{32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -4980517, 10843782, -7957600, -14435730},
{2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -21494559, 8550130, 28346258, 1994730}},
{{-19578299, 8085545, -14000519, -3948622, 2785838, -16231307, -19516951, 7174894, 22628102, 8115180},
{-30405132, 955511, -11133838, -15078069, -32447087, -13278079, -25651578, 3317160, -9943017, 930272},
{-15303681, -6833769, 28856490, 1357446, 23421993, 1057177, 24091212, -1388970, -22765376, -10650715}},
{{-22751231, -5303997, -12907607, -12768866, -15811511, -7797053, -14839018, -16554220, -1867018, 8398970},
{-31969310, 2106403, -4736360, 1362501, 12813763, 16200670, 22981545, -6291273, 18009408, -15772772},
{-17220923, -9545221, -27784654, 14166835, 29815394, 7444469, 29551787, -3727419, 19288549, 1325865}},
{{15100157, -15835752, -23923978, -1005098, -26450192, 15509408, 12376730, -3479146, 33166107, -8042750},
{20909231, 13023121, -9209752, 16251778, -5778415, -8094914, 12412151, 10018715, 2213263, -13878373},
{32529814, -11074689, 30361439, -16689753, -9135940, 1513226, 22922121, 6382134, -5766928, 8371348}}
}, {
{{9923462, 11271500, 12616794, 3544722, -29998368, -1721626, 12891687, -8193132, -26442943, 10486144},
{-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, 2610596, -23921530, -11455195},
{5408411, -1136691, -4969122, 10561668, 24145918, 14240566, 31319731, -4235541, 19985175, -3436086}},
{{-13994457, 16616821, 14549246, 3341099, 32155958, 13648976, -17577068, 8849297, 65030, 8370684},
{-8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -19442942, 6922164, 12743482, -9800518},
{-2361371, 12678785, 28815050, 4759974, -23893047, 4884717, 23783145, 11038569, 18800704, 255233}},
{{-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, 9066957, 19258688, -14753793},
{-2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -31934921, 2209390, -1524053, 2055794},
{580882, 16705327, 5468415, -2683018, -30926419, -14696000, -7203346, -8994389, -30021019, 7394435}},
{{23838809, 1822728, -15738443, 15242727, 8318092, -3733104, -21672180, -3492205, -4821741, 14799921},
{13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, 13496856, -9056018, 7402518},
{2286874, -4435931, -20042458, -2008336, -13696227, 5038122, 11006906, -15760352, 8205061, 1607563}},
{{14414086, -8002132, 3331830, -3208217, 22249151, -5594188, 18364661, -2906958, 30019587, -9029278},
{-27688051, 1585953, -10775053, 931069, -29120221, -11002319, -14410829, 12029093, 9944378, 8024},
{4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -16114594, -999085, -8142388, 5640030}},
{{10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, -16694564, 15219798, -14327783},
{27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, -1173195, -18342183, 9742717},
{6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, 7406442, 12420155, 1994844}},
{{14012521, -5024720, -18384453, -9578469, -26485342, -3936439, -13033478, -10909803, 24319929, -6446333},
{16412690, -4507367, 10772641, 15929391, -17068788, -4658621, 10555945, -10484049, -30102368, -4739048},
{22397382, -7767684, -9293161, -12792868, 17166287, -9755136, -27333065, 6199366, 21880021, -12250760}},
{{-4283307, 5368523, -31117018, 8163389, -30323063, 3209128, 16557151, 8890729, 8840445, 4957760},
{-15447727, 709327, -6919446, -10870178, -29777922, 6522332, -21720181, 12130072, -14796503, 5005757},
{-2114751, -14308128, 23019042, 15765735, -25269683, 6002752, 10183197, -13239326, -16395286, -2176112}}
}, {
{{-19025756, 1632005, 13466291, -7995100, -23640451, 16573537, -32013908, -3057104, 22208662, 2000468},
{3065073, -1412761, -25598674, -361432, -17683065, -5703415, -8164212, 11248527, -3691214, -7414184},
{10379208, -6045554, 8877319, 1473647, -29291284, -12507580, 16690915, 2553332, -3132688, 16400289}},
{{15716668, 1254266, -18472690, 7446274, -8448918, 6344164, -22097271, -7285580, 26894937, 9132066},
{24158887, 12938817, 11085297, -8177598, -28063478, -4457083, -30576463, 64452, -6817084, -2692882},
{13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, -3418511, -4688006, 2364226}},
{{16335052, 9132434, 25640582, 6678888, 1725628, 8517937, -11807024, -11697457, 15445875, -7798101},
{29004207, -7867081, 28661402, -640412, -12794003, -7943086, 31863255, -4135540, -278050, -15759279},
{-6122061, -14866665, -28614905, 14569919, -10857999, -3591829, 10343412, -6976290, -29828287, -10815811}},
{{27081650, 3463984, 14099042, -4517604, 1616303, -6205604, 29542636, 15372179, 17293797, 960709},
{20263915, 11434237, -5765435, 11236810, 13505955, -10857102, -16111345, 6493122, -19384511, 7639714},
{-2830798, -14839232, 25403038, -8215196, -8317012, -16173699, 18006287, -16043750, 29994677, -15808121}},
{{9769828, 5202651, -24157398, -13631392, -28051003, -11561624, -24613141, -13860782, -31184575, 709464},
{12286395, 13076066, -21775189, -1176622, -25003198, 4057652, -32018128, -8890874, 16102007, 13205847},
{13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, 8525972, 10151379, 10394400}},
{{4024660, -16137551, 22436262, 12276534, -9099015, -2686099, 19698229, 11743039, -33302334, 8934414},
{-15879800, -4525240, -8580747, -2934061, 14634845, -698278, -9449077, 3137094, -11536886, 11721158},
{17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, 8835153, -9205489, -1280045}},
{{-461409, -7830014, 20614118, 16688288, -7514766, -4807119, 22300304, 505429, 6108462, -6183415},
{-5070281, 12367917, -30663534, 3234473, 32617080, -8422642, 29880583, -13483331, -26898490, -7867459},
{-31975283, 5726539, 26934134, 10237677, -3173717, -605053, 24199304, 3795095, 7592688, -14992079}},
{{21594432, -14964228, 17466408, -4077222, 32537084, 2739898, 6407723, 12018833, -28256052, 4298412},
{-20650503, -11961496, -27236275, 570498, 3767144, -1717540, 13891942, -1569194, 13717174, 10805743},
{-14676630, -15644296, 15287174, 11927123, 24177847, -8175568, -796431, 14860609, -26938930, -5863836}}
}, {
{{12962541, 5311799, -10060768, 11658280, 18855286, -7954201, 13286263, -12808704, -4381056, 9882022},
{18512079, 11319350, -20123124, 15090309, 18818594, 5271736, -22727904, 3666879, -23967430, -3299429},
{-6789020, -3146043, 16192429, 13241070, 15898607, -14206114, -10084880, -6661110, -2403099, 5276065}},
{{30169808, -5317648, 26306206, -11750859, 27814964, 7069267, 7152851, 3684982, 1449224, 13082861},
{10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, 15056736, -21016438, -8202000},
{-33150110, 3261608, 22745853, 7948688, 19370557, -15177665, -26171976, 6482814, -10300080, -11060101}},
{{32869458, -5408545, 25609743, 15678670, -10687769, -15471071, 26112421, 2521008, -22664288, 6904815},
{29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, 3841096, -29003639, -6657642},
{10340844, -6630377, -18656632, -2278430, 12621151, -13339055, 30878497, -11824370, -25584551, 5181966}},
{{25940115, -12658025, 17324188, -10307374, -8671468, 15029094, 24396252, -16450922, -2322852, -12388574},
{-21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, 12641087, 20603771, -6561742},
{-18882287, -11673380, 24849422, 11501709, 13161720, -4768874, 1925523, 11914390, 4662781, 7820689}},
{{12241050, -425982, 8132691, 9393934, 32846760, -1599620, 29749456, 12172924, 16136752, 15264020},
{-10349955, -14680563, -8211979, 2330220, -17662549, -14545780, 10658213, 6671822, 19012087, 3772772},
{3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, -15762884, 20527771, 12988982}},
{{-14822485, -5797269, -3707987, 12689773, -898983, -10914866, -24183046, -10564943, 3299665, -12424953},
{-16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, 6461331, -25583147, 8991218},
{-17226263, 1816362, -1673288, -6086439, 31783888, -8175991, -32948145, 7417950, -30242287, 1507265}},
{{29692663, 6829891, -10498800, 4334896, 20945975, -11906496, -28887608, 8209391, 14606362, -10647073},
{-3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, 9761487, 4170404, -2085325},
{-11587470, 14855945, -4127778, -1531857, -26649089, 15084046, 22186522, 16002000, -14276837, -8400798}},
{{-4811456, 13761029, -31703877, -2483919, -3312471, 7869047, -7113572, -9620092, 13240845, 10965870},
{-7742563, -8256762, -14768334, -13656260, -23232383, 12387166, 4498947, 14147411, 29514390, 4302863},
{-13413405, -12407859, 20757302, -13801832, 14785143, 8976368, -5061276, -2144373, 17846988, -13971927}}
}, {
{{-2244452, -754728, -4597030, -1066309, -6247172, 1455299, -21647728, -9214789, -5222701, 12650267},
{-9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, 13770293, -19134326, 10958663},
{22470984, 12369526, 23446014, -5441109, -21520802, -9698723, -11772496, -11574455, -25083830, 4271862}},
{{-25169565, -10053642, -19909332, 15361595, -5984358, 2159192, 75375, -4278529, -32526221, 8469673},
{15854970, 4148314, -8893890, 7259002, 11666551, 13824734, -30531198, 2697372, 24154791, -9460943},
{15446137, -15806644, 29759747, 14019369, 30811221, -9610191, -31582008, 12840104, 24913809, 9815020}},
{{-4709286, -5614269, -31841498, -12288893, -14443537, 10799414, -9103676, 13438769, 18735128, 9466238},
{11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, -10896103, -22728655, 16199064},
{14576810, 379472, -26786533, -8317236, -29426508, -10812974, -102766, 1876699, 30801119, 2164795}},
{{15995086, 3199873, 13672555, 13712240, -19378835, -4647646, -13081610, -15496269, -13492807, 1268052},
{-10290614, -3659039, -3286592, 10948818, 23037027, 3794475, -3470338, -12600221, -17055369, 3565904},
{29210088, -9419337, -5919792, -4952785, 10834811, -13327726, -16512102, -10820713, -27162222, -14030531}},
{{-13161890, 15508588, 16663704, -8156150, -28349942, 9019123, -29183421, -3769423, 2244111, -14001979},
{-5152875, -3800936, -9306475, -6071583, 16243069, 14684434, -25673088, -16180800, 13491506, 4641841},
{10813417, 643330, -19188515, -728916, 30292062, -16600078, 27548447, -7721242, 14476989, -12767431}},
{{10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, -1644259, -27912810, 12651324},
{-31185513, -813383, 22271204, 11835308, 10201545, 15351028, 17099662, 3988035, 21721536, -3148940},
{10202177, -6545839, -31373232, -9574638, -32150642, -8119683, -12906320, 3852694, 13216206, 14842320}},
{{-15815640, -10601066, -6538952, -7258995, -6984659, -6581778, -31500847, 13765824, -27434397, 9900184},
{14465505, -13833331, -32133984, -14738873, -27443187, 12990492, 33046193, 15796406, -7051866, -8040114},
{30924417, -8279620, 6359016, -12816335, 16508377, 9071735, -25488601, 15413635, 9524356, -7018878}},
{{12274201, -13175547, 32627641, -1785326, 6736625, 13267305, 5237659, -5109483, 15663516, 4035784},
{-2951309, 8903985, 17349946, 601635, -16432815, -4612556, -13732739, -15889334, -22258478, 4659091},
{-16916263, -4952973, -30393711, -15158821, 20774812, 15897498, 5736189, 15026997, -2178256, -13455585}}
}, {
{{-8858980, -2219056, 28571666, -10155518, -474467, -10105698, -3801496, 278095, 23440562, -290208},
{10226241, -5928702, 15139956, 120818, -14867693, 5218603, 32937275, 11551483, -16571960, -7442864},
{17932739, -12437276, -24039557, 10749060, 11316803, 7535897, 22503767, 5561594, -3646624, 3898661}},
{{7749907, -969567, -16339731, -16464, -25018111, 15122143, -1573531, 7152530, 21831162, 1245233},
{26958459, -14658026, 4314586, 8346991, -5677764, 11960072, -32589295, -620035, -30402091, -16716212},
{-12165896, 9166947, 33491384, 13673479, 29787085, 13096535, 6280834, 14587357, -22338025, 13987525}},
{{-24349909, 7778775, 21116000, 15572597, -4833266, -5357778, -4300898, -5124639, -7469781, -2858068},
{9681908, -6737123, -31951644, 13591838, -6883821, 386950, 31622781, 6439245, -14581012, 4091397},
{-8426427, 1470727, -28109679, -1596990, 3978627, -5123623, -19622683, 12092163, 29077877, -14741988}},
{{5269168, -6859726, -13230211, -8020715, 25932563, 1763552, -5606110, -5505881, -20017847, 2357889},
{32264008, -15407652, -5387735, -1160093, -2091322, -3946900, 23104804, -12869908, 5727338, 189038},
{14609123, -8954470, -6000566, -16622781, -14577387, -7743898, -26745169, 10942115, -25888931, -14884697}},
{{20513500, 5557931, -15604613, 7829531, 26413943, -2019404, -21378968, 7471781, 13913677, -5137875},
{-25574376, 11967826, 29233242, 12948236, -6754465, 4713227, -8940970, 14059180, 12878652, 8511905},
{-25656801, 3393631, -2955415, -7075526, -2250709, 9366908, -30223418, 6812974, 5568676, -3127656}},
{{11630004, 12144454, 2116339, 13606037, 27378885, 15676917, -17408753, -13504373, -14395196, 8070818},
{27117696, -10007378, -31282771, -5570088, 1127282, 12772488, -29845906, 10483306, -11552749, -1028714},
{10637467, -5688064, 5674781, 1072708, -26343588, -6982302, -1683975, 9177853, -27493162, 15431203}},
{{20525145, 10892566, -12742472, 12779443, -29493034, 16150075, -28240519, 14943142, -15056790, -7935931},
{-30024462, 5626926, -551567, -9981087, 753598, 11981191, 25244767, -3239766, -3356550, 9594024},
{-23752644, 2636870, -5163910, -10103818, 585134, 7877383, 11345683, -6492290, 13352335, -10977084}},
{{-1931799, -5407458, 3304649, -12884869, 17015806, -4877091, -29783850, -7752482, -13215537, -319204},
{20239939, 6607058, 6203985, 3483793, -18386976, -779229, -20723742, 15077870, -22750759, 14523817},
{27406042, -6041657, 27423596, -4497394, 4996214, 10002360, -28842031, -4545494, -30172742, -4805667}}
}, {
{{11374242, 12660715, 17861383, -12540833, 10935568, 1099227, -13886076, -9091740, -27727044, 11358504},
{-12730809, 10311867, 1510375, 10778093, -2119455, -9145702, 32676003, 11149336, -26123651, 4985768},
{-19096303, 341147, -6197485, -239033, 15756973, -8796662, -983043, 13794114, -19414307, -15621255}},
{{6490081, 11940286, 25495923, -7726360, 8668373, -8751316, 3367603, 6970005, -1691065, -9004790},
{1656497, 13457317, 15370807, 6364910, 13605745, 8362338, -19174622, -5475723, -16796596, -5031438},
{-22273315, -13524424, -64685, -4334223, -18605636, -10921968, -20571065, -7007978, -99853, -10237333}},
{{17747465, 10039260, 19368299, -4050591, -20630635, -16041286, 31992683, -15857976, -29260363, -5511971},
{31932027, -4986141, -19612382, 16366580, 22023614, 88450, 11371999, -3744247, 4882242, -10626905},
{29796507, 37186, 19818052, 10115756, -11829032, 3352736, 18551198, 3272828, -5190932, -4162409}},
{{12501286, 4044383, -8612957, -13392385, -32430052, 5136599, -19230378, -3529697, 330070, -3659409},
{6384877, 2899513, 17807477, 7663917, -2358888, 12363165, 25366522, -8573892, -271295, 12071499},
{-8365515, -4042521, 25133448, -4517355, -6211027, 2265927, -32769618, 1936675, -5159697, 3829363}},
{{28425966, -5835433, -577090, -4697198, -14217555, 6870930, 7921550, -6567787, 26333140, 14267664},
{-11067219, 11871231, 27385719, -10559544, -4585914, -11189312, 10004786, -8709488, -21761224, 8930324},
{-21197785, -16396035, 25654216, -1725397, 12282012, 11008919, 1541940, 4757911, -26491501, -16408940}},
{{13537262, -7759490, -20604840, 10961927, -5922820, -13218065, -13156584, 6217254, -15943699, 13814990},
{-17422573, 15157790, 18705543, 29619, 24409717, -260476, 27361681, 9257833, -1956526, -1776914},
{-25045300, -10191966, 15366585, 15166509, -13105086, 8423556, -29171540, 12361135, -18685978, 4578290}},
{{24579768, 3711570, 1342322, -11180126, -27005135, 14124956, -22544529, 14074919, 21964432, 8235257},
{-6528613, -2411497, 9442966, -5925588, 12025640, -1487420, -2981514, -1669206, 13006806, 2355433},
{-16304899, -13605259, -6632427, -5142349, 16974359, -10911083, 27202044, 1719366, 1141648, -12796236}},
{{-12863944, -13219986, -8318266, -11018091, -6810145, -4843894, 13475066, -3133972, 32674895, 13715045},
{11423335, -5468059, 32344216, 8962751, 24989809, 9241752, -13265253, 16086212, -28740881, -15642093},
{-1409668, 12530728, -6368726, 10847387, 19531186, -14132160, -11709148, 7791794, -27245943, 4383347}}
}, {
{{-28970898, 5271447, -1266009, -9736989, -12455236, 16732599, -4862407, -4906449, 27193557, 6245191},
{-15193956, 5362278, -1783893, 2695834, 4960227, 12840725, 23061898, 3260492, 22510453, 8577507},
{-12632451, 11257346, -32692994, 13548177, -721004, 10879011, 31168030, 13952092, -29571492, -3635906}},
{{3877321, -9572739, 32416692, 5405324, -11004407, -13656635, 3759769, 11935320, 5611860, 8164018},
{-16275802, 14667797, 15906460, 12155291, -22111149, -9039718, 32003002, -8832289, 5773085, -8422109},
{-23788118, -8254300, 1950875, 8937633, 18686727, 16459170, -905725, 12376320, 31632953, 190926}},
{{-24593607, -16138885, -8423991, 13378746, 14162407, 6901328, -8288749, 4508564, -25341555, -3627528},
{8884438, -5884009, 6023974, 10104341, -6881569, -4941533, 18722941, -14786005, -1672488, 827625},
{-32720583, -16289296, -32503547, 7101210, 13354605, 2659080, -1800575, -14108036, -24878478, 1541286}},
{{2901347, -1117687, 3880376, -10059388, -17620940, -3612781, -21802117, -3567481, 20456845, -1885033},
{27019610, 12299467, -13658288, -1603234, -12861660, -4861471, -19540150, -5016058, 29439641, 15138866},
{21536104, -6626420, -32447818, -10690208, -22408077, 5175814, -5420040, -16361163, 7779328, 109896}},
{{30279744, 14648750, -8044871, 6425558, 13639621, -743509, 28698390, 12180118, 23177719, -554075},
{26572847, 3405927, -31701700, 12890905, -19265668, 5335866, -6493768, 2378492, 4439158, -13279347},
{-22716706, 3489070, -9225266, -332753, 18875722, -1140095, 14819434, -12731527, -17717757, -5461437}},
{{-5056483, 16566551, 15953661, 3767752, -10436499, 15627060, -820954, 2177225, 8550082, -15114165},
{-18473302, 16596775, -381660, 15663611, 22860960, 15585581, -27844109, -3582739, -23260460, -8428588},
{-32480551, 15707275, -8205912, -5652081, 29464558, 2713815, -22725137, 15860482, -21902570, 1494193}},
{{-19562091, -14087393, -25583872, -9299552, 13127842, 759709, 21923482, 16529112, 8742704, 12967017},
{-28464899, 1553205, 32536856, -10473729, -24691605, -406174, -8914625, -2933896, -29903758, 15553883},
{21877909, 3230008, 9881174, 10539357, -4797115, 2841332, 11543572, 14513274, 19375923, -12647961}},
{{8832269, -14495485, 13253511, 5137575, 5037871, 4078777, 24880818, -6222716, 2862653, 9455043},
{29306751, 5123106, 20245049, -14149889, 9592566, 8447059, -2077124, -2990080, 15511449, 4789663},
{-20679756, 7004547, 8824831, -9434977, -4045704, -3750736, -5754762, 108893, 23513200, 16652362}}
}, {
{{-33256173, 4144782, -4476029, -6579123, 10770039, -7155542, -6650416, -12936300, -18319198, 10212860},
{2756081, 8598110, 7383731, -6859892, 22312759, -1105012, 21179801, 2600940, -9988298, -12506466},
{-24645692, 13317462, -30449259, -15653928, 21365574, -10869657, 11344424, 864440, -2499677, -16710063}},
{{-26432803, 6148329, -17184412, -14474154, 18782929, -275997, -22561534, 211300, 2719757, 4940997},
{-1323882, 3911313, -6948744, 14759765, -30027150, 7851207, 21690126, 8518463, 26699843, 5276295},
{-13149873, -6429067, 9396249, 365013, 24703301, -10488939, 1321586, 149635, -15452774, 7159369}},
{{9987780, -3404759, 17507962, 9505530, 9731535, -2165514, 22356009, 8312176, 22477218, -8403385},
{18155857, -16504990, 19744716, 9006923, 15154154, -10538976, 24256460, -4864995, -22548173, 9334109},
{2986088, -4911893, 10776628, -3473844, 10620590, -7083203, -21413845, 14253545, -22587149, 536906}},
{{4377756, 8115836, 24567078, 15495314, 11625074, 13064599, 7390551, 10589625, 10838060, -15420424},
{-19342404, 867880, 9277171, -3218459, -14431572, -1986443, 19295826, -15796950, 6378260, 699185},
{7895026, 4057113, -7081772, -13077756, -17886831, -323126, -716039, 15693155, -5045064, -13373962}},
{{-7737563, -5869402, -14566319, -7406919, 11385654, 13201616, 31730678, -10962840, -3918636, -9669325},
{10188286, -15770834, -7336361, 13427543, 22223443, 14896287, 30743455, 7116568, -21786507, 5427593},
{696102, 13206899, 27047647, -10632082, 15285305, -9853179, 10798490, -4578720, 19236243, 12477404}},
{{-11229439, 11243796, -17054270, -8040865, -788228, -8167967, -3897669, 11180504, -23169516, 7733644},
{17800790, -14036179, -27000429, -11766671, 23887827, 3149671, 23466177, -10538171, 10322027, 15313801},
{26246234, 11968874, 32263343, -5468728, 6830755, -13323031, -15794704, -101982, -24449242, 10890804}},
{{-31365647, 10271363, -12660625, -6267268, 16690207, -13062544, -14982212, 16484931, 25180797, -5334884},
{-586574, 10376444, -32586414, -11286356, 19801893, 10997610, 2276632, 9482883, 316878, 13820577},
{-9882808, -4510367, -2115506, 16457136, -11100081, 11674996, 30756178, -7515054, 30696930, -3712849}},
{{32988917, -9603412, 12499366, 7910787, -10617257, -11931514, -7342816, -9985397, -32349517, 7392473},
{-8855661, 15927861, 9866406, -3649411, -2396914, -16655781, -30409476, -9134995, 25112947, -2926644},
{-2504044, -436966, 25621774, -5678772, 15085042, -5479877, -24884878, -13526194, 5537438, -13914319}}
}, {
{{-11225584, 2320285, -9584280, 10149187, -33444663, 5808648, -14876251, -1729667, 31234590, 6090599},
{-9633316, 116426, 26083934, 2897444, -6364437, -2688086, 609721, 15878753, -6970405, -9034768},
{-27757857, 247744, -15194774, -9002551, 23288161, -10011936, -23869595, 6503646, 20650474, 1804084}},
{{-27589786, 15456424, 8972517, 8469608, 15640622, 4439847, 3121995, -10329713, 27842616, -202328},
{-15306973, 2839644, 22530074, 10026331, 4602058, 5048462, 28248656, 5031932, -11375082, 12714369},
{20807691, -7270825, 29286141, 11421711, -27876523, -13868230, -21227475, 1035546, -19733229, 12796920}},
{{12076899, -14301286, -8785001, -11848922, -25012791, 16400684, -17591495, -12899438, 3480665, -15182815},
{-32361549, 5457597, 28548107, 7833186, 7303070, -11953545, -24363064, -15921875, -33374054, 2771025},
{-21389266, 421932, 26597266, 6860826, 22486084, -6737172, -17137485, -4210226, -24552282, 15673397}},
{{-20184622, 2338216, 19788685, -9620956, -4001265, -8740893, -20271184, 4733254, 3727144, -12934448},
{6120119, 814863, -11794402, -622716, 6812205, -15747771, 2019594, 7975683, 31123697, -10958981},
{30069250, -11435332, 30434654, 2958439, 18399564, -976289, 12296869, 9204260, -16432438, 9648165}},
{{32705432, -1550977, 30705658, 7451065, -11805606, 9631813, 3305266, 5248604, -26008332, -11377501},
{17219865, 2375039, -31570947, -5575615, -19459679, 9219903, 294711, 15298639, 2662509, -16297073},
{-1172927, -7558695, -4366770, -4287744, -21346413, -8434326, 32087529, -1222777, 32247248, -14389861}},
{{14312628, 1221556, 17395390, -8700143, -4945741, -8684635, -28197744, -9637817, -16027623, -13378845},
{-1428825, -9678990, -9235681, 6549687, -7383069, -468664, 23046502, 9803137, 17597934, 2346211},
{18510800, 15337574, 26171504, 981392, -22241552, 7827556, -23491134, -11323352, 3059833, -11782870}},
{{10141598, 6082907, 17829293, -1947643, 9830092, 13613136, -25556636, -5544586, -33502212, 3592096},
{33114168, -15889352, -26525686, -13343397, 33076705, 8716171, 1151462, 1521897, -982665, -6837803},
{-32939165, -4255815, 23947181, -324178, -33072974, -12305637, -16637686, 3891704, 26353178, 693168}},
{{30374239, 1595580, -16884039, 13186931, 4600344, 406904, 9585294, -400668, 31375464, 14369965},
{-14370654, -7772529, 1510301, 6434173, -18784789, -6262728, 32732230, -13108839, 17901441, 16011505},
{18171223, -11934626, -12500402, 15197122, -11038147, -15230035, -19172240, -16046376, 8764035, 12309598}}
}, {
{{5975908, -5243188, -19459362, -9681747, -11541277, 14015782, -23665757, 1228319, 17544096, -10593782},
{5811932, -1715293, 3442887, -2269310, -18367348, -8359541, -18044043, -15410127, -5565381, 12348900},
{-31399660, 11407555, 25755363, 6891399, -3256938, 14872274, -24849353, 8141295, -10632534, -585479}},
{{-12675304, 694026, -5076145, 13300344, 14015258, -14451394, -9698672, -11329050, 30944593, 1130208},
{8247766, -6710942, -26562381, -7709309, -14401939, -14648910, 4652152, 2488540, 23550156, -271232},
{17294316, -3788438, 7026748, 15626851, 22990044, 113481, 2267737, -5908146, -408818, -137719}},
{{16091085, -16253926, 18599252, 7340678, 2137637, -1221657, -3364161, 14550936, 3260525, -7166271},
{-4910104, -13332887, 18550887, 10864893, -16459325, -7291596, -23028869, -13204905, -12748722, 2701326},
{-8574695, 16099415, 4629974, -16340524, -20786213, -6005432, -10018363, 9276971, 11329923, 1862132}},
{{14763076, -15903608, -30918270, 3689867, 3511892, 10313526, -21951088, 12219231, -9037963, -940300},
{8894987, -3446094, 6150753, 3013931, 301220, 15693451, -31981216, -2909717, -15438168, 11595570},
{15214962, 3537601, -26238722, -14058872, 4418657, -15230761, 13947276, 10730794, -13489462, -4363670}},
{{-2538306, 7682793, 32759013, 263109, -29984731, -7955452, -22332124, -10188635, 977108, 699994},
{-12466472, 4195084, -9211532, 550904, -15565337, 12917920, 19118110, -439841, -30534533, -14337913},
{31788461, -14507657, 4799989, 7372237, 8808585, -14747943, 9408237, -10051775, 12493932, -5409317}},
{{-25680606, 5260744, -19235809, -6284470, -3695942, 16566087, 27218280, 2607121, 29375955, 6024730},
{842132, -2794693, -4763381, -8722815, 26332018, -12405641, 11831880, 6985184, -9940361, 2854096},
{-4847262, -7969331, 2516242, -5847713, 9695691, -7221186, 16512645, 960770, 12121869, 16648078}},
{{-15218652, 14667096, -13336229, 2013717, 30598287, -464137, -31504922, -7882064, 20237806, 2838411},
{-19288047, 4453152, 15298546, -16178388, 22115043, -15972604, 12544294, -13470457, 1068881, -12499905},
{-9558883, -16518835, 33238498, 13506958, 30505848, -1114596, -8486907, -2630053, 12521378, 4845654}},
{{-28198521, 10744108, -2958380, 10199664, 7759311, -13088600, 3409348, -873400, -6482306, -12885870},
{-23561822, 6230156, -20382013, 10655314, -24040585, -11621172, 10477734, -1240216, -3113227, 13974498},
{12966261, 15550616, -32038948, -1615346, 21025980, -629444, 5642325, 7188737, 18895762, 12629579}}
}, {
{{14741879, -14946887, 22177208, -11721237, 1279741, 8058600, 11758140, 789443, 32195181, 3895677},
{10758205, 15755439, -4509950, 9243698, -4879422, 6879879, -2204575, -3566119, -8982069, 4429647},
{-2453894, 15725973, -20436342, -10410672, -5803908, -11040220, -7135870, -11642895, 18047436, -15281743}},
{{-25173001, -11307165, 29759956, 11776784, -22262383, -15820455, 10993114, -12850837, -17620701, -9408468},
{21987233, 700364, -24505048, 14972008, -7774265, -5718395, 32155026, 2581431, -29958985, 8773375},
{-25568350, 454463, -13211935, 16126715, 25240068, 8594567, 20656846, 12017935, -7874389, -13920155}},
{{6028182, 6263078, -31011806, -11301710, -818919, 2461772, -31841174, -5468042, -1721788, -2776725},
{-12278994, 16624277, 987579, -5922598, 32908203, 1248608, 7719845, -4166698, 28408820, 6816612},
{-10358094, -8237829, 19549651, -12169222, 22082623, 16147817, 20613181, 13982702, -10339570, 5067943}},
{{-30505967, -3821767, 12074681, 13582412, -19877972, 2443951, -19719286, 12746132, 5331210, -10105944},
{30528811, 3601899, -1957090, 4619785, -27361822, -15436388, 24180793, -12570394, 27679908, -1648928},
{9402404, -13957065, 32834043, 10838634, -26580150, -13237195, 26653274, -8685565, 22611444, -12715406}},
{{22190590, 1118029, 22736441, 15130463, -30460692, -5991321, 19189625, -4648942, 4854859, 6622139},
{-8310738, -2953450, -8262579, -3388049, -10401731, -271929, 13424426, -3567227, 26404409, 13001963},
{-31241838, -15415700, -2994250, 8939346, 11562230, -12840670, -26064365, -11621720, -15405155, 11020693}},
{{1866042, -7949489, -7898649, -10301010, 12483315, 13477547, 3175636, -12424163, 28761762, 1406734},
{-448555, -1777666, 13018551, 3194501, -9580420, -11161737, 24760585, -4347088, 25577411, -13378680},
{-24290378, 4759345, -690653, -1852816, 2066747, 10693769, -29595790, 9884936, -9368926, 4745410}},
{{-9141284, 6049714, -19531061, -4341411, -31260798, 9944276, -15462008, -11311852, 10931924, -11931931},
{-16561513, 14112680, -8012645, 4817318, -8040464, -11414606, -22853429, 10856641, -20470770, 13434654},
{22759489, -10073434, -16766264, -1871422, 13637442, -10168091, 1765144, -12654326, 28445307, -5364710}},
{{29875063, 12493613, 2795536, -3786330, 1710620, 15181182, -10195717, -8788675, 9074234, 1167180},
{-26205683, 11014233, -9842651, -2635485, -26908120, 7532294, -18716888, -9535498, 3843903, 9367684},
{-10969595, -6403711, 9591134, 9582310, 11349256, 108879, 16235123, 8601684, -139197, 4242895}}
}, {
{{22092954, -13191123, -2042793, -11968512, 32186753, -11517388, -6574341, 2470660, -27417366, 16625501},
{-11057722, 3042016, 13770083, -9257922, 584236, -544855, -7770857, 2602725, -27351616, 14247413},
{6314175, -10264892, -32772502, 15957557, -10157730, 168750, -8618807, 14290061, 27108877, -1180880}},
{{-8586597, -7170966, 13241782, 10960156, -32991015, -13794596, 33547976, -11058889, -27148451, 981874},
{22833440, 9293594, -32649448, -13618667, -9136966, 14756819, -22928859, -13970780, -10479804, -16197962},
{-7768587, 3326786, -28111797, 10783824, 19178761, 14905060, 22680049, 13906969, -15933690, 3797899}},
{{21721356, -4212746, -12206123, 9310182, -3882239, -13653110, 23740224, -2709232, 20491983, -8042152},
{9209270, -15135055, -13256557, -6167798, -731016, 15289673, 25947805, 15286587, 30997318, -6703063},
{7392032, 16618386, 23946583, -8039892, -13265164, -1533858, -14197445, -2321576, 17649998, -250080}},
{{-9301088, -14193827, 30609526, -3049543, -25175069, -1283752, -15241566, -9525724, -2233253, 7662146},
{-17558673, 1763594, -33114336, 15908610, -30040870, -12174295, 7335080, -8472199, -3174674, 3440183},
{-19889700, -5977008, -24111293, -9688870, 10799743, -16571957, 40450, -4431835, 4862400, 1133}},
{{-32856209, -7873957, -5422389, 14860950, -16319031, 7956142, 7258061, 311861, -30594991, -7379421},
{-3773428, -1565936, 28985340, 7499440, 24445838, 9325937, 29727763, 16527196, 18278453, 15405622},
{-4381906, 8508652, -19898366, -3674424, -5984453, 15149970, -13313598, 843523, -21875062, 13626197}},
{{2281448, -13487055, -10915418, -2609910, 1879358, 16164207, -10783882, 3953792, 13340839, 15928663},
{31727126, -7179855, -18437503, -8283652, 2875793, -16390330, -25269894, -7014826, -23452306, 5964753},
{4100420, -5959452, -17179337, 6017714, -18705837, 12227141, -26684835, 11344144, 2538215, -7570755}},
{{-9433605, 6123113, 11159803, -2156608, 30016280, 14966241, -20474983, 1485421, -629256, -15958862},
{-26804558, 4260919, 11851389, 9658551, -32017107, 16367492, -20205425, -13191288, 11659922, -11115118},
{26180396, 10015009, -30844224, -8581293, 5418197, 9480663, 2231568, -10170080, 33100372, -1306171}},
{{15121113, -5201871, -10389905, 15427821, -27509937, -15992507, 21670947, 4486675, -5931810, -14466380},
{16166486, -9483733, -11104130, 6023908, -31926798, -1364923, 2340060, -16254968, -10735770, -10039824},
{28042865, -3557089, -12126526, 12259706, -3717498, -6945899, 6766453, -8689599, 18036436, 5803270}}
}, {
{{-817581, 6763912, 11803561, 1585585, 10958447, -2671165, 23855391, 4598332, -6159431, -14117438},
{-31031306, -14256194, 17332029, -2383520, 31312682, -5967183, 696309, 50292, -20095739, 11763584},
{-594563, -2514283, -32234153, 12643980, 12650761, 14811489, 665117, -12613632, -19773211, -10713562}},
{{30464590, -11262872, -4127476, -12734478, 19835327, -7105613, -24396175, 2075773, -17020157, 992471},
{18357185, -6994433, 7766382, 16342475, -29324918, 411174, 14578841, 8080033, -11574335, -10601610},
{19598397, 10334610, 12555054, 2555664, 18821899, -10339780, 21873263, 16014234, 26224780, 16452269}},
{{-30223925, 5145196, 5944548, 16385966, 3976735, 2009897, -11377804, -7618186, -20533829, 3698650},
{14187449, 3448569, -10636236, -10810935, -22663880, -3433596, 7268410, -10890444, 27394301, 12015369},
{19695761, 16087646, 28032085, 12999827, 6817792, 11427614, 20244189, -1312777, -13259127, -3402461}},
{{30860103, 12735208, -1888245, -4699734, -16974906, 2256940, -8166013, 12298312, -8550524, -10393462},
{-5719826, -11245325, -1910649, 15569035, 26642876, -7587760, -5789354, -15118654, -4976164, 12651793},
{-2848395, 9953421, 11531313, -5282879, 26895123, -12697089, -13118820, -16517902, 9768698, -2533218}},
{{-24719459, 1894651, -287698, -4704085, 15348719, -8156530, 32767513, 12765450, 4940095, 10678226},
{18860224, 15980149, -18987240, -1562570, -26233012, -11071856, -7843882, 13944024, -24372348, 16582019},
{-15504260, 4970268, -29893044, 4175593, -20993212, -2199756, -11704054, 15444560, -11003761, 7989037}},
{{31490452, 5568061, -2412803, 2182383, -32336847, 4531686, -32078269, 6200206, -19686113, -14800171},
{-17308668, -15879940, -31522777, -2831, -32887382, 16375549, 8680158, -16371713, 28550068, -6857132},
{-28126887, -5688091, 16837845, -1820458, -6850681, 12700016, -30039981, 4364038, 1155602, 5988841}},
{{21890435, -13272907, -12624011, 12154349, -7831873, 15300496, 23148983, -4470481, 24618407, 8283181},
{-33136107, -10512751, 9975416, 6841041, -31559793, 16356536, 3070187, -7025928, 1466169, 10740210},
{-1509399, -15488185, -13503385, -10655916, 32799044, 909394, -13938903, -5779719, -32164649, -15327040}},
{{3960823, -14267803, -28026090, -15918051, -19404858, 13146868, 15567327, 951507, -3260321, -573935},
{24740841, 5052253, -30094131, 8961361, 25877428, 6165135, -24368180, 14397372, -7380369, -6144105},
{-28888365, 3510803, -28103278, -1158478, -11238128, -10631454, -15441463, -14453128, -1625486, -6494814}}
}, {
{{793299, -9230478, 8836302, -6235707, -27360908, -2369593, 33152843, -4885251, -9906200, -621852},
{5666233, 525582, 20782575, -8038419, -24538499, 14657740, 16099374, 1468826, -6171428, -15186581},
{-4859255, -3779343, -2917758, -6748019, 7778750, 11688288, -30404353, -9871238, -1558923, -9863646}},
{{10896332, -7719704, 824275, 472601, -19460308, 3009587, 25248958, 14783338, -30581476, -15757844},
{10566929, 12612572, -31944212, 11118703, -12633376, 12362879, 21752402, 8822496, 24003793, 14264025},
{27713862, -7355973, -11008240, 9227530, 27050101, 2504721, 23886875, -13117525, 13958495, -5732453}},
{{-23481610, 4867226, -27247128, 3900521, 29838369, -8212291, -31889399, -10041781, 7340521, -15410068},
{4646514, -8011124, -22766023, -11532654, 23184553, 8566613, 31366726, -1381061, -15066784, -10375192},
{-17270517, 12723032, -16993061, 14878794, 21619651, -6197576, 27584817, 3093888, -8843694, 3849921}},
{{-9064912, 2103172, 25561640, -15125738, -5239824, 9582958, 32477045, -9017955, 5002294, -15550259},
{-12057553, -11177906, 21115585, -13365155, 8808712, -12030708, 16489530, 13378448, -25845716, 12741426},
{-5946367, 10645103, -30911586, 15390284, -3286982, -7118677, 24306472, 15852464, 28834118, -7646072}},
{{-17335748, -9107057, -24531279, 9434953, -8472084, -583362, -13090771, 455841, 20461858, 5491305},
{13669248, -16095482, -12481974, -10203039, -14569770, -11893198, -24995986, 11293807, -28588204, -9421832},
{28497928, 6272777, -33022994, 14470570, 8906179, -1225630, 18504674, -14165166, 29867745, -8795943}},
{{-16207023, 13517196, -27799630, -13697798, 24009064, -6373891, -6367600, -13175392, 22853429, -4012011},
{24191378, 16712145, -13931797, 15217831, 14542237, 1646131, 18603514, -11037887, 12876623, -2112447},
{17902668, 4518229, -411702, -2829247, 26878217, 5258055, -12860753, 608397, 16031844, 3723494}},
{{-28632773, 12763728, -20446446, 7577504, 33001348, -13017745, 17558842, -7872890, 23896954, -4314245},
{-20005381, -12011952, 31520464, 605201, 2543521, 5991821, -2945064, 7229064, -9919646, -8826859},
{28816045, 298879, -28165016, -15920938, 19000928, -1665890, -12680833, -2949325, -18051778, -2082915}},
{{16000882, -344896, 3493092, -11447198, -29504595, -13159789, 12577740, 16041268, -19715240, 7847707},
{10151868, 10572098, 27312476, 7922682, 14825339, 4723128, -32855931, -6519018, -10020567, 3852848},
{-11430470, 15697596, -21121557, -4420647, 5386314, 15063598, 16514493, -15932110, 29330899, -15076224}}
}, {
{{-25499735, -4378794, -15222908, -6901211, 16615731, 2051784, 3303702, 15490, -27548796, 12314391},
{15683520, -6003043, 18109120, -9980648, 15337968, -5997823, -16717435, 15921866, 16103996, -3731215},
{-23169824, -10781249, 13588192, -1628807, -3798557, -1074929, -19273607, 5402699, -29815713, -9841101}},
{{23190676, 2384583, -32714340, 3462154, -29903655, -1529132, -11266856, 8911517, -25205859, 2739713},
{21374101, -3554250, -33524649, 9874411, 15377179, 11831242, -33529904, 6134907, 4931255, 11987849},
{-7732, -2978858, -16223486, 7277597, 105524, -322051, -31480539, 13861388, -30076310, 10117930}},
{{-29501170, -10744872, -26163768, 13051539, -25625564, 5089643, -6325503, 6704079, 12890019, 15728940},
{-21972360, -11771379, -951059, -4418840, 14704840, 2695116, 903376, -10428139, 12885167, 8311031},
{-17516482, 5352194, 10384213, -13811658, 7506451, 13453191, 26423267, 4384730, 1888765, -5435404}},
{{-25817338, -3107312, -13494599, -3182506, 30896459, -13921729, -32251644, -12707869, -19464434, -3340243},
{-23607977, -2665774, -526091, 4651136, 5765089, 4618330, 6092245, 14845197, 17151279, -9854116},
{-24830458, -12733720, -15165978, 10367250, -29530908, -265356, 22825805, -7087279, -16866484, 16176525}},
{{-23583256, 6564961, 20063689, 3798228, -4740178, 7359225, 2006182, -10363426, -28746253, -10197509},
{-10626600, -4486402, -13320562, -5125317, 3432136, -6393229, 23632037, -1940610, 32808310, 1099883},
{15030977, 5768825, -27451236, -2887299, -6427378, -15361371, -15277896, -6809350, 2051441, -15225865}},
{{-3362323, -7239372, 7517890, 9824992, 23555850, 295369, 5148398, -14154188, -22686354, 16633660},
{4577086, -16752288, 13249841, -15304328, 19958763, -14537274, 18559670, -10759549, 8402478, -9864273},
{-28406330, -1051581, -26790155, -907698, -17212414, -11030789, 9453451, -14980072, 17983010, 9967138}},
{{-25762494, 6524722, 26585488, 9969270, 24709298, 1220360, -1677990, 7806337, 17507396, 3651560},
{-10420457, -4118111, 14584639, 15971087, -15768321, 8861010, 26556809, -5574557, -18553322, -11357135},
{2839101, 14284142, 4029895, 3472686, 14402957, 12689363, -26642121, 8459447, -5605463, -7621941}},
{{-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, -849066, 17258084, -7977739},
{18164541, -10595176, -17154882, -1542417, 19237078, -9745295, 23357533, -15217008, 26908270, 12150756},
{-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, -5537701, -32302074, 16215819}}
}, {
{{-6898905, 9824394, -12304779, -4401089, -31397141, -6276835, 32574489, 12532905, -7503072, -8675347},
{-27343522, -16515468, -27151524, -10722951, 946346, 16291093, 254968, 7168080, 21676107, -1943028},
{21260961, -8424752, -16831886, -11920822, -23677961, 3968121, -3651949, -6215466, -3556191, -7913075}},
{{16544754, 13250366, -16804428, 15546242, -4583003, 12757258, -2462308, -8680336, -18907032, -9662799},
{-2415239, -15577728, 18312303, 4964443, -15272530, -12653564, 26820651, 16690659, 25459437, -4564609},
{-25144690, 11425020, 28423002, -11020557, -6144921, -15826224, 9142795, -2391602, -6432418, -1644817}},
{{-23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989},
{-30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523},
{4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278}},
{{31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045},
{19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377},
{24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480}},
{{17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016},
{510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426},
{18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525}},
{{13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396},
{9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080},
{12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892}},
{{15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275},
{11038231, -11582396, -27310482, -7316562, -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)) */

3008
src/crypto/shen_ed25519_ref/crypto-ops-old.c Normal file
View File

File diff suppressed because it is too large Load Diff

148
src/crypto/shen_ed25519_ref/crypto-ops.h Normal file
View File

@ -0,0 +1,148 @@
// Copyright (c) 2014-2015, 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 <stdint.h>
#pragma once
/* From fe.h */
//this guy may throw errors in windows
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 *);
/* 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_double_scalarmult_precomp_vartime(ge_p2 *, const unsigned char *, const ge_p3 *, 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;
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 *);
int sc_check(const unsigned char *);
int sc_isnonzero(const unsigned char *); /* Doesn't normalize */

6
src/crypto/shen_ed25519_ref/crypto_int32.h Executable file
View File

@ -0,0 +1,6 @@
#ifndef crypto_int32_h
#define crypto_int32_h
typedef int crypto_int32;
#endif

13
src/crypto/shen_ed25519_ref/crypto_sign.h Executable file
View File

@ -0,0 +1,13 @@
#ifndef crypto_sign_edwards25519sha512batch_H
#define crypto_sign_edwards25519sha512batch_H
#define SECRETKEYBYTES 64
#define PUBLICKEYBYTES 32
#define SIGNATUREBYTES 64
extern int crypto_sign(unsigned char *,unsigned long long *,const unsigned char *,unsigned long long,const unsigned char *);
extern int crypto_sign_open(unsigned char *,unsigned long long *,const unsigned char *,unsigned long long,const unsigned char *);
extern int crypto_sign_keypair(unsigned char *,unsigned char *);
extern int crypto_sign_publickey(unsigned char *pk, unsigned char *sk, unsigned char *seed);
#endif

6
src/crypto/shen_ed25519_ref/crypto_uint32.h Executable file
View File

@ -0,0 +1,6 @@
#ifndef crypto_uint32_h
#define crypto_uint32_h
typedef unsigned int crypto_uint32;
#endif

7
src/crypto/shen_ed25519_ref/crypto_verify_32.h Executable file
View File

@ -0,0 +1,7 @@
#ifndef crypto_verify_32_H
#define crypto_verify_32_H
#define crypto_verify_32_ref_BYTES 32
extern int crypto_verify_32(const unsigned char *,const unsigned char *);
#endif

1402
src/crypto/shen_ed25519_ref/ietf.txt Normal file
View File

File diff suppressed because it is too large Load Diff

62
src/crypto/shen_ed25519_ref/include/Makefile.am Normal file
View File

@ -0,0 +1,62 @@
SODIUM_EXPORT = \
sodium.h \
sodium/core.h \
sodium/crypto_aead_chacha20poly1305.h \
sodium/crypto_auth.h \
sodium/crypto_auth_hmacsha256.h \
sodium/crypto_auth_hmacsha512.h \
sodium/crypto_auth_hmacsha512256.h \
sodium/crypto_box.h \
sodium/crypto_box_curve25519xsalsa20poly1305.h \
sodium/crypto_core_hsalsa20.h \
sodium/crypto_core_salsa20.h \
sodium/crypto_core_salsa2012.h \
sodium/crypto_core_salsa208.h \
sodium/crypto_generichash.h \
sodium/crypto_generichash_blake2b.h \
sodium/crypto_hash.h \
sodium/crypto_hash_sha256.h \
sodium/crypto_hash_sha512.h \
sodium/crypto_onetimeauth.h \
sodium/crypto_onetimeauth_poly1305.h \
sodium/crypto_pwhash_scryptsalsa208sha256.h \
sodium/crypto_scalarmult.h \
sodium/crypto_scalarmult_curve25519.h \
sodium/crypto_secretbox.h \
sodium/crypto_secretbox_xsalsa20poly1305.h \
sodium/crypto_shorthash.h \
sodium/crypto_shorthash_siphash24.h \
sodium/crypto_sign.h \
sodium/crypto_sign_ed25519.h \
sodium/crypto_sign_edwards25519sha512batch.h \
sodium/crypto_stream.h \
sodium/crypto_stream_aes128ctr.h \
sodium/crypto_stream_chacha20.h \
sodium/crypto_stream_salsa20.h \
sodium/crypto_stream_salsa2012.h \
sodium/crypto_stream_salsa208.h \
sodium/crypto_stream_xsalsa20.h \
sodium/crypto_int32.h \
sodium/crypto_int64.h \
sodium/crypto_uint16.h \
sodium/crypto_uint32.h \
sodium/crypto_uint64.h \
sodium/crypto_uint8.h \
sodium/crypto_verify_16.h \
sodium/crypto_verify_32.h \
sodium/crypto_verify_64.h \
sodium/export.h \
sodium/randombytes.h \
sodium/randombytes_salsa20_random.h \
sodium/randombytes_sysrandom.h \
sodium/runtime.h \
sodium/utils.h
EXTRA_SRC = $(SODIUM_EXPORT) \
sodium/version.h.in
nobase_include_HEADERS = $(SODIUM_EXPORT)
nobase_nodist_include_HEADERS = \
sodium/version.h

16
src/crypto/shen_ed25519_ref/include/libsodium_LICENSE Normal file
View File

@ -0,0 +1,16 @@
/*
* Copyright (c) 2013-2015
* Frank Denis <j at pureftpd dot org>
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/

50
src/crypto/shen_ed25519_ref/include/sodium.h Normal file
View File

@ -0,0 +1,50 @@
#ifndef sodium_H
#define sodium_H
#include "sodium/core.h"
#include "sodium/crypto_aead_chacha20poly1305.h"
#include "sodium/crypto_auth.h"
#include "sodium/crypto_auth_hmacsha256.h"
#include "sodium/crypto_auth_hmacsha512.h"
#include "sodium/crypto_auth_hmacsha512256.h"
#include "sodium/crypto_box.h"
#include "sodium/crypto_box_curve25519xsalsa20poly1305.h"
#include "sodium/crypto_core_hsalsa20.h"
#include "sodium/crypto_core_salsa20.h"
#include "sodium/crypto_core_salsa2012.h"
#include "sodium/crypto_core_salsa208.h"
#include "sodium/crypto_generichash.h"
#include "sodium/crypto_generichash_blake2b.h"
#include "sodium/crypto_hash.h"
#include "sodium/crypto_hash_sha256.h"
#include "sodium/crypto_hash_sha512.h"
#include "sodium/crypto_onetimeauth.h"
#include "sodium/crypto_onetimeauth_poly1305.h"
#include "sodium/crypto_pwhash_scryptsalsa208sha256.h"
#include "sodium/crypto_scalarmult.h"
#include "sodium/crypto_scalarmult_curve25519.h"
#include "sodium/crypto_secretbox.h"
#include "sodium/crypto_secretbox_xsalsa20poly1305.h"
#include "sodium/crypto_shorthash.h"
#include "sodium/crypto_shorthash_siphash24.h"
#include "sodium/crypto_sign.h"
#include "sodium/crypto_sign_ed25519.h"
#include "sodium/crypto_stream.h"
#include "sodium/crypto_stream_aes128ctr.h"
#include "sodium/crypto_stream_chacha20.h"
#include "sodium/crypto_stream_salsa20.h"
#include "sodium/crypto_stream_salsa2012.h"
#include "sodium/crypto_stream_salsa208.h"
#include "sodium/crypto_stream_xsalsa20.h"
#include "sodium/crypto_verify_16.h"
#include "sodium/crypto_verify_32.h"
#include "sodium/crypto_verify_64.h"
#include "sodium/randombytes.h"
#include "sodium/randombytes_salsa20_random.h"
#include "sodium/randombytes_sysrandom.h"
#include "sodium/runtime.h"
#include "sodium/utils.h"
#include "sodium/version.h"
#endif

8
src/crypto/shen_ed25519_ref/include/sodium/crypto_int32.h Normal file
View File

@ -0,0 +1,8 @@
#ifndef crypto_int32_H
#define crypto_int32_H
#include <stdint.h>
typedef int32_t crypto_int32;
#endif

8
src/crypto/shen_ed25519_ref/include/sodium/crypto_int64.h Normal file
View File

@ -0,0 +1,8 @@
#ifndef crypto_int64_H
#define crypto_int64_H
#include <stdint.h>
typedef int64_t crypto_int64;
#endif

8
src/crypto/shen_ed25519_ref/include/sodium/crypto_uint16.h Normal file
View File

@ -0,0 +1,8 @@
#ifndef crypto_uint16_H
#define crypto_uint16_H
#include <stdint.h>
typedef uint16_t crypto_uint16;
#endif

8
src/crypto/shen_ed25519_ref/include/sodium/crypto_uint32.h Normal file
View File

@ -0,0 +1,8 @@
#ifndef crypto_uint32_H
#define crypto_uint32_H
#include <stdint.h>
typedef uint32_t crypto_uint32;
#endif

8
src/crypto/shen_ed25519_ref/include/sodium/crypto_uint64.h Normal file
View File

@ -0,0 +1,8 @@
#ifndef crypto_uint64_H
#define crypto_uint64_H
#include <stdint.h>
typedef uint64_t crypto_uint64;
#endif

8
src/crypto/shen_ed25519_ref/include/sodium/crypto_uint8.h Normal file
View File

@ -0,0 +1,8 @@
#ifndef crypto_uint8_H
#define crypto_uint8_H
#include <stdint.h>
typedef uint8_t crypto_uint8;
#endif

22
src/crypto/shen_ed25519_ref/include/sodium/crypto_verify_32.h Normal file
View File

@ -0,0 +1,22 @@
#ifndef crypto_verify_32_H
#define crypto_verify_32_H
#include <stddef.h>
#include "export.h"
#ifdef __cplusplus
extern "C" {
#endif
#define crypto_verify_32_BYTES 32U
SODIUM_EXPORT
size_t crypto_verify_32_bytes(void);
SODIUM_EXPORT
int crypto_verify_32(const unsigned char *x, const unsigned char *y);
#ifdef __cplusplus
}
#endif
#endif

58
src/crypto/shen_ed25519_ref/include/sodium/randombytes.h Normal file
View File

@ -0,0 +1,58 @@
#ifndef randombytes_H
#define randombytes_H
#include <sys/types.h>
#include <stddef.h>
#include <stdint.h>
#include "export.h"
#ifdef __cplusplus
# if __GNUC__
# pragma GCC diagnostic ignored "-Wlong-long"
# endif
extern "C" {
#endif
typedef struct randombytes_implementation {
const char *(*implementation_name)(void); /* required */
uint32_t (*random)(void); /* required */
void (*stir)(void); /* optional */
uint32_t (*uniform)(const uint32_t upper_bound); /* optional, a default implementation will be used if NULL */
void (*buf)(void * const buf, const size_t size); /* required */
int (*close)(void); /* optional */
} randombytes_implementation;
SODIUM_EXPORT
void randombytes_buf(void * const buf, const size_t size);
SODIUM_EXPORT
uint32_t randombytes_random(void);
SODIUM_EXPORT
uint32_t randombytes_uniform(const uint32_t upper_bound);
SODIUM_EXPORT
void randombytes_stir(void);
SODIUM_EXPORT
int randombytes_close(void);
SODIUM_EXPORT
int randombytes_set_implementation(randombytes_implementation *impl);
SODIUM_EXPORT
const char *randombytes_implementation_name(void);
/* -- NaCl compatibility interface -- */
SODIUM_EXPORT
void randombytes(unsigned char * const buf, const unsigned long long buf_len);
#ifdef __cplusplus
}
#endif
#endif

52
src/crypto/shen_ed25519_ref/randombytes.c Executable file
View File

@ -0,0 +1,52 @@
#ifndef _WIN32
#include <sys/types.h>
#include <sys/stat.h>
#include <fcntl.h>
#include <unistd.h>
/* it's really stupid that there isn't a syscall for this */
static int ed25519_random_fd = -1;
static inline void ed25519_randombytes(unsigned char *x,unsigned long long xlen)
{
int i;
if (ed25519_random_fd == -1) {
for (;;) {
ed25519_random_fd = open("/dev/urandom",O_RDONLY);
if (ed25519_random_fd != -1) break;
sleep(1);
}
}
while (xlen > 0) {
if (xlen < 1048576) i = xlen; else i = 1048576;
i = read(ed25519_random_fd,x,i);
if (i < 1) {
sleep(1);
continue;
}
x += i;
xlen -= i;
}
}
#else
#include <windows.h>
#include <wincrypt.h>
static inline void ed25519_randombytes(unsigned char *x,unsigned long long xlen)
{
HCRYPTPROV prov = 0;
CryptAcquireContextW(&prov, NULL, NULL,
PROV_RSA_FULL, CRYPT_VERIFYCONTEXT | CRYPT_SILENT);
CryptGenRandom(prov, xlen, x);
CryptReleaseContext(prov, 0);
}
#endif /* _WIN32 */

41
src/crypto/shen_ed25519_ref/ref10/Makefile Normal file
View File

@ -0,0 +1,41 @@
all: d.h d2.h sqrtm1.h base.h base2.h \
ge_add.h ge_sub.h \
ge_madd.h ge_msub.h \
ge_p2_dbl.h \
pow225521.h pow22523.h
d.h: d.py
python d.py > d.h
d2.h: d2.py
python d2.py > d2.h
sqrtm1.h: sqrtm1.py
python sqrtm1.py > sqrtm1.h
base.h: base.py
python base.py > base.h
base2.h: base2.py
python base2.py > base2.h
ge_add.h: ge_add.q q2h.sh
./q2h.sh < ge_add.q > ge_add.h
ge_sub.h: ge_sub.q q2h.sh
./q2h.sh < ge_sub.q > ge_sub.h
ge_madd.h: ge_madd.q q2h.sh
./q2h.sh < ge_madd.q > ge_madd.h
ge_msub.h: ge_msub.q q2h.sh
./q2h.sh < ge_msub.q > ge_msub.h
ge_p2_dbl.h: ge_p2_dbl.q q2h.sh
./q2h.sh < ge_p2_dbl.q > ge_p2_dbl.h
pow22523.h: pow22523.q q2h.sh
./q2h.sh < pow22523.q > pow22523.h
pow225521.h: pow225521.q q2h.sh
./q2h.sh < pow225521.q > pow225521.h

4
src/crypto/shen_ed25519_ref/ref10/api.h Normal file
View File

@ -0,0 +1,4 @@
#define CRYPTO_SECRETKEYBYTES 64
#define CRYPTO_PUBLICKEYBYTES 32
#define CRYPTO_BYTES 64
#define CRYPTO_DETERMINISTIC 1

1344
src/crypto/shen_ed25519_ref/ref10/base.h Normal file
View File

File diff suppressed because it is too large Load Diff

65
src/crypto/shen_ed25519_ref/ref10/base.py Normal file
View File

@ -0,0 +1,65 @@
b = 256
q = 2**255 - 19
l = 2**252 + 27742317777372353535851937790883648493
def expmod(b,e,m):
if e == 0: return 1
t = expmod(b,e/2,m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x,q-2,q)
d = -121665 * inv(121666)
I = expmod(2,(q-1)/4,q)
def xrecover(y):
xx = (y*y-1) * inv(d*y*y+1)
x = expmod(xx,(q+3)/8,q)
if (x*x - xx) % q != 0: x = (x*I) % q
if x % 2 != 0: x = q-x
return x
By = 4 * inv(5)
Bx = xrecover(By)
B = [Bx % q,By % q]
def edwards(P,Q):
x1 = P[0]
y1 = P[1]
x2 = Q[0]
y2 = Q[1]
x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
return [x3 % q,y3 % q]
def radix255(x):
x = x % q
if x + x > q: x -= q
x = [x,0,0,0,0,0,0,0,0,0]
bits = [26,25,26,25,26,25,26,25,26,25]
for i in range(9):
carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
x[i] -= carry * 2**bits[i]
x[i + 1] += carry
result = ""
for i in range(9):
result = result+str(x[i])+","
result = result+str(x[9])
return result
Bi = B
for i in range(32):
print "{"
Bij = Bi
for j in range(8):
print " {"
print " {",radix255(Bij[1]+Bij[0]),"},"
print " {",radix255(Bij[1]-Bij[0]),"},"
print " {",radix255(2*d*Bij[0]*Bij[1]),"},"
Bij = edwards(Bij,Bi)
print " },"
print "},"
for k in range(8):
Bi = edwards(Bi,Bi)

40
src/crypto/shen_ed25519_ref/ref10/base2.h Normal file
View File

@ -0,0 +1,40 @@
{
{ 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 },
},

60
src/crypto/shen_ed25519_ref/ref10/base2.py Normal file
View File

@ -0,0 +1,60 @@
b = 256
q = 2**255 - 19
l = 2**252 + 27742317777372353535851937790883648493
def expmod(b,e,m):
if e == 0: return 1
t = expmod(b,e/2,m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x,q-2,q)
d = -121665 * inv(121666)
I = expmod(2,(q-1)/4,q)
def xrecover(y):
xx = (y*y-1) * inv(d*y*y+1)
x = expmod(xx,(q+3)/8,q)
if (x*x - xx) % q != 0: x = (x*I) % q
if x % 2 != 0: x = q-x
return x
By = 4 * inv(5)
Bx = xrecover(By)
B = [Bx % q,By % q]
def edwards(P,Q):
x1 = P[0]
y1 = P[1]
x2 = Q[0]
y2 = Q[1]
x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
return [x3 % q,y3 % q]
def radix255(x):
x = x % q
if x + x > q: x -= q
x = [x,0,0,0,0,0,0,0,0,0]
bits = [26,25,26,25,26,25,26,25,26,25]
for i in range(9):
carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
x[i] -= carry * 2**bits[i]
x[i + 1] += carry
result = ""
for i in range(9):
result = result+str(x[i])+","
result = result+str(x[9])
return result
Bi = B
for i in range(8):
print " {"
print " {",radix255(Bi[1]+Bi[0]),"},"
print " {",radix255(Bi[1]-Bi[0]),"},"
print " {",radix255(2*d*Bi[0]*Bi[1]),"},"
print " },"
Bi = edwards(B,edwards(B,Bi))

1
src/crypto/shen_ed25519_ref/ref10/d.h Normal file
View File

@ -0,0 +1 @@
-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116

28
src/crypto/shen_ed25519_ref/ref10/d.py Normal file
View File

@ -0,0 +1,28 @@
q = 2**255 - 19
def expmod(b,e,m):
if e == 0: return 1
t = expmod(b,e/2,m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x,q-2,q)
def radix255(x):
x = x % q
if x + x > q: x -= q
x = [x,0,0,0,0,0,0,0,0,0]
bits = [26,25,26,25,26,25,26,25,26,25]
for i in range(9):
carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
x[i] -= carry * 2**bits[i]
x[i + 1] += carry
result = ""
for i in range(9):
result = result+str(x[i])+","
result = result+str(x[9])
return result
d = -121665 * inv(121666)
print radix255(d)

1
src/crypto/shen_ed25519_ref/ref10/d2.h Normal file
View File

@ -0,0 +1 @@
-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199

28
src/crypto/shen_ed25519_ref/ref10/d2.py Normal file
View File

@ -0,0 +1,28 @@
q = 2**255 - 19
def expmod(b,e,m):
if e == 0: return 1
t = expmod(b,e/2,m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x,q-2,q)
def radix255(x):
x = x % q
if x + x > q: x -= q
x = [x,0,0,0,0,0,0,0,0,0]
bits = [26,25,26,25,26,25,26,25,26,25]
for i in range(9):
carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
x[i] -= carry * 2**bits[i]
x[i + 1] += carry
result = ""
for i in range(9):
result = result+str(x[i])+","
result = result+str(x[9])
return result
d = -121665 * inv(121666)
print radix255(d*2)

2
src/crypto/shen_ed25519_ref/ref10/description Normal file
View File

@ -0,0 +1,2 @@
EdDSA signatures using Curve25519
from http://hyperelliptic.org/ebats/supercop-20141124.tar.bz2

5
src/crypto/shen_ed25519_ref/ref10/designers Normal file
View File

@ -0,0 +1,5 @@
Daniel J. Bernstein
Niels Duif
Tanja Lange
Peter Schwabe
Bo-Yin Yang

56
src/crypto/shen_ed25519_ref/ref10/fe.h Normal file
View File

@ -0,0 +1,56 @@
#ifndef FE_H
#define FE_H
#include "crypto_int32.h"
typedef crypto_int32 fe[10];
/*
fe means field element.
Here the field is \Z/(2^255-19).
An element t, entries t[0]...t[9], represents the integer
t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
Bounds on each t[i] vary depending on context.
*/
#define fe_frombytes crypto_sign_ed25519_ref10_fe_frombytes
#define fe_tobytes crypto_sign_ed25519_ref10_fe_tobytes
#define fe_copy crypto_sign_ed25519_ref10_fe_copy
#define fe_isnonzero crypto_sign_ed25519_ref10_fe_isnonzero
#define fe_isnegative crypto_sign_ed25519_ref10_fe_isnegative
#define fe_0 crypto_sign_ed25519_ref10_fe_0
#define fe_1 crypto_sign_ed25519_ref10_fe_1
#define fe_cswap crypto_sign_ed25519_ref10_fe_cswap
#define fe_cmov crypto_sign_ed25519_ref10_fe_cmov
#define fe_add crypto_sign_ed25519_ref10_fe_add
#define fe_sub crypto_sign_ed25519_ref10_fe_sub
#define fe_neg crypto_sign_ed25519_ref10_fe_neg
#define fe_mul crypto_sign_ed25519_ref10_fe_mul
#define fe_sq crypto_sign_ed25519_ref10_fe_sq
#define fe_sq2 crypto_sign_ed25519_ref10_fe_sq2
#define fe_mul121666 crypto_sign_ed25519_ref10_fe_mul121666
#define fe_invert crypto_sign_ed25519_ref10_fe_invert
#define fe_pow22523 crypto_sign_ed25519_ref10_fe_pow22523
extern void fe_frombytes(fe,const unsigned char *);
extern void fe_tobytes(unsigned char *,const fe);
extern void fe_copy(fe,const fe);
extern int fe_isnonzero(const fe);
extern int fe_isnegative(const fe);
extern void fe_0(fe);
extern void fe_1(fe);
extern void fe_cswap(fe,fe,unsigned int);
extern void fe_cmov(fe,const fe,unsigned int);
extern void fe_add(fe,const fe,const fe);
extern void fe_sub(fe,const fe,const fe);
extern void fe_neg(fe,const fe);
extern void fe_mul(fe,const fe,const fe);
extern void fe_sq(fe,const fe);
extern void fe_sq2(fe,const fe);
extern void fe_mul121666(fe,const fe);
extern void fe_invert(fe,const fe);
extern void fe_pow22523(fe,const fe);
#endif

19
src/crypto/shen_ed25519_ref/ref10/fe_0.c Normal file
View File

@ -0,0 +1,19 @@
#include "fe.h"
/*
h = 0
*/
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;
}

19
src/crypto/shen_ed25519_ref/ref10/fe_1.c Normal file
View File

@ -0,0 +1,19 @@
#include "fe.h"
/*
h = 1
*/
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;
}

57
src/crypto/shen_ed25519_ref/ref10/fe_add.c Normal file
View File

@ -0,0 +1,57 @@
#include "fe.h"
/*
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)
{
crypto_int32 f0 = f[0];
crypto_int32 f1 = f[1];
crypto_int32 f2 = f[2];
crypto_int32 f3 = f[3];
crypto_int32 f4 = f[4];
crypto_int32 f5 = f[5];
crypto_int32 f6 = f[6];
crypto_int32 f7 = f[7];
crypto_int32 f8 = f[8];
crypto_int32 f9 = f[9];
crypto_int32 g0 = g[0];
crypto_int32 g1 = g[1];
crypto_int32 g2 = g[2];
crypto_int32 g3 = g[3];
crypto_int32 g4 = g[4];
crypto_int32 g5 = g[5];
crypto_int32 g6 = g[6];
crypto_int32 g7 = g[7];
crypto_int32 g8 = g[8];
crypto_int32 g9 = g[9];
crypto_int32 h0 = f0 + g0;
crypto_int32 h1 = f1 + g1;
crypto_int32 h2 = f2 + g2;
crypto_int32 h3 = f3 + g3;
crypto_int32 h4 = f4 + g4;
crypto_int32 h5 = f5 + g5;
crypto_int32 h6 = f6 + g6;
crypto_int32 h7 = f7 + g7;
crypto_int32 h8 = f8 + g8;
crypto_int32 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;
}

63
src/crypto/shen_ed25519_ref/ref10/fe_cmov.c Normal file
View File

@ -0,0 +1,63 @@
#include "fe.h"
/*
Replace (f,g) with (g,g) if b == 1;
replace (f,g) with (f,g) if b == 0.
Preconditions: b in {0,1}.
*/
void fe_cmov(fe f,const fe g,unsigned int b)
{
crypto_int32 f0 = f[0];
crypto_int32 f1 = f[1];
crypto_int32 f2 = f[2];
crypto_int32 f3 = f[3];
crypto_int32 f4 = f[4];
crypto_int32 f5 = f[5];
crypto_int32 f6 = f[6];
crypto_int32 f7 = f[7];
crypto_int32 f8 = f[8];
crypto_int32 f9 = f[9];
crypto_int32 g0 = g[0];
crypto_int32 g1 = g[1];
crypto_int32 g2 = g[2];
crypto_int32 g3 = g[3];
crypto_int32 g4 = g[4];
crypto_int32 g5 = g[5];
crypto_int32 g6 = g[6];
crypto_int32 g7 = g[7];
crypto_int32 g8 = g[8];
crypto_int32 g9 = g[9];
crypto_int32 x0 = f0 ^ g0;
crypto_int32 x1 = f1 ^ g1;
crypto_int32 x2 = f2 ^ g2;
crypto_int32 x3 = f3 ^ g3;
crypto_int32 x4 = f4 ^ g4;
crypto_int32 x5 = f5 ^ g5;
crypto_int32 x6 = f6 ^ g6;
crypto_int32 x7 = f7 ^ g7;
crypto_int32 x8 = f8 ^ g8;
crypto_int32 x9 = f9 ^ g9;
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;
}

29
src/crypto/shen_ed25519_ref/ref10/fe_copy.c Normal file
View File

@ -0,0 +1,29 @@
#include "fe.h"
/*
h = f
*/
void fe_copy(fe h,const fe f)
{
crypto_int32 f0 = f[0];
crypto_int32 f1 = f[1];
crypto_int32 f2 = f[2];
crypto_int32 f3 = f[3];
crypto_int32 f4 = f[4];
crypto_int32 f5 = f[5];
crypto_int32 f6 = f[6];
crypto_int32 f7 = f[7];
crypto_int32 f8 = f[8];
crypto_int32 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;
}

73
src/crypto/shen_ed25519_ref/ref10/fe_frombytes.c Normal file
View File

@ -0,0 +1,73 @@
#include "fe.h"
#include "crypto_int64.h"
#include "crypto_uint64.h"
static crypto_uint64 load_3(const unsigned char *in)
{
crypto_uint64 result;
result = (crypto_uint64) in[0];
result |= ((crypto_uint64) in[1]) << 8;
result |= ((crypto_uint64) in[2]) << 16;
return result;
}
static crypto_uint64 load_4(const unsigned char *in)
{
crypto_uint64 result;
result = (crypto_uint64) in[0];
result |= ((crypto_uint64) in[1]) << 8;
result |= ((crypto_uint64) in[2]) << 16;
result |= ((crypto_uint64) in[3]) << 24;
return result;
}
/*
Ignores top bit of h.
*/
void fe_frombytes(fe h,const unsigned char *s)
{
crypto_int64 h0 = load_4(s);
crypto_int64 h1 = load_3(s + 4) << 6;
crypto_int64 h2 = load_3(s + 7) << 5;
crypto_int64 h3 = load_3(s + 10) << 3;
crypto_int64 h4 = load_3(s + 13) << 2;
crypto_int64 h5 = load_4(s + 16);
crypto_int64 h6 = load_3(s + 20) << 7;
crypto_int64 h7 = load_3(s + 23) << 5;
crypto_int64 h8 = load_3(s + 26) << 4;
crypto_int64 h9 = (load_3(s + 29) & 8388607) << 2;
crypto_int64 carry0;
crypto_int64 carry1;
crypto_int64 carry2;
crypto_int64 carry3;
crypto_int64 carry4;
crypto_int64 carry5;
crypto_int64 carry6;
crypto_int64 carry7;
crypto_int64 carry8;
crypto_int64 carry9;
carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 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;
}

14
src/crypto/shen_ed25519_ref/ref10/fe_invert.c Normal file
View File

@ -0,0 +1,14 @@
#include "fe.h"
void fe_invert(fe out,const fe z)
{
fe t0;
fe t1;
fe t2;
fe t3;
int i;
#include "pow225521.h"
return;
}

16
src/crypto/shen_ed25519_ref/ref10/fe_isnegative.c Normal file
View File

@ -0,0 +1,16 @@
#include "fe.h"
/*
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.
*/
int fe_isnegative(const fe f)
{
unsigned char s[32];
fe_tobytes(s,f);
return s[0] & 1;
}

19
src/crypto/shen_ed25519_ref/ref10/fe_isnonzero.c Normal file
View File

@ -0,0 +1,19 @@
#include "fe.h"
#include "crypto_verify_32.h"
/*
return 1 if f == 0
return 0 if f != 0
Preconditions:
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/
static const unsigned char zero[32];
int fe_isnonzero(const fe f)
{
unsigned char s[32];
fe_tobytes(s,f);
return crypto_verify_32(s,zero);
}

253
src/crypto/shen_ed25519_ref/ref10/fe_mul.c Normal file
View File

@ -0,0 +1,253 @@
#include "fe.h"
#include "crypto_int64.h"
/*
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.
*/
void fe_mul(fe h,const fe f,const fe g)
{
crypto_int32 f0 = f[0];
crypto_int32 f1 = f[1];
crypto_int32 f2 = f[2];
crypto_int32 f3 = f[3];
crypto_int32 f4 = f[4];
crypto_int32 f5 = f[5];
crypto_int32 f6 = f[6];
crypto_int32 f7 = f[7];
crypto_int32 f8 = f[8];
crypto_int32 f9 = f[9];
crypto_int32 g0 = g[0];
crypto_int32 g1 = g[1];
crypto_int32 g2 = g[2];
crypto_int32 g3 = g[3];
crypto_int32 g4 = g[4];
crypto_int32 g5 = g[5];
crypto_int32 g6 = g[6];
crypto_int32 g7 = g[7];
crypto_int32 g8 = g[8];
crypto_int32 g9 = g[9];
crypto_int32 g1_19 = 19 * g1; /* 1.959375*2^29 */
crypto_int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
crypto_int32 g3_19 = 19 * g3;
crypto_int32 g4_19 = 19 * g4;
crypto_int32 g5_19 = 19 * g5;
crypto_int32 g6_19 = 19 * g6;
crypto_int32 g7_19 = 19 * g7;
crypto_int32 g8_19 = 19 * g8;
crypto_int32 g9_19 = 19 * g9;
crypto_int32 f1_2 = 2 * f1;
crypto_int32 f3_2 = 2 * f3;
crypto_int32 f5_2 = 2 * f5;
crypto_int32 f7_2 = 2 * f7;
crypto_int32 f9_2 = 2 * f9;
crypto_int64 f0g0 = f0 * (crypto_int64) g0;
crypto_int64 f0g1 = f0 * (crypto_int64) g1;
crypto_int64 f0g2 = f0 * (crypto_int64) g2;
crypto_int64 f0g3 = f0 * (crypto_int64) g3;
crypto_int64 f0g4 = f0 * (crypto_int64) g4;
crypto_int64 f0g5 = f0 * (crypto_int64) g5;
crypto_int64 f0g6 = f0 * (crypto_int64) g6;
crypto_int64 f0g7 = f0 * (crypto_int64) g7;
crypto_int64 f0g8 = f0 * (crypto_int64) g8;
crypto_int64 f0g9 = f0 * (crypto_int64) g9;
crypto_int64 f1g0 = f1 * (crypto_int64) g0;
crypto_int64 f1g1_2 = f1_2 * (crypto_int64) g1;
crypto_int64 f1g2 = f1 * (crypto_int64) g2;
crypto_int64 f1g3_2 = f1_2 * (crypto_int64) g3;
crypto_int64 f1g4 = f1 * (crypto_int64) g4;
crypto_int64 f1g5_2 = f1_2 * (crypto_int64) g5;
crypto_int64 f1g6 = f1 * (crypto_int64) g6;
crypto_int64 f1g7_2 = f1_2 * (crypto_int64) g7;
crypto_int64 f1g8 = f1 * (crypto_int64) g8;
crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19;
crypto_int64 f2g0 = f2 * (crypto_int64) g0;
crypto_int64 f2g1 = f2 * (crypto_int64) g1;
crypto_int64 f2g2 = f2 * (crypto_int64) g2;
crypto_int64 f2g3 = f2 * (crypto_int64) g3;
crypto_int64 f2g4 = f2 * (crypto_int64) g4;
crypto_int64 f2g5 = f2 * (crypto_int64) g5;
crypto_int64 f2g6 = f2 * (crypto_int64) g6;
crypto_int64 f2g7 = f2 * (crypto_int64) g7;
crypto_int64 f2g8_19 = f2 * (crypto_int64) g8_19;
crypto_int64 f2g9_19 = f2 * (crypto_int64) g9_19;
crypto_int64 f3g0 = f3 * (crypto_int64) g0;
crypto_int64 f3g1_2 = f3_2 * (crypto_int64) g1;
crypto_int64 f3g2 = f3 * (crypto_int64) g2;
crypto_int64 f3g3_2 = f3_2 * (crypto_int64) g3;
crypto_int64 f3g4 = f3 * (crypto_int64) g4;
crypto_int64 f3g5_2 = f3_2 * (crypto_int64) g5;
crypto_int64 f3g6 = f3 * (crypto_int64) g6;
crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19;
crypto_int64 f3g8_19 = f3 * (crypto_int64) g8_19;
crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19;
crypto_int64 f4g0 = f4 * (crypto_int64) g0;
crypto_int64 f4g1 = f4 * (crypto_int64) g1;
crypto_int64 f4g2 = f4 * (crypto_int64) g2;
crypto_int64 f4g3 = f4 * (crypto_int64) g3;
crypto_int64 f4g4 = f4 * (crypto_int64) g4;
crypto_int64 f4g5 = f4 * (crypto_int64) g5;
crypto_int64 f4g6_19 = f4 * (crypto_int64) g6_19;
crypto_int64 f4g7_19 = f4 * (crypto_int64) g7_19;
crypto_int64 f4g8_19 = f4 * (crypto_int64) g8_19;
crypto_int64 f4g9_19 = f4 * (crypto_int64) g9_19;
crypto_int64 f5g0 = f5 * (crypto_int64) g0;
crypto_int64 f5g1_2 = f5_2 * (crypto_int64) g1;
crypto_int64 f5g2 = f5 * (crypto_int64) g2;
crypto_int64 f5g3_2 = f5_2 * (crypto_int64) g3;
crypto_int64 f5g4 = f5 * (crypto_int64) g4;
crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19;
crypto_int64 f5g6_19 = f5 * (crypto_int64) g6_19;
crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19;
crypto_int64 f5g8_19 = f5 * (crypto_int64) g8_19;
crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19;
crypto_int64 f6g0 = f6 * (crypto_int64) g0;
crypto_int64 f6g1 = f6 * (crypto_int64) g1;
crypto_int64 f6g2 = f6 * (crypto_int64) g2;
crypto_int64 f6g3 = f6 * (crypto_int64) g3;
crypto_int64 f6g4_19 = f6 * (crypto_int64) g4_19;
crypto_int64 f6g5_19 = f6 * (crypto_int64) g5_19;
crypto_int64 f6g6_19 = f6 * (crypto_int64) g6_19;
crypto_int64 f6g7_19 = f6 * (crypto_int64) g7_19;
crypto_int64 f6g8_19 = f6 * (crypto_int64) g8_19;
crypto_int64 f6g9_19 = f6 * (crypto_int64) g9_19;
crypto_int64 f7g0 = f7 * (crypto_int64) g0;
crypto_int64 f7g1_2 = f7_2 * (crypto_int64) g1;
crypto_int64 f7g2 = f7 * (crypto_int64) g2;
crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19;
crypto_int64 f7g4_19 = f7 * (crypto_int64) g4_19;
crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19;
crypto_int64 f7g6_19 = f7 * (crypto_int64) g6_19;
crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19;
crypto_int64 f7g8_19 = f7 * (crypto_int64) g8_19;
crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19;
crypto_int64 f8g0 = f8 * (crypto_int64) g0;
crypto_int64 f8g1 = f8 * (crypto_int64) g1;
crypto_int64 f8g2_19 = f8 * (crypto_int64) g2_19;
crypto_int64 f8g3_19 = f8 * (crypto_int64) g3_19;
crypto_int64 f8g4_19 = f8 * (crypto_int64) g4_19;
crypto_int64 f8g5_19 = f8 * (crypto_int64) g5_19;
crypto_int64 f8g6_19 = f8 * (crypto_int64) g6_19;
crypto_int64 f8g7_19 = f8 * (crypto_int64) g7_19;
crypto_int64 f8g8_19 = f8 * (crypto_int64) g8_19;
crypto_int64 f8g9_19 = f8 * (crypto_int64) g9_19;
crypto_int64 f9g0 = f9 * (crypto_int64) g0;
crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19;
crypto_int64 f9g2_19 = f9 * (crypto_int64) g2_19;
crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19;
crypto_int64 f9g4_19 = f9 * (crypto_int64) g4_19;
crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19;
crypto_int64 f9g6_19 = f9 * (crypto_int64) g6_19;
crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19;
crypto_int64 f9g8_19 = f9 * (crypto_int64) g8_19;
crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19;
crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
crypto_int64 h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
crypto_int64 h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
crypto_int64 h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
crypto_int64 h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
crypto_int64 h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
crypto_int64 h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
crypto_int64 h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
crypto_int64 h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
crypto_int64 h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
crypto_int64 carry0;
crypto_int64 carry1;
crypto_int64 carry2;
crypto_int64 carry3;
crypto_int64 carry4;
crypto_int64 carry5;
crypto_int64 carry6;
crypto_int64 carry7;
crypto_int64 carry8;
crypto_int64 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 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (crypto_int64) (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 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (crypto_int64) (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 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (crypto_int64) (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 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (crypto_int64) (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 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (crypto_int64) (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 + (crypto_int64) (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 + (crypto_int64) (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;
}

45
src/crypto/shen_ed25519_ref/ref10/fe_neg.c Normal file
View File

@ -0,0 +1,45 @@
#include "fe.h"
/*
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.
*/
void fe_neg(fe h,const fe f)
{
crypto_int32 f0 = f[0];
crypto_int32 f1 = f[1];
crypto_int32 f2 = f[2];
crypto_int32 f3 = f[3];
crypto_int32 f4 = f[4];
crypto_int32 f5 = f[5];
crypto_int32 f6 = f[6];
crypto_int32 f7 = f[7];
crypto_int32 f8 = f[8];
crypto_int32 f9 = f[9];
crypto_int32 h0 = -f0;
crypto_int32 h1 = -f1;
crypto_int32 h2 = -f2;
crypto_int32 h3 = -f3;
crypto_int32 h4 = -f4;
crypto_int32 h5 = -f5;
crypto_int32 h6 = -f6;
crypto_int32 h7 = -f7;
crypto_int32 h8 = -f8;
crypto_int32 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;
}

13
src/crypto/shen_ed25519_ref/ref10/fe_pow22523.c Normal file
View File

@ -0,0 +1,13 @@
#include "fe.h"
void fe_pow22523(fe out,const fe z)
{
fe t0;
fe t1;
fe t2;
int i;
#include "pow22523.h"
return;
}

149
src/crypto/shen_ed25519_ref/ref10/fe_sq.c Normal file
View File

@ -0,0 +1,149 @@
#include "fe.h"
#include "crypto_int64.h"
/*
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.
*/
void fe_sq(fe h,const fe f)
{
crypto_int32 f0 = f[0];
crypto_int32 f1 = f[1];
crypto_int32 f2 = f[2];
crypto_int32 f3 = f[3];
crypto_int32 f4 = f[4];
crypto_int32 f5 = f[5];
crypto_int32 f6 = f[6];
crypto_int32 f7 = f[7];
crypto_int32 f8 = f[8];
crypto_int32 f9 = f[9];
crypto_int32 f0_2 = 2 * f0;
crypto_int32 f1_2 = 2 * f1;
crypto_int32 f2_2 = 2 * f2;
crypto_int32 f3_2 = 2 * f3;
crypto_int32 f4_2 = 2 * f4;
crypto_int32 f5_2 = 2 * f5;
crypto_int32 f6_2 = 2 * f6;
crypto_int32 f7_2 = 2 * f7;
crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
crypto_int64 f0f0 = f0 * (crypto_int64) f0;
crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1;
crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2;
crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3;
crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4;
crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5;
crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6;
crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7;
crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8;
crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9;
crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1;
crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2;
crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2;
crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4;
crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2;
crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6;
crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2;
crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8;
crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
crypto_int64 f2f2 = f2 * (crypto_int64) f2;
crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3;
crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4;
crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5;
crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6;
crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7;
crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38;
crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3;
crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4;
crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2;
crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6;
crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
crypto_int64 f4f4 = f4 * (crypto_int64) f4;
crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5;
crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38;
crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38;
crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38;
crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19;
crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38;
crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38;
crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38;
crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19;
crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38;
crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38;
crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
crypto_int64 carry0;
crypto_int64 carry1;
crypto_int64 carry2;
crypto_int64 carry3;
crypto_int64 carry4;
crypto_int64 carry5;
crypto_int64 carry6;
crypto_int64 carry7;
crypto_int64 carry8;
crypto_int64 carry9;
carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
carry0 = (h0 + (crypto_int64) (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;
}

160
src/crypto/shen_ed25519_ref/ref10/fe_sq2.c Normal file
View File

@ -0,0 +1,160 @@
#include "fe.h"
#include "crypto_int64.h"
/*
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.
*/
void fe_sq2(fe h,const fe f)
{
crypto_int32 f0 = f[0];
crypto_int32 f1 = f[1];
crypto_int32 f2 = f[2];
crypto_int32 f3 = f[3];
crypto_int32 f4 = f[4];
crypto_int32 f5 = f[5];
crypto_int32 f6 = f[6];
crypto_int32 f7 = f[7];
crypto_int32 f8 = f[8];
crypto_int32 f9 = f[9];
crypto_int32 f0_2 = 2 * f0;
crypto_int32 f1_2 = 2 * f1;
crypto_int32 f2_2 = 2 * f2;
crypto_int32 f3_2 = 2 * f3;
crypto_int32 f4_2 = 2 * f4;
crypto_int32 f5_2 = 2 * f5;
crypto_int32 f6_2 = 2 * f6;
crypto_int32 f7_2 = 2 * f7;
crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
crypto_int64 f0f0 = f0 * (crypto_int64) f0;
crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1;
crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2;
crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3;
crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4;
crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5;
crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6;
crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7;
crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8;
crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9;
crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1;
crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2;
crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2;
crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4;
crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2;
crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6;
crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2;
crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8;
crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
crypto_int64 f2f2 = f2 * (crypto_int64) f2;
crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3;
crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4;
crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5;
crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6;
crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7;
crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38;
crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3;
crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4;
crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2;
crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6;
crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
crypto_int64 f4f4 = f4 * (crypto_int64) f4;
crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5;
crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38;
crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38;
crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38;
crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19;
crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38;
crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38;
crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38;
crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19;
crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38;
crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38;
crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
crypto_int64 carry0;
crypto_int64 carry1;
crypto_int64 carry2;
crypto_int64 carry3;
crypto_int64 carry4;
crypto_int64 carry5;
crypto_int64 carry6;
crypto_int64 carry7;
crypto_int64 carry8;
crypto_int64 carry9;
h0 += h0;
h1 += h1;
h2 += h2;
h3 += h3;
h4 += h4;
h5 += h5;
h6 += h6;
h7 += h7;
h8 += h8;
h9 += h9;
carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
carry0 = (h0 + (crypto_int64) (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;
}

57
src/crypto/shen_ed25519_ref/ref10/fe_sub.c Normal file
View File

@ -0,0 +1,57 @@
#include "fe.h"
/*
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_sub(fe h,const fe f,const fe g)
{
crypto_int32 f0 = f[0];
crypto_int32 f1 = f[1];
crypto_int32 f2 = f[2];
crypto_int32 f3 = f[3];
crypto_int32 f4 = f[4];
crypto_int32 f5 = f[5];
crypto_int32 f6 = f[6];
crypto_int32 f7 = f[7];
crypto_int32 f8 = f[8];
crypto_int32 f9 = f[9];
crypto_int32 g0 = g[0];
crypto_int32 g1 = g[1];
crypto_int32 g2 = g[2];
crypto_int32 g3 = g[3];
crypto_int32 g4 = g[4];
crypto_int32 g5 = g[5];
crypto_int32 g6 = g[6];
crypto_int32 g7 = g[7];
crypto_int32 g8 = g[8];
crypto_int32 g9 = g[9];
crypto_int32 h0 = f0 - g0;
crypto_int32 h1 = f1 - g1;
crypto_int32 h2 = f2 - g2;
crypto_int32 h3 = f3 - g3;
crypto_int32 h4 = f4 - g4;
crypto_int32 h5 = f5 - g5;
crypto_int32 h6 = f6 - g6;
crypto_int32 h7 = f7 - g7;
crypto_int32 h8 = f8 - g8;
crypto_int32 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;
}

119
src/crypto/shen_ed25519_ref/ref10/fe_tobytes.c Normal file
View File

@ -0,0 +1,119 @@
#include "fe.h"
/*
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<y<1.
Write r=h-pq.
Have 0<=r<=p-1=2^255-20.
Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
Write x=r+19(2^-255)r+y.
Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
*/
void fe_tobytes(unsigned char *s,const fe h)
{
crypto_int32 h0 = h[0];
crypto_int32 h1 = h[1];
crypto_int32 h2 = h[2];
crypto_int32 h3 = h[3];
crypto_int32 h4 = h[4];
crypto_int32 h5 = h[5];
crypto_int32 h6 = h[6];
crypto_int32 h7 = h[7];
crypto_int32 h8 = h[8];
crypto_int32 h9 = h[9];
crypto_int32 q;
crypto_int32 carry0;
crypto_int32 carry1;
crypto_int32 carry2;
crypto_int32 carry3;
crypto_int32 carry4;
crypto_int32 carry5;
crypto_int32 carry6;
crypto_int32 carry7;
crypto_int32 carry8;
crypto_int32 carry9;
q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 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;
}

95
src/crypto/shen_ed25519_ref/ref10/ge.h Normal file
View File

@ -0,0 +1,95 @@
#ifndef GE_H
#define GE_H
/*
ge means group element.
Here the group is the set of pairs (x,y) of field elements (see fe.h)
satisfying -x^2 + y^2 = 1 + d x^2y^2
where d = -121665/121666.
Representations:
ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
ge_precomp (Duif): (y+x,y-x,2dxy)
*/
#include "fe.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;
#define ge_frombytes_negate_vartime crypto_sign_ed25519_ref10_ge_frombytes_negate_vartime
#define ge_tobytes crypto_sign_ed25519_ref10_ge_tobytes
#define ge_p3_tobytes crypto_sign_ed25519_ref10_ge_p3_tobytes
#define ge_p2_0 crypto_sign_ed25519_ref10_ge_p2_0
#define ge_p3_0 crypto_sign_ed25519_ref10_ge_p3_0
#define ge_precomp_0 crypto_sign_ed25519_ref10_ge_precomp_0
#define ge_p3_to_p2 crypto_sign_ed25519_ref10_ge_p3_to_p2
#define ge_p3_to_cached crypto_sign_ed25519_ref10_ge_p3_to_cached
#define ge_p1p1_to_p2 crypto_sign_ed25519_ref10_ge_p1p1_to_p2
#define ge_p1p1_to_p3 crypto_sign_ed25519_ref10_ge_p1p1_to_p3
#define ge_p2_dbl crypto_sign_ed25519_ref10_ge_p2_dbl
#define ge_p3_dbl crypto_sign_ed25519_ref10_ge_p3_dbl
#define ge_madd crypto_sign_ed25519_ref10_ge_madd
#define ge_msub crypto_sign_ed25519_ref10_ge_msub
#define ge_add crypto_sign_ed25519_ref10_ge_add
#define ge_sub crypto_sign_ed25519_ref10_ge_sub
#define ge_scalarmult_base crypto_sign_ed25519_ref10_ge_scalarmult_base
#define ge_double_scalarmult_vartime crypto_sign_ed25519_ref10_ge_double_scalarmult_vartime
extern void ge_tobytes(unsigned char *,const ge_p2 *);
extern void ge_p3_tobytes(unsigned char *,const ge_p3 *);
extern int ge_frombytes_negate_vartime(ge_p3 *,const unsigned char *);
extern void ge_p2_0(ge_p2 *);
extern void ge_p3_0(ge_p3 *);
extern void ge_precomp_0(ge_precomp *);
extern void ge_p3_to_p2(ge_p2 *,const ge_p3 *);
extern void ge_p3_to_cached(ge_cached *,const ge_p3 *);
extern void ge_p1p1_to_p2(ge_p2 *,const ge_p1p1 *);
extern void ge_p1p1_to_p3(ge_p3 *,const ge_p1p1 *);
extern void ge_p2_dbl(ge_p1p1 *,const ge_p2 *);
extern void ge_p3_dbl(ge_p1p1 *,const ge_p3 *);
extern void ge_madd(ge_p1p1 *,const ge_p3 *,const ge_precomp *);
extern void ge_msub(ge_p1p1 *,const ge_p3 *,const ge_precomp *);
extern void ge_add(ge_p1p1 *,const ge_p3 *,const ge_cached *);
extern void ge_sub(ge_p1p1 *,const ge_p3 *,const ge_cached *);
extern void ge_scalarmult_base(ge_p3 *,const unsigned char *);
extern void ge_double_scalarmult_vartime(ge_p2 *,const unsigned char *,const ge_p3 *,const unsigned char *);
#endif

11
src/crypto/shen_ed25519_ref/ref10/ge_add.c Normal file
View File

@ -0,0 +1,11 @@
#include "ge.h"
/*
r = p + q
*/
void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
fe t0;
#include "ge_add.h"
}

97
src/crypto/shen_ed25519_ref/ref10/ge_add.h Normal file
View File

@ -0,0 +1,97 @@
/* qhasm: enter ge_add */
/* qhasm: fe X1 */
/* qhasm: fe Y1 */
/* qhasm: fe Z1 */
/* qhasm: fe Z2 */
/* qhasm: fe T1 */
/* qhasm: fe ZZ */
/* qhasm: fe YpX2 */
/* qhasm: fe YmX2 */
/* qhasm: fe T2d2 */
/* qhasm: fe X3 */
/* qhasm: fe Y3 */
/* qhasm: fe Z3 */
/* qhasm: fe T3 */
/* qhasm: fe YpX1 */
/* qhasm: fe YmX1 */
/* qhasm: fe A */
/* qhasm: fe B */
/* qhasm: fe C */
/* qhasm: fe D */
/* qhasm: YpX1 = Y1+X1 */
/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
fe_add(r->X,p->Y,p->X);
/* qhasm: YmX1 = Y1-X1 */
/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
fe_sub(r->Y,p->Y,p->X);
/* qhasm: A = YpX1*YpX2 */
/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YpX2=fe#15); */
/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YpX2=q->YplusX); */
fe_mul(r->Z,r->X,q->YplusX);
/* qhasm: B = YmX1*YmX2 */
/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YmX2=fe#16); */
/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YmX2=q->YminusX); */
fe_mul(r->Y,r->Y,q->YminusX);
/* qhasm: C = T2d2*T1 */
/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
fe_mul(r->T,q->T2d,p->T);
/* qhasm: ZZ = Z1*Z2 */
/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
fe_mul(r->X,p->Z,q->Z);
/* qhasm: D = 2*ZZ */
/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
fe_add(t0,r->X,r->X);
/* qhasm: X3 = A-B */
/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
fe_sub(r->X,r->Z,r->Y);
/* qhasm: Y3 = A+B */
/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
fe_add(r->Y,r->Z,r->Y);
/* qhasm: Z3 = D+C */
/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
fe_add(r->Z,t0,r->T);
/* qhasm: T3 = D-C */
/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
fe_sub(r->T,t0,r->T);
/* qhasm: return */

49
src/crypto/shen_ed25519_ref/ref10/ge_add.q Normal file
View File

@ -0,0 +1,49 @@
:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->YplusX:q->YminusX:q->Z:q->T2d:
fe r:var/r=fe:
enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>YpX2=fe#15:>YmX2=fe#16:>Z2=fe#17:>T2d2=fe#18:
return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
:
enter ge_add
fe X1
fe Y1
fe Z1
fe Z2
fe T1
fe ZZ
fe YpX2
fe YmX2
fe T2d2
fe X3
fe Y3
fe Z3
fe T3
fe YpX1
fe YmX1
fe A
fe B
fe C
fe D
YpX1 = Y1+X1
YmX1 = Y1-X1
A = YpX1*YpX2
B = YmX1*YmX2
C = T2d2*T1
ZZ = Z1*Z2
D = 2*ZZ
X3 = A-B
Y3 = A+B
Z3 = D+C
T3 = D-C
return

96
src/crypto/shen_ed25519_ref/ref10/ge_double_scalarmult.c Normal file
View File

@ -0,0 +1,96 @@
#include "ge.h"
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;
}
}
}
}
static ge_precomp Bi[8] = {
#include "base2.h"
} ;
/*
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_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_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
ge_p1p1 t;
ge_p3 u;
ge_p3 A2;
int i;
slide(aslide,a);
slide(bslide,b);
ge_p3_to_cached(&Ai[0],A);
ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t);
ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u);
ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u);
ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u);
ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u);
ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u);
ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u);
ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u);
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,&Bi[bslide[i]/2]);
} else if (bslide[i] < 0) {
ge_p1p1_to_p3(&u,&t);
ge_msub(&t,&u,&Bi[(-bslide[i])/2]);
}
ge_p1p1_to_p2(r,&t);
}
}

50
src/crypto/shen_ed25519_ref/ref10/ge_frombytes.c Normal file
View File

@ -0,0 +1,50 @@
#include "ge.h"
static const fe d = {
#include "d.h"
} ;
static const fe sqrtm1 = {
#include "sqrtm1.h"
} ;
int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s)
{
fe u;
fe v;
fe v3;
fe vxx;
fe check;
fe_frombytes(h->Y,s);
fe_1(h->Z);
fe_sq(u,h->Y);
fe_mul(v,u,d);
fe_sub(u,u,h->Z); /* u = y^2-1 */
fe_add(v,v,h->Z); /* v = dy^2+1 */
fe_sq(v3,v);
fe_mul(v3,v3,v); /* v3 = v^3 */
fe_sq(h->X,v3);
fe_mul(h->X,h->X,v);
fe_mul(h->X,h->X,u); /* x = uv^7 */
fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */
fe_mul(h->X,h->X,v3);
fe_mul(h->X,h->X,u); /* 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,sqrtm1);
}
if (fe_isnegative(h->X) == (s[31] >> 7))
fe_neg(h->X,h->X);
fe_mul(h->T,h->X,h->Y);
return 0;
}

11
src/crypto/shen_ed25519_ref/ref10/ge_madd.c Normal file
View File

@ -0,0 +1,11 @@
#include "ge.h"
/*
r = p + q
*/
void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
fe t0;
#include "ge_madd.h"
}

88
src/crypto/shen_ed25519_ref/ref10/ge_madd.h Normal file
View File

@ -0,0 +1,88 @@
/* qhasm: enter ge_madd */
/* qhasm: fe X1 */
/* qhasm: fe Y1 */
/* qhasm: fe Z1 */
/* qhasm: fe T1 */
/* qhasm: fe ypx2 */
/* qhasm: fe ymx2 */
/* qhasm: fe xy2d2 */
/* qhasm: fe X3 */
/* qhasm: fe Y3 */
/* qhasm: fe Z3 */
/* qhasm: fe T3 */
/* qhasm: fe YpX1 */
/* qhasm: fe YmX1 */
/* qhasm: fe A */
/* qhasm: fe B */
/* qhasm: fe C */
/* qhasm: fe D */
/* qhasm: YpX1 = Y1+X1 */
/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
fe_add(r->X,p->Y,p->X);
/* qhasm: YmX1 = Y1-X1 */
/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
fe_sub(r->Y,p->Y,p->X);
/* qhasm: A = YpX1*ypx2 */
/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ypx2=fe#15); */
/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ypx2=q->yplusx); */
fe_mul(r->Z,r->X,q->yplusx);
/* qhasm: B = YmX1*ymx2 */
/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ymx2=fe#16); */
/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ymx2=q->yminusx); */
fe_mul(r->Y,r->Y,q->yminusx);
/* qhasm: C = xy2d2*T1 */
/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
fe_mul(r->T,q->xy2d,p->T);
/* qhasm: D = 2*Z1 */
/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
fe_add(t0,p->Z,p->Z);
/* qhasm: X3 = A-B */
/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
fe_sub(r->X,r->Z,r->Y);
/* qhasm: Y3 = A+B */
/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
fe_add(r->Y,r->Z,r->Y);
/* qhasm: Z3 = D+C */
/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
fe_add(r->Z,t0,r->T);
/* qhasm: T3 = D-C */
/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
fe_sub(r->T,t0,r->T);
/* qhasm: return */

46
src/crypto/shen_ed25519_ref/ref10/ge_madd.q Normal file
View File

@ -0,0 +1,46 @@
:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->yplusx:q->yminusx:q->xy2d:
fe r:var/r=fe:
enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>ypx2=fe#15:>ymx2=fe#16:>xy2d2=fe#17:
return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
:
enter ge_madd
fe X1
fe Y1
fe Z1
fe T1
fe ypx2
fe ymx2
fe xy2d2
fe X3
fe Y3
fe Z3
fe T3
fe YpX1
fe YmX1
fe A
fe B
fe C
fe D
YpX1 = Y1+X1
YmX1 = Y1-X1
A = YpX1*ypx2
B = YmX1*ymx2
C = xy2d2*T1
D = 2*Z1
X3 = A-B
Y3 = A+B
Z3 = D+C
T3 = D-C
return

11
src/crypto/shen_ed25519_ref/ref10/ge_msub.c Normal file
View File

@ -0,0 +1,11 @@
#include "ge.h"
/*
r = p - q
*/
void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
{
fe t0;
#include "ge_msub.h"
}

88
src/crypto/shen_ed25519_ref/ref10/ge_msub.h Normal file
View File

@ -0,0 +1,88 @@
/* qhasm: enter ge_msub */
/* qhasm: fe X1 */
/* qhasm: fe Y1 */
/* qhasm: fe Z1 */
/* qhasm: fe T1 */
/* qhasm: fe ypx2 */
/* qhasm: fe ymx2 */
/* qhasm: fe xy2d2 */
/* qhasm: fe X3 */
/* qhasm: fe Y3 */
/* qhasm: fe Z3 */
/* qhasm: fe T3 */
/* qhasm: fe YpX1 */
/* qhasm: fe YmX1 */
/* qhasm: fe A */
/* qhasm: fe B */
/* qhasm: fe C */
/* qhasm: fe D */
/* qhasm: YpX1 = Y1+X1 */
/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
fe_add(r->X,p->Y,p->X);
/* qhasm: YmX1 = Y1-X1 */
/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
fe_sub(r->Y,p->Y,p->X);
/* qhasm: A = YpX1*ymx2 */
/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ymx2=fe#16); */
/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ymx2=q->yminusx); */
fe_mul(r->Z,r->X,q->yminusx);
/* qhasm: B = YmX1*ypx2 */
/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ypx2=fe#15); */
/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ypx2=q->yplusx); */
fe_mul(r->Y,r->Y,q->yplusx);
/* qhasm: C = xy2d2*T1 */
/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
fe_mul(r->T,q->xy2d,p->T);
/* qhasm: D = 2*Z1 */
/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
fe_add(t0,p->Z,p->Z);
/* qhasm: X3 = A-B */
/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
fe_sub(r->X,r->Z,r->Y);
/* qhasm: Y3 = A+B */
/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
fe_add(r->Y,r->Z,r->Y);
/* qhasm: Z3 = D-C */
/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
fe_sub(r->Z,t0,r->T);
/* qhasm: T3 = D+C */
/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
fe_add(r->T,t0,r->T);
/* qhasm: return */

46
src/crypto/shen_ed25519_ref/ref10/ge_msub.q Normal file
View File

@ -0,0 +1,46 @@
:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->yplusx:q->yminusx:q->xy2d:
fe r:var/r=fe:
enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>ypx2=fe#15:>ymx2=fe#16:>xy2d2=fe#17:
return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
:
enter ge_msub
fe X1
fe Y1
fe Z1
fe T1
fe ypx2
fe ymx2
fe xy2d2
fe X3
fe Y3
fe Z3
fe T3
fe YpX1
fe YmX1
fe A
fe B
fe C
fe D
YpX1 = Y1+X1
YmX1 = Y1-X1
A = YpX1*ymx2
B = YmX1*ypx2
C = xy2d2*T1
D = 2*Z1
X3 = A-B
Y3 = A+B
Z3 = D-C
T3 = D+C
return

12
src/crypto/shen_ed25519_ref/ref10/ge_p1p1_to_p2.c Normal file
View File

@ -0,0 +1,12 @@
#include "ge.h"
/*
r = p
*/
extern 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);
}

13
src/crypto/shen_ed25519_ref/ref10/ge_p1p1_to_p3.c Normal file
View File

@ -0,0 +1,13 @@
#include "ge.h"
/*
r = p
*/
extern 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);
}

8
src/crypto/shen_ed25519_ref/ref10/ge_p2_0.c Normal file
View File

@ -0,0 +1,8 @@
#include "ge.h"
void ge_p2_0(ge_p2 *h)
{
fe_0(h->X);
fe_1(h->Y);
fe_1(h->Z);
}

11
src/crypto/shen_ed25519_ref/ref10/ge_p2_dbl.c Normal file
View File

@ -0,0 +1,11 @@
#include "ge.h"
/*
r = 2 * p
*/
void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p)
{
fe t0;
#include "ge_p2_dbl.h"
}

73
src/crypto/shen_ed25519_ref/ref10/ge_p2_dbl.h Normal file
View File

@ -0,0 +1,73 @@
/* qhasm: enter ge_p2_dbl */
/* qhasm: fe X1 */
/* qhasm: fe Y1 */
/* qhasm: fe Z1 */
/* qhasm: fe A */
/* qhasm: fe AA */
/* qhasm: fe XX */
/* qhasm: fe YY */
/* qhasm: fe B */
/* qhasm: fe X3 */
/* qhasm: fe Y3 */
/* qhasm: fe Z3 */
/* qhasm: fe T3 */
/* qhasm: XX=X1^2 */
/* asm 1: fe_sq(>XX=fe#1,<X1=fe#11); */
/* asm 2: fe_sq(>XX=r->X,<X1=p->X); */
fe_sq(r->X,p->X);
/* qhasm: YY=Y1^2 */
/* asm 1: fe_sq(>YY=fe#3,<Y1=fe#12); */
/* asm 2: fe_sq(>YY=r->Z,<Y1=p->Y); */
fe_sq(r->Z,p->Y);
/* qhasm: B=2*Z1^2 */
/* asm 1: fe_sq2(>B=fe#4,<Z1=fe#13); */
/* asm 2: fe_sq2(>B=r->T,<Z1=p->Z); */
fe_sq2(r->T,p->Z);
/* qhasm: A=X1+Y1 */
/* asm 1: fe_add(>A=fe#2,<X1=fe#11,<Y1=fe#12); */
/* asm 2: fe_add(>A=r->Y,<X1=p->X,<Y1=p->Y); */
fe_add(r->Y,p->X,p->Y);
/* qhasm: AA=A^2 */
/* asm 1: fe_sq(>AA=fe#5,<A=fe#2); */
/* asm 2: fe_sq(>AA=t0,<A=r->Y); */
fe_sq(t0,r->Y);
/* qhasm: Y3=YY+XX */
/* asm 1: fe_add(>Y3=fe#2,<YY=fe#3,<XX=fe#1); */
/* asm 2: fe_add(>Y3=r->Y,<YY=r->Z,<XX=r->X); */
fe_add(r->Y,r->Z,r->X);
/* qhasm: Z3=YY-XX */
/* asm 1: fe_sub(>Z3=fe#3,<YY=fe#3,<XX=fe#1); */
/* asm 2: fe_sub(>Z3=r->Z,<YY=r->Z,<XX=r->X); */
fe_sub(r->Z,r->Z,r->X);
/* qhasm: X3=AA-Y3 */
/* asm 1: fe_sub(>X3=fe#1,<AA=fe#5,<Y3=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<AA=t0,<Y3=r->Y); */
fe_sub(r->X,t0,r->Y);
/* qhasm: T3=B-Z3 */
/* asm 1: fe_sub(>T3=fe#4,<B=fe#4,<Z3=fe#3); */
/* asm 2: fe_sub(>T3=r->T,<B=r->T,<Z3=r->Z); */
fe_sub(r->T,r->T,r->Z);
/* qhasm: return */

41
src/crypto/shen_ed25519_ref/ref10/ge_p2_dbl.q Normal file
View File

@ -0,0 +1,41 @@
:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:
fe r:var/r=fe:
enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:
return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
h=2*f^2:<f=fe:>h=fe:asm/fe_sq2(>h,<f);:
h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
:
enter ge_p2_dbl
fe X1
fe Y1
fe Z1
fe A
fe AA
fe XX
fe YY
fe B
fe X3
fe Y3
fe Z3
fe T3
XX=X1^2
YY=Y1^2
B=2*Z1^2
A=X1+Y1
AA=A^2
Y3=YY+XX
Z3=YY-XX
X3=AA-Y3
T3=B-Z3
return

9
src/crypto/shen_ed25519_ref/ref10/ge_p3_0.c Normal file
View File

@ -0,0 +1,9 @@
#include "ge.h"
void ge_p3_0(ge_p3 *h)
{
fe_0(h->X);
fe_1(h->Y);
fe_1(h->Z);
fe_0(h->T);
}

12
src/crypto/shen_ed25519_ref/ref10/ge_p3_dbl.c Normal file
View File

@ -0,0 +1,12 @@
#include "ge.h"
/*
r = 2 * p
*/
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);
}

17
src/crypto/shen_ed25519_ref/ref10/ge_p3_to_cached.c Normal file
View File

@ -0,0 +1,17 @@
#include "ge.h"
/*
r = p
*/
static const fe d2 = {
#include "d2.h"
} ;
extern 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,d2);
}

12
src/crypto/shen_ed25519_ref/ref10/ge_p3_to_p2.c Normal file
View File

@ -0,0 +1,12 @@
#include "ge.h"
/*
r = p
*/
extern 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);
}

14
src/crypto/shen_ed25519_ref/ref10/ge_p3_tobytes.c Normal file
View File

@ -0,0 +1,14 @@
#include "ge.h"
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;
}

8
src/crypto/shen_ed25519_ref/ref10/ge_precomp_0.c Normal file
View File

@ -0,0 +1,8 @@
#include "ge.h"
void ge_precomp_0(ge_precomp *h)
{
fe_1(h->yplusx);
fe_1(h->yminusx);
fe_0(h->xy2d);
}

105
src/crypto/shen_ed25519_ref/ref10/ge_scalarmult_base.c Normal file
View File

@ -0,0 +1,105 @@
#include "ge.h"
#include "crypto_uint32.h"
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 */
crypto_uint32 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 cmov(ge_precomp *t,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);
}
/* base[i][j] = (j+1)*256^i*B */
static ge_precomp base[32][8] = {
#include "base.h"
} ;
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);
cmov(t,&base[pos][0],equal(babs,1));
cmov(t,&base[pos][1],equal(babs,2));
cmov(t,&base[pos][2],equal(babs,3));
cmov(t,&base[pos][3],equal(babs,4));
cmov(t,&base[pos][4],equal(babs,5));
cmov(t,&base[pos][5],equal(babs,6));
cmov(t,&base[pos][6],equal(babs,7));
cmov(t,&base[pos][7],equal(babs,8));
fe_copy(minust.yplusx,t->yminusx);
fe_copy(minust.yminusx,t->yplusx);
fe_neg(minust.xy2d,t->xy2d);
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);
}
}

11
src/crypto/shen_ed25519_ref/ref10/ge_sub.c Normal file
View File

@ -0,0 +1,11 @@
#include "ge.h"
/*
r = p - q
*/
void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
{
fe t0;
#include "ge_sub.h"
}

97
src/crypto/shen_ed25519_ref/ref10/ge_sub.h Normal file
View File

@ -0,0 +1,97 @@
/* qhasm: enter ge_sub */
/* qhasm: fe X1 */
/* qhasm: fe Y1 */
/* qhasm: fe Z1 */
/* qhasm: fe Z2 */
/* qhasm: fe T1 */
/* qhasm: fe ZZ */
/* qhasm: fe YpX2 */
/* qhasm: fe YmX2 */
/* qhasm: fe T2d2 */
/* qhasm: fe X3 */
/* qhasm: fe Y3 */
/* qhasm: fe Z3 */
/* qhasm: fe T3 */
/* qhasm: fe YpX1 */
/* qhasm: fe YmX1 */
/* qhasm: fe A */
/* qhasm: fe B */
/* qhasm: fe C */
/* qhasm: fe D */
/* qhasm: YpX1 = Y1+X1 */
/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
fe_add(r->X,p->Y,p->X);
/* qhasm: YmX1 = Y1-X1 */
/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
fe_sub(r->Y,p->Y,p->X);
/* qhasm: A = YpX1*YmX2 */
/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YmX2=fe#16); */
/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YmX2=q->YminusX); */
fe_mul(r->Z,r->X,q->YminusX);
/* qhasm: B = YmX1*YpX2 */
/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YpX2=fe#15); */
/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YpX2=q->YplusX); */
fe_mul(r->Y,r->Y,q->YplusX);
/* qhasm: C = T2d2*T1 */
/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
fe_mul(r->T,q->T2d,p->T);
/* qhasm: ZZ = Z1*Z2 */
/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
fe_mul(r->X,p->Z,q->Z);
/* qhasm: D = 2*ZZ */
/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
fe_add(t0,r->X,r->X);
/* qhasm: X3 = A-B */
/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
fe_sub(r->X,r->Z,r->Y);
/* qhasm: Y3 = A+B */
/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
fe_add(r->Y,r->Z,r->Y);
/* qhasm: Z3 = D-C */
/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
fe_sub(r->Z,t0,r->T);
/* qhasm: T3 = D+C */
/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
fe_add(r->T,t0,r->T);
/* qhasm: return */

49
src/crypto/shen_ed25519_ref/ref10/ge_sub.q Normal file
View File

@ -0,0 +1,49 @@
:name:fe:r->X:r->Y:r->Z:r->T:t0:t1:t2:t3:t4:t5:p->X:p->Y:p->Z:p->T:q->YplusX:q->YminusX:q->Z:q->T2d:
fe r:var/r=fe:
enter f:enter/f:>X1=fe#11:>Y1=fe#12:>Z1=fe#13:>T1=fe#14:>YpX2=fe#15:>YmX2=fe#16:>Z2=fe#17:>T2d2=fe#18:
return:nofallthrough:<X3=fe#1:<Y3=fe#2:<Z3=fe#3:<T3=fe#4:leave:
h=f+g:<f=fe:<g=fe:>h=fe:asm/fe_add(>h,<f,<g);:
h=f-g:<f=fe:<g=fe:>h=fe:asm/fe_sub(>h,<f,<g);:
h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
h=f^2:<f=fe:>h=fe:asm/fe_sq(>h,<f);:
h=2*g:<g=fe:>h=fe:asm/fe_add(>h,<g,<g);:
:
enter ge_sub
fe X1
fe Y1
fe Z1
fe Z2
fe T1
fe ZZ
fe YpX2
fe YmX2
fe T2d2
fe X3
fe Y3
fe Z3
fe T3
fe YpX1
fe YmX1
fe A
fe B
fe C
fe D
YpX1 = Y1+X1
YmX1 = Y1-X1
A = YpX1*YmX2
B = YmX1*YpX2
C = T2d2*T1
ZZ = Z1*Z2
D = 2*ZZ
X3 = A-B
Y3 = A+B
Z3 = D-C
T3 = D+C
return

14
src/crypto/shen_ed25519_ref/ref10/ge_tobytes.c Normal file
View File

@ -0,0 +1,14 @@
#include "ge.h"
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;
}

23
src/crypto/shen_ed25519_ref/ref10/keypair.c Normal file
View File

@ -0,0 +1,23 @@
#include <string.h>
#include "randombytes.h"
#include "crypto_sign.h"
#include "crypto_hash_sha512.h"
#include "ge.h"
int crypto_sign_keypair(unsigned char *pk,unsigned char *sk)
{
unsigned char az[64];
ge_p3 A;
randombytes(sk,32);
crypto_hash_sha512(az,sk,32);
az[0] &= 248;
az[31] &= 63;
az[31] |= 64;
ge_scalarmult_base(&A,az);
ge_p3_tobytes(pk,&A);
memmove(sk + 32,pk,32);
return 0;
}

48
src/crypto/shen_ed25519_ref/ref10/open.c Normal file
View File

@ -0,0 +1,48 @@
#include <string.h>
#include "crypto_sign.h"
#include "crypto_hash_sha512.h"
#include "crypto_verify_32.h"
#include "ge.h"
#include "sc.h"
int crypto_sign_open(
unsigned char *m,unsigned long long *mlen,
const unsigned char *sm,unsigned long long smlen,
const unsigned char *pk
)
{
unsigned char pkcopy[32];
unsigned char rcopy[32];
unsigned char scopy[32];
unsigned char h[64];
unsigned char rcheck[32];
ge_p3 A;
ge_p2 R;
if (smlen < 64) goto badsig;
if (sm[63] & 224) goto badsig;
if (ge_frombytes_negate_vartime(&A,pk) != 0) goto badsig;
memmove(pkcopy,pk,32);
memmove(rcopy,sm,32);
memmove(scopy,sm + 32,32);
memmove(m,sm,smlen);
memmove(m + 32,pkcopy,32);
crypto_hash_sha512(h,m,smlen);
sc_reduce(h);
ge_double_scalarmult_vartime(&R,h,&A,scopy);
ge_tobytes(rcheck,&R);
if (crypto_verify_32(rcheck,rcopy) == 0) {
memmove(m,m + 64,smlen - 64);
memset(m + smlen - 64,0,64);
*mlen = smlen - 64;
return 0;
}
badsig:
*mlen = -1;
memset(m,0,smlen);
return -1;
}

160
src/crypto/shen_ed25519_ref/ref10/pow22523.h Normal file
View File

@ -0,0 +1,160 @@
/* qhasm: fe z1 */
/* qhasm: fe z2 */
/* qhasm: fe z8 */
/* qhasm: fe z9 */
/* qhasm: fe z11 */
/* qhasm: fe z22 */
/* qhasm: fe z_5_0 */
/* qhasm: fe z_10_5 */
/* qhasm: fe z_10_0 */
/* qhasm: fe z_20_10 */
/* qhasm: fe z_20_0 */
/* qhasm: fe z_40_20 */
/* qhasm: fe z_40_0 */
/* qhasm: fe z_50_10 */
/* qhasm: fe z_50_0 */
/* qhasm: fe z_100_50 */
/* qhasm: fe z_100_0 */
/* qhasm: fe z_200_100 */
/* qhasm: fe z_200_0 */
/* qhasm: fe z_250_50 */
/* qhasm: fe z_250_0 */
/* qhasm: fe z_252_2 */
/* qhasm: fe z_252_3 */
/* qhasm: enter pow22523 */
/* qhasm: z2 = z1^2^1 */
/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
/* qhasm: z8 = z2^2^2 */
/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
/* qhasm: z9 = z1*z8 */
/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
fe_mul(t1,z,t1);
/* qhasm: z11 = z2*z9 */
/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
fe_mul(t0,t0,t1);
/* qhasm: z22 = z11^2^1 */
/* asm 1: fe_sq(>z22=fe#1,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#1,>z22=fe#1); */
/* asm 2: fe_sq(>z22=t0,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t0,>z22=t0); */
fe_sq(t0,t0); for (i = 1;i < 1;++i) fe_sq(t0,t0);
/* qhasm: z_5_0 = z9*z22 */
/* asm 1: fe_mul(>z_5_0=fe#1,<z9=fe#2,<z22=fe#1); */
/* asm 2: fe_mul(>z_5_0=t0,<z9=t1,<z22=t0); */
fe_mul(t0,t1,t0);
/* qhasm: z_10_5 = z_5_0^2^5 */
/* asm 1: fe_sq(>z_10_5=fe#2,<z_5_0=fe#1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#2,>z_10_5=fe#2); */
/* asm 2: fe_sq(>z_10_5=t1,<z_5_0=t0); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t1,>z_10_5=t1); */
fe_sq(t1,t0); for (i = 1;i < 5;++i) fe_sq(t1,t1);
/* qhasm: z_10_0 = z_10_5*z_5_0 */
/* asm 1: fe_mul(>z_10_0=fe#1,<z_10_5=fe#2,<z_5_0=fe#1); */
/* asm 2: fe_mul(>z_10_0=t0,<z_10_5=t1,<z_5_0=t0); */
fe_mul(t0,t1,t0);
/* qhasm: z_20_10 = z_10_0^2^10 */
/* asm 1: fe_sq(>z_20_10=fe#2,<z_10_0=fe#1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#2,>z_20_10=fe#2); */
/* asm 2: fe_sq(>z_20_10=t1,<z_10_0=t0); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t1,>z_20_10=t1); */
fe_sq(t1,t0); for (i = 1;i < 10;++i) fe_sq(t1,t1);
/* qhasm: z_20_0 = z_20_10*z_10_0 */
/* asm 1: fe_mul(>z_20_0=fe#2,<z_20_10=fe#2,<z_10_0=fe#1); */
/* asm 2: fe_mul(>z_20_0=t1,<z_20_10=t1,<z_10_0=t0); */
fe_mul(t1,t1,t0);
/* qhasm: z_40_20 = z_20_0^2^20 */
/* asm 1: fe_sq(>z_40_20=fe#3,<z_20_0=fe#2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#3,>z_40_20=fe#3); */
/* asm 2: fe_sq(>z_40_20=t2,<z_20_0=t1); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t2,>z_40_20=t2); */
fe_sq(t2,t1); for (i = 1;i < 20;++i) fe_sq(t2,t2);
/* qhasm: z_40_0 = z_40_20*z_20_0 */
/* asm 1: fe_mul(>z_40_0=fe#2,<z_40_20=fe#3,<z_20_0=fe#2); */
/* asm 2: fe_mul(>z_40_0=t1,<z_40_20=t2,<z_20_0=t1); */
fe_mul(t1,t2,t1);
/* qhasm: z_50_10 = z_40_0^2^10 */
/* asm 1: fe_sq(>z_50_10=fe#2,<z_40_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#2,>z_50_10=fe#2); */
/* asm 2: fe_sq(>z_50_10=t1,<z_40_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t1,>z_50_10=t1); */
fe_sq(t1,t1); for (i = 1;i < 10;++i) fe_sq(t1,t1);
/* qhasm: z_50_0 = z_50_10*z_10_0 */
/* asm 1: fe_mul(>z_50_0=fe#1,<z_50_10=fe#2,<z_10_0=fe#1); */
/* asm 2: fe_mul(>z_50_0=t0,<z_50_10=t1,<z_10_0=t0); */
fe_mul(t0,t1,t0);
/* qhasm: z_100_50 = z_50_0^2^50 */
/* asm 1: fe_sq(>z_100_50=fe#2,<z_50_0=fe#1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#2,>z_100_50=fe#2); */
/* asm 2: fe_sq(>z_100_50=t1,<z_50_0=t0); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t1,>z_100_50=t1); */
fe_sq(t1,t0); for (i = 1;i < 50;++i) fe_sq(t1,t1);
/* qhasm: z_100_0 = z_100_50*z_50_0 */
/* asm 1: fe_mul(>z_100_0=fe#2,<z_100_50=fe#2,<z_50_0=fe#1); */
/* asm 2: fe_mul(>z_100_0=t1,<z_100_50=t1,<z_50_0=t0); */
fe_mul(t1,t1,t0);
/* qhasm: z_200_100 = z_100_0^2^100 */
/* asm 1: fe_sq(>z_200_100=fe#3,<z_100_0=fe#2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#3,>z_200_100=fe#3); */
/* asm 2: fe_sq(>z_200_100=t2,<z_100_0=t1); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t2,>z_200_100=t2); */
fe_sq(t2,t1); for (i = 1;i < 100;++i) fe_sq(t2,t2);
/* qhasm: z_200_0 = z_200_100*z_100_0 */
/* asm 1: fe_mul(>z_200_0=fe#2,<z_200_100=fe#3,<z_100_0=fe#2); */
/* asm 2: fe_mul(>z_200_0=t1,<z_200_100=t2,<z_100_0=t1); */
fe_mul(t1,t2,t1);
/* qhasm: z_250_50 = z_200_0^2^50 */
/* asm 1: fe_sq(>z_250_50=fe#2,<z_200_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#2,>z_250_50=fe#2); */
/* asm 2: fe_sq(>z_250_50=t1,<z_200_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t1,>z_250_50=t1); */
fe_sq(t1,t1); for (i = 1;i < 50;++i) fe_sq(t1,t1);
/* qhasm: z_250_0 = z_250_50*z_50_0 */
/* asm 1: fe_mul(>z_250_0=fe#1,<z_250_50=fe#2,<z_50_0=fe#1); */
/* asm 2: fe_mul(>z_250_0=t0,<z_250_50=t1,<z_50_0=t0); */
fe_mul(t0,t1,t0);
/* qhasm: z_252_2 = z_250_0^2^2 */
/* asm 1: fe_sq(>z_252_2=fe#1,<z_250_0=fe#1); for (i = 1;i < 2;++i) fe_sq(>z_252_2=fe#1,>z_252_2=fe#1); */
/* asm 2: fe_sq(>z_252_2=t0,<z_250_0=t0); for (i = 1;i < 2;++i) fe_sq(>z_252_2=t0,>z_252_2=t0); */
fe_sq(t0,t0); for (i = 1;i < 2;++i) fe_sq(t0,t0);
/* qhasm: z_252_3 = z_252_2*z1 */
/* asm 1: fe_mul(>z_252_3=fe#12,<z_252_2=fe#1,<z1=fe#11); */
/* asm 2: fe_mul(>z_252_3=out,<z_252_2=t0,<z1=z); */
fe_mul(out,t0,z);
/* qhasm: return */

61
src/crypto/shen_ed25519_ref/ref10/pow22523.q Normal file
View File

@ -0,0 +1,61 @@
:name:fe:t0:t1:t2:t3:t4:t5:t6:t7:t8:t9:z:out:
fe r:var/r=fe:
enter f:enter/f:>z1=fe#11:
return:nofallthrough:<z_252_3=fe#12:leave:
h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
h=f^2^k:<f=fe:>h=fe:#k:asm/fe_sq(>h,<f); for (i = 1;i !lt; #k;++i) fe_sq(>h,>h);:
:
fe z1
fe z2
fe z8
fe z9
fe z11
fe z22
fe z_5_0
fe z_10_5
fe z_10_0
fe z_20_10
fe z_20_0
fe z_40_20
fe z_40_0
fe z_50_10
fe z_50_0
fe z_100_50
fe z_100_0
fe z_200_100
fe z_200_0
fe z_250_50
fe z_250_0
fe z_252_2
fe z_252_3
enter pow22523
z2 = z1^2^1
z8 = z2^2^2
z9 = z1*z8
z11 = z2*z9
z22 = z11^2^1
z_5_0 = z9*z22
z_10_5 = z_5_0^2^5
z_10_0 = z_10_5*z_5_0
z_20_10 = z_10_0^2^10
z_20_0 = z_20_10*z_10_0
z_40_20 = z_20_0^2^20
z_40_0 = z_40_20*z_20_0
z_50_10 = z_40_0^2^10
z_50_0 = z_50_10*z_10_0
z_100_50 = z_50_0^2^50
z_100_0 = z_100_50*z_50_0
z_200_100 = z_100_0^2^100
z_200_0 = z_200_100*z_100_0
z_250_50 = z_200_0^2^50
z_250_0 = z_250_50*z_50_0
z_252_2 = z_250_0^2^2
z_252_3 = z_252_2*z1
return

160
src/crypto/shen_ed25519_ref/ref10/pow225521.h Normal file
View File

@ -0,0 +1,160 @@
/* qhasm: fe z1 */
/* qhasm: fe z2 */
/* qhasm: fe z8 */
/* qhasm: fe z9 */
/* qhasm: fe z11 */
/* qhasm: fe z22 */
/* qhasm: fe z_5_0 */
/* qhasm: fe z_10_5 */
/* qhasm: fe z_10_0 */
/* qhasm: fe z_20_10 */
/* qhasm: fe z_20_0 */
/* qhasm: fe z_40_20 */
/* qhasm: fe z_40_0 */
/* qhasm: fe z_50_10 */
/* qhasm: fe z_50_0 */
/* qhasm: fe z_100_50 */
/* qhasm: fe z_100_0 */
/* qhasm: fe z_200_100 */
/* qhasm: fe z_200_0 */
/* qhasm: fe z_250_50 */
/* qhasm: fe z_250_0 */
/* qhasm: fe z_255_5 */
/* qhasm: fe z_255_21 */
/* qhasm: enter pow225521 */
/* qhasm: z2 = z1^2^1 */
/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
/* qhasm: z8 = z2^2^2 */
/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
/* qhasm: z9 = z1*z8 */
/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
fe_mul(t1,z,t1);
/* qhasm: z11 = z2*z9 */
/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
fe_mul(t0,t0,t1);
/* qhasm: z22 = z11^2^1 */
/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */
/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */
fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2);
/* qhasm: z_5_0 = z9*z22 */
/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */
/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */
fe_mul(t1,t1,t2);
/* qhasm: z_10_5 = z_5_0^2^5 */
/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */
/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */
fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2);
/* qhasm: z_10_0 = z_10_5*z_5_0 */
/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */
/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */
fe_mul(t1,t2,t1);
/* qhasm: z_20_10 = z_10_0^2^10 */
/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */
/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */
fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2);
/* qhasm: z_20_0 = z_20_10*z_10_0 */
/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */
/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */
fe_mul(t2,t2,t1);
/* qhasm: z_40_20 = z_20_0^2^20 */
/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */
/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */
fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3);
/* qhasm: z_40_0 = z_40_20*z_20_0 */
/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */
/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */
fe_mul(t2,t3,t2);
/* qhasm: z_50_10 = z_40_0^2^10 */
/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */
/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */
fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2);
/* qhasm: z_50_0 = z_50_10*z_10_0 */
/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */
/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */
fe_mul(t1,t2,t1);
/* qhasm: z_100_50 = z_50_0^2^50 */
/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */
/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */
fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2);
/* qhasm: z_100_0 = z_100_50*z_50_0 */
/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */
/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */
fe_mul(t2,t2,t1);
/* qhasm: z_200_100 = z_100_0^2^100 */
/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */
/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */
fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3);
/* qhasm: z_200_0 = z_200_100*z_100_0 */
/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
fe_mul(t2,t3,t2);
/* qhasm: z_250_50 = z_200_0^2^50 */
/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */
/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */
fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2);
/* qhasm: z_250_0 = z_250_50*z_50_0 */
/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */
/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */
fe_mul(t1,t2,t1);
/* qhasm: z_255_5 = z_250_0^2^5 */
/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */
/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */
fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1);
/* qhasm: z_255_21 = z_255_5*z11 */
/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
fe_mul(out,t1,t0);
/* qhasm: return */

61
src/crypto/shen_ed25519_ref/ref10/pow225521.q Normal file
View File

@ -0,0 +1,61 @@
:name:fe:t0:t1:t2:t3:t4:t5:t6:t7:t8:t9:z:out:
fe r:var/r=fe:
enter f:enter/f:>z1=fe#11:
return:nofallthrough:<z_255_21=fe#12:leave:
h=f*g:<f=fe:<g=fe:>h=fe:asm/fe_mul(>h,<f,<g);:
h=f^2^k:<f=fe:>h=fe:#k:asm/fe_sq(>h,<f); for (i = 1;i !lt; #k;++i) fe_sq(>h,>h);:
:
fe z1
fe z2
fe z8
fe z9
fe z11
fe z22
fe z_5_0
fe z_10_5
fe z_10_0
fe z_20_10
fe z_20_0
fe z_40_20
fe z_40_0
fe z_50_10
fe z_50_0
fe z_100_50
fe z_100_0
fe z_200_100
fe z_200_0
fe z_250_50
fe z_250_0
fe z_255_5
fe z_255_21
enter pow225521
z2 = z1^2^1
z8 = z2^2^2
z9 = z1*z8
z11 = z2*z9
z22 = z11^2^1
z_5_0 = z9*z22
z_10_5 = z_5_0^2^5
z_10_0 = z_10_5*z_5_0
z_20_10 = z_10_0^2^10
z_20_0 = z_20_10*z_10_0
z_40_20 = z_20_0^2^20
z_40_0 = z_40_20*z_20_0
z_50_10 = z_40_0^2^10
z_50_0 = z_50_10*z_10_0
z_100_50 = z_50_0^2^50
z_100_0 = z_100_50*z_50_0
z_200_100 = z_100_0^2^100
z_200_0 = z_200_100*z_100_0
z_250_50 = z_200_0^2^50
z_250_0 = z_250_50*z_50_0
z_255_5 = z_250_0^2^5
z_255_21 = z_255_5*z11
return

4
src/crypto/shen_ed25519_ref/ref10/q2h.sh Normal file
View File

@ -0,0 +1,4 @@
#!/bin/sh
sed 's/^#.*//' \
| qhasm-generic \
| sed 's_//\(.*\)$_/*\1 */_'

15
src/crypto/shen_ed25519_ref/ref10/sc.h Normal file
View File

@ -0,0 +1,15 @@
#ifndef SC_H
#define SC_H
/*
The set of scalars is \Z/l
where l = 2^252 + 27742317777372353535851937790883648493.
*/
#define sc_reduce crypto_sign_ed25519_ref10_sc_reduce
#define sc_muladd crypto_sign_ed25519_ref10_sc_muladd
extern void sc_reduce(unsigned char *);
extern void sc_muladd(unsigned char *,const unsigned char *,const unsigned char *,const unsigned char *);
#endif

368
src/crypto/shen_ed25519_ref/ref10/sc_muladd.c Normal file
View File

@ -0,0 +1,368 @@
#include "sc.h"
#include "crypto_int64.h"
#include "crypto_uint32.h"
#include "crypto_uint64.h"
static crypto_uint64 load_3(const unsigned char *in)
{
crypto_uint64 result;
result = (crypto_uint64) in[0];
result |= ((crypto_uint64) in[1]) << 8;
result |= ((crypto_uint64) in[2]) << 16;
return result;
}
static crypto_uint64 load_4(const unsigned char *in)
{
crypto_uint64 result;
result = (crypto_uint64) in[0];
result |= ((crypto_uint64) in[1]) << 8;
result |= ((crypto_uint64) in[2]) << 16;
result |= ((crypto_uint64) in[3]) << 24;
return result;
}
/*
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] = (ab+c) 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)
{
crypto_int64 a0 = 2097151 & load_3(a);
crypto_int64 a1 = 2097151 & (load_4(a + 2) >> 5);
crypto_int64 a2 = 2097151 & (load_3(a + 5) >> 2);
crypto_int64 a3 = 2097151 & (load_4(a + 7) >> 7);
crypto_int64 a4 = 2097151 & (load_4(a + 10) >> 4);
crypto_int64 a5 = 2097151 & (load_3(a + 13) >> 1);
crypto_int64 a6 = 2097151 & (load_4(a + 15) >> 6);
crypto_int64 a7 = 2097151 & (load_3(a + 18) >> 3);
crypto_int64 a8 = 2097151 & load_3(a + 21);
crypto_int64 a9 = 2097151 & (load_4(a + 23) >> 5);
crypto_int64 a10 = 2097151 & (load_3(a + 26) >> 2);
crypto_int64 a11 = (load_4(a + 28) >> 7);
crypto_int64 b0 = 2097151 & load_3(b);
crypto_int64 b1 = 2097151 & (load_4(b + 2) >> 5);
crypto_int64 b2 = 2097151 & (load_3(b + 5) >> 2);
crypto_int64 b3 = 2097151 & (load_4(b + 7) >> 7);
crypto_int64 b4 = 2097151 & (load_4(b + 10) >> 4);
crypto_int64 b5 = 2097151 & (load_3(b + 13) >> 1);
crypto_int64 b6 = 2097151 & (load_4(b + 15) >> 6);
crypto_int64 b7 = 2097151 & (load_3(b + 18) >> 3);
crypto_int64 b8 = 2097151 & load_3(b + 21);
crypto_int64 b9 = 2097151 & (load_4(b + 23) >> 5);
crypto_int64 b10 = 2097151 & (load_3(b + 26) >> 2);
crypto_int64 b11 = (load_4(b + 28) >> 7);
crypto_int64 c0 = 2097151 & load_3(c);
crypto_int64 c1 = 2097151 & (load_4(c + 2) >> 5);
crypto_int64 c2 = 2097151 & (load_3(c + 5) >> 2);
crypto_int64 c3 = 2097151 & (load_4(c + 7) >> 7);
crypto_int64 c4 = 2097151 & (load_4(c + 10) >> 4);
crypto_int64 c5 = 2097151 & (load_3(c + 13) >> 1);
crypto_int64 c6 = 2097151 & (load_4(c + 15) >> 6);
crypto_int64 c7 = 2097151 & (load_3(c + 18) >> 3);
crypto_int64 c8 = 2097151 & load_3(c + 21);
crypto_int64 c9 = 2097151 & (load_4(c + 23) >> 5);
crypto_int64 c10 = 2097151 & (load_3(c + 26) >> 2);
crypto_int64 c11 = (load_4(c + 28) >> 7);
crypto_int64 s0;
crypto_int64 s1;
crypto_int64 s2;
crypto_int64 s3;
crypto_int64 s4;
crypto_int64 s5;
crypto_int64 s6;
crypto_int64 s7;
crypto_int64 s8;
crypto_int64 s9;
crypto_int64 s10;
crypto_int64 s11;
crypto_int64 s12;
crypto_int64 s13;
crypto_int64 s14;
crypto_int64 s15;
crypto_int64 s16;
crypto_int64 s17;
crypto_int64 s18;
crypto_int64 s19;
crypto_int64 s20;
crypto_int64 s21;
crypto_int64 s22;
crypto_int64 s23;
crypto_int64 carry0;
crypto_int64 carry1;
crypto_int64 carry2;
crypto_int64 carry3;
crypto_int64 carry4;
crypto_int64 carry5;
crypto_int64 carry6;
crypto_int64 carry7;
crypto_int64 carry8;
crypto_int64 carry9;
crypto_int64 carry10;
crypto_int64 carry11;
crypto_int64 carry12;
crypto_int64 carry13;
crypto_int64 carry14;
crypto_int64 carry15;
crypto_int64 carry16;
crypto_int64 carry17;
crypto_int64 carry18;
crypto_int64 carry19;
crypto_int64 carry20;
crypto_int64 carry21;
crypto_int64 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;
s23 = 0;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s22 = 0;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s21 = 0;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s20 = 0;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s19 = 0;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
s18 = 0;
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;
s17 = 0;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s16 = 0;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s15 = 0;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s14 = 0;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s13 = 0;
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;
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;
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;
}

275
src/crypto/shen_ed25519_ref/ref10/sc_reduce.c Normal file
View File

@ -0,0 +1,275 @@
#include "sc.h"
#include "crypto_int64.h"
#include "crypto_uint32.h"
#include "crypto_uint64.h"
static crypto_uint64 load_3(const unsigned char *in)
{
crypto_uint64 result;
result = (crypto_uint64) in[0];
result |= ((crypto_uint64) in[1]) << 8;
result |= ((crypto_uint64) in[2]) << 16;
return result;
}
static crypto_uint64 load_4(const unsigned char *in)
{
crypto_uint64 result;
result = (crypto_uint64) in[0];
result |= ((crypto_uint64) in[1]) << 8;
result |= ((crypto_uint64) in[2]) << 16;
result |= ((crypto_uint64) in[3]) << 24;
return result;
}
/*
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)
{
crypto_int64 s0 = 2097151 & load_3(s);
crypto_int64 s1 = 2097151 & (load_4(s + 2) >> 5);
crypto_int64 s2 = 2097151 & (load_3(s + 5) >> 2);
crypto_int64 s3 = 2097151 & (load_4(s + 7) >> 7);
crypto_int64 s4 = 2097151 & (load_4(s + 10) >> 4);
crypto_int64 s5 = 2097151 & (load_3(s + 13) >> 1);
crypto_int64 s6 = 2097151 & (load_4(s + 15) >> 6);
crypto_int64 s7 = 2097151 & (load_3(s + 18) >> 3);
crypto_int64 s8 = 2097151 & load_3(s + 21);
crypto_int64 s9 = 2097151 & (load_4(s + 23) >> 5);
crypto_int64 s10 = 2097151 & (load_3(s + 26) >> 2);
crypto_int64 s11 = 2097151 & (load_4(s + 28) >> 7);
crypto_int64 s12 = 2097151 & (load_4(s + 31) >> 4);
crypto_int64 s13 = 2097151 & (load_3(s + 34) >> 1);
crypto_int64 s14 = 2097151 & (load_4(s + 36) >> 6);
crypto_int64 s15 = 2097151 & (load_3(s + 39) >> 3);
crypto_int64 s16 = 2097151 & load_3(s + 42);
crypto_int64 s17 = 2097151 & (load_4(s + 44) >> 5);
crypto_int64 s18 = 2097151 & (load_3(s + 47) >> 2);
crypto_int64 s19 = 2097151 & (load_4(s + 49) >> 7);
crypto_int64 s20 = 2097151 & (load_4(s + 52) >> 4);
crypto_int64 s21 = 2097151 & (load_3(s + 55) >> 1);
crypto_int64 s22 = 2097151 & (load_4(s + 57) >> 6);
crypto_int64 s23 = (load_4(s + 60) >> 3);
crypto_int64 carry0;
crypto_int64 carry1;
crypto_int64 carry2;
crypto_int64 carry3;
crypto_int64 carry4;
crypto_int64 carry5;
crypto_int64 carry6;
crypto_int64 carry7;
crypto_int64 carry8;
crypto_int64 carry9;
crypto_int64 carry10;
crypto_int64 carry11;
crypto_int64 carry12;
crypto_int64 carry13;
crypto_int64 carry14;
crypto_int64 carry15;
crypto_int64 carry16;
s11 += s23 * 666643;
s12 += s23 * 470296;
s13 += s23 * 654183;
s14 -= s23 * 997805;
s15 += s23 * 136657;
s16 -= s23 * 683901;
s23 = 0;
s10 += s22 * 666643;
s11 += s22 * 470296;
s12 += s22 * 654183;
s13 -= s22 * 997805;
s14 += s22 * 136657;
s15 -= s22 * 683901;
s22 = 0;
s9 += s21 * 666643;
s10 += s21 * 470296;
s11 += s21 * 654183;
s12 -= s21 * 997805;
s13 += s21 * 136657;
s14 -= s21 * 683901;
s21 = 0;
s8 += s20 * 666643;
s9 += s20 * 470296;
s10 += s20 * 654183;
s11 -= s20 * 997805;
s12 += s20 * 136657;
s13 -= s20 * 683901;
s20 = 0;
s7 += s19 * 666643;
s8 += s19 * 470296;
s9 += s19 * 654183;
s10 -= s19 * 997805;
s11 += s19 * 136657;
s12 -= s19 * 683901;
s19 = 0;
s6 += s18 * 666643;
s7 += s18 * 470296;
s8 += s18 * 654183;
s9 -= s18 * 997805;
s10 += s18 * 136657;
s11 -= s18 * 683901;
s18 = 0;
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;
s17 = 0;
s4 += s16 * 666643;
s5 += s16 * 470296;
s6 += s16 * 654183;
s7 -= s16 * 997805;
s8 += s16 * 136657;
s9 -= s16 * 683901;
s16 = 0;
s3 += s15 * 666643;
s4 += s15 * 470296;
s5 += s15 * 654183;
s6 -= s15 * 997805;
s7 += s15 * 136657;
s8 -= s15 * 683901;
s15 = 0;
s2 += s14 * 666643;
s3 += s14 * 470296;
s4 += s14 * 654183;
s5 -= s14 * 997805;
s6 += s14 * 136657;
s7 -= s14 * 683901;
s14 = 0;
s1 += s13 * 666643;
s2 += s13 * 470296;
s3 += s13 * 654183;
s4 -= s13 * 997805;
s5 += s13 * 136657;
s6 -= s13 * 683901;
s13 = 0;
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;
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;
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;
}

41
src/crypto/shen_ed25519_ref/ref10/sign.c Normal file
View File

@ -0,0 +1,41 @@
#include <string.h>
#include "crypto_sign.h"
#include "crypto_hash_sha512.h"
#include "ge.h"
#include "sc.h"
int crypto_sign(
unsigned char *sm,unsigned long long *smlen,
const unsigned char *m,unsigned long long mlen,
const unsigned char *sk
)
{
unsigned char pk[32];
unsigned char az[64];
unsigned char nonce[64];
unsigned char hram[64];
ge_p3 R;
memmove(pk,sk + 32,32);
crypto_hash_sha512(az,sk,32);
az[0] &= 248;
az[31] &= 63;
az[31] |= 64;
*smlen = mlen + 64;
memmove(sm + 64,m,mlen);
memmove(sm + 32,az + 32,32);
crypto_hash_sha512(nonce,sm + 32,mlen + 32);
memmove(sm + 32,pk,32);
sc_reduce(nonce);
ge_scalarmult_base(&R,nonce);
ge_p3_tobytes(sm,&R);
crypto_hash_sha512(hram,sm,mlen + 64);
sc_reduce(hram);
sc_muladd(sm + 32,hram,az,nonce);
return 0;
}

1
src/crypto/shen_ed25519_ref/ref10/sqrtm1.h Normal file
View File

@ -0,0 +1 @@
-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482

28
src/crypto/shen_ed25519_ref/ref10/sqrtm1.py Normal file
View File

@ -0,0 +1,28 @@
q = 2**255 - 19
def expmod(b,e,m):
if e == 0: return 1
t = expmod(b,e/2,m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x,q-2,q)
def radix255(x):
x = x % q
if x + x > q: x -= q
x = [x,0,0,0,0,0,0,0,0,0]
bits = [26,25,26,25,26,25,26,25,26,25]
for i in range(9):
carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
x[i] -= carry * 2**bits[i]
x[i + 1] += carry
result = ""
for i in range(9):
result = result+str(x[i])+","
result = result+str(x[9])
return result
I = expmod(2,(q-1)/4,q)
print radix255(I)

261
src/crypto/shen_ed25519_ref/ref10CommentedCombined/MakeCryptoOps.py Normal file
View File

@ -0,0 +1,261 @@
#assumes you have gnu sed, osx sed might need slight syntax changeo
#c.f. http://unix.stackexchange.com/questions/112023/how-can-i-replace-a-string-in-a-files
#written by shen-noether monero research labs
import os #for copying and sed etc.
import glob #for copy files
import textwrap #for comments etc
print("make sure you have cat and grep installed")
print("also assumes gnu sed syntax, c.f. :http://unix.stackexchange.com/questions/112023/how-can-i-replace-a-string-in-a-files")
print("I believe osx may have slightly different version of sed")
print("maybe someone smart can replace the sed with perl..")
a = ""
license = textwrap.dedent("""\
// Copyright (c) 2014-2015, 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
""")
crypto_ops_includes = textwrap.dedent("""\
#include <assert.h>
#include <stdint.h>
#include "warnings.h"
#include "crypto-ops.h"
DISABLE_VS_WARNINGS(4146 4244)
""")
predeclarations = textwrap.dedent("""\
/* Predeclarations */
static void fe_mul(fe, const fe, const fe);
static void fe_sq(fe, const fe);
static void fe_tobytes(unsigned char *, const fe);
static int fe_isnonzero(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 ge_sub(ge_p1p1 *, const ge_p3 *, const ge_cached *);
static void fe_divpowm1(fe, const fe, const fe);
""")
fe_comments = textwrap.dedent("""\
/*
fe means field element.
Here the field is \Z/(2^255-19).
An element t, entries t[0]...t[9], represents the integer
t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
Bounds on each t[i] vary depending on context.
*/
""")
sc_comments = textwrap.dedent("""\
/*
*
* sc code
*
*
The set of scalars is \Z/l
where l = 2^252 + 27742317777372353535851937790883648493.
This is the order of the curve ed25519.
The point is that if a is a scalar and P is a point,
and b is congruent to a mod l, then aP = bP.
Thus, reducing mod l can possibly give you a smaller scalar,
so your elliptic curve operations take less time
*/
""")
ge_comments = textwrap.dedent("""\
/*
*
* ge code
*
*
ge means group element.
Here the group is the set of pairs (x,y) of field elements (see fe.h)
satisfying -x^2 + y^2 = 1 + d x^2y^2
where d = -121665/121666.
Representations:
ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
ge_precomp (Duif): (y+x,y-x,2dxy)
*/
""")
xmr_comments = textwrap.dedent("""\
/*
*
* xmr specific code
*
*
This code is from the original CryptoNote.
Some additional functions were needed to compute ring signatures
which are not needed for signing.
Note that sc_sub and sc_mulsub have been given their own file
since these have been rewritten
*/
""")
def qhasmToC(fi, header, out):
#replaces mentiones of "header" in "fi" with output in "out"
#also removes qhasm comments
out1 = out+".tmp"
rem_qhasm = " |grep -v 'qhasm' |grep -v ' asm'"
com = "sed -e '/#include \""+header+"\"/ {' -e 'r "+header+"' -e 'd' -e '}' "+fi+rem_qhasm+" > "+out1
com2 = "awk 'NF' "+out1+" > "+out
print(com)
os.system(com)
print(com2)
os.system(com2)
os.remove(out1) #temporary
while (a != "m") and (a != "m") and (a != "c"):
a = raw_input("Make / Clean/ Quit m / c / q?")
if a == "m":
print("making crypto-ops.c and crypto-ops.h")
#ref10 header files
#ref10 c files
#fe things
#still need to do d2, d, sqrtm1
print("making fe.c")
print(fe_comments)
fe = glob.glob("fe*.c")
for g in fe:
os.system("cp "+g+" "+g.replace("fe", "fe.monero."))
qhasmToC("fe_pow22523.c", "pow22523.h", "fe.monero._pow22523.c")
qhasmToC("fe_invert.c", "pow225521.h", "fe.monero._invert.c")
os.system("rm fe.monero._isnonzero.c") #since it's modified, it's in xmrSpecificOld
os.system("cat fe.monero.*.c | grep -v '^#include' > fe.monero.c")
#sc things
print("\nmaking sc.c")
print(sc_comments)
#so you don't get multiple "loads"
os.system("tail -n +24 sc_reduce.c > sc.monero._reduce.c") #also good on linux
os.system("tail -n +24 sc_muladd.c > sc.monero._muladd.c")
os.system("tail -n +31 sc_sub.xmr.c > sc.monero._sub.xmr.c") #careful with the tails if you change these files!
os.system("cat sc.monero.*.c | grep -v '^#include' > sc.monero.c")
#ge stuff
print("making ge.c")
ge = glob.glob("ge*.c")
for g in ge:
os.system("cp "+g+" "+g.replace("ge", "ge.monero."))
print(ge_comments)
#need to substitute the below lines for their .h files in the appropriate places
qhasmToC("ge_add.c", "ge_add.h", "ge.monero._add.c")
qhasmToC("ge_madd.c", "ge_madd.h", "ge.monero._madd.c")
qhasmToC("ge_sub.c", "ge_sub.h", "ge.monero._sub.c")
qhasmToC("ge_msub.c", "ge_msub.h", "ge.monero._msub.c")
qhasmToC("ge_p2_dbl.c", "ge_p2_dbl.h", "ge.monero._p2_dbl.c")
qhasmToC("ge_frombytes.c", "d.h", "ge.monero._frombytes.c")
qhasmToC("ge.monero._frombytes.c", "sqrtm1.h", "ge.monero._frombytes.c")
qhasmToC("ge_p3_to_cached.c", "d2.h", "ge.monero._p3_to_cached.c")
#also ge_double_scalarmult needs base2.h for ge_precomp Bi
#note, base2.h is a large file!
#also in ge_scalarmult_base ge_precomp base needs base.h included
qhasmToC("ge_double_scalarmult.c", "base2.h", "ge.monero._double_scalarmult.c")
qhasmToC("ge_scalarmult_base.c", "base.h", "ge.monero._scalarmult_base.c")
#qhasmToC("ge.monero._scalarmult_base.c", "base.h", "ge.monero._scalarmult_base.c")
os.system("sed -i 's/ cmov/ ge_precomp_cmov/g' ge.monero._scalarmult_base.c")
os.system("cat ge.monero.*.c | grep -v '^#include' > ge.monero.c")
print("making crypto-ops.c")
#sqrtm1 things
#comments
with open("fe.monero.comments", "w") as text_file:
text_file.write(fe_comments)
with open("ge.monero.comments", "w") as text_file:
text_file.write(ge_comments)
with open("sc.monero.comments", "w") as text_file:
text_file.write(sc_comments)
with open("xmr.monero.comments", "w") as text_file:
text_file.write(xmr_comments)
with open("xmr.monero.predeclarations", "w") as text_file:
text_file.write(predeclarations)
#license
with open("monero.license", "w") as text_file:
text_file.write(license)
#crypto-ops.c includes
with open("crypto-ops.monero.includes", "w") as text_file:
text_file.write(crypto_ops_includes)
#note you may have duplicates of load_3, load_4 and possibly some other functions ...
os.system("cat monero.license crypto-ops.monero.includes xmr.monero.predeclarations fe.monero.comments fe.monero.c sc.monero.comments sc.monero.c ge.monero.comments ge.monero.c xmr.monero.comments xmrSpecificOld.c > crypto-ops.c")
#monero specific header files
#print("making crypto-ops-tmp.h")
#os.system("cat fe.h ge.h sc.h |grep -v crypto_sign_ed25519 |grep -v fe.h > crypto-ops-tmp.h")
#we'll just use the old header crypto-ops.h
#replace crypto_ints
os.system("sed -i 's/crypto_int32/int32_t/g' crypto-ops.c")
os.system("sed -i 's/crypto_int64/int64_t/g' crypto-ops.c")
os.system("sed -i 's/crypto_uint32/uint32_t/g' crypto-ops.c")
os.system("sed -i 's/crypto_uint64/uint64_t/g' crypto-ops.c")
#cleaning up
os.system("rm *monero*")
#monero specific c files
if a == "c":
#turn the directory back into ref10
os.system("rm *monero*")
os.system("rm crypto-ops.c")

4
src/crypto/shen_ed25519_ref/ref10CommentedCombined/api.h Normal file
View File

@ -0,0 +1,4 @@
#define CRYPTO_SECRETKEYBYTES 64
#define CRYPTO_PUBLICKEYBYTES 32
#define CRYPTO_BYTES 64
#define CRYPTO_DETERMINISTIC 1

1344
src/crypto/shen_ed25519_ref/ref10CommentedCombined/base.h Normal file
View File

File diff suppressed because it is too large Load Diff

65
src/crypto/shen_ed25519_ref/ref10CommentedCombined/base.py Normal file
View File

@ -0,0 +1,65 @@
b = 256
q = 2**255 - 19
l = 2**252 + 27742317777372353535851937790883648493
def expmod(b,e,m):
if e == 0: return 1
t = expmod(b,e/2,m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x,q-2,q)
d = -121665 * inv(121666)
I = expmod(2,(q-1)/4,q)
def xrecover(y):
xx = (y*y-1) * inv(d*y*y+1)
x = expmod(xx,(q+3)/8,q)
if (x*x - xx) % q != 0: x = (x*I) % q
if x % 2 != 0: x = q-x
return x
By = 4 * inv(5)
Bx = xrecover(By)
B = [Bx % q,By % q]
def edwards(P,Q):
x1 = P[0]
y1 = P[1]
x2 = Q[0]
y2 = Q[1]
x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
return [x3 % q,y3 % q]
def radix255(x):
x = x % q
if x + x > q: x -= q
x = [x,0,0,0,0,0,0,0,0,0]
bits = [26,25,26,25,26,25,26,25,26,25]
for i in range(9):
carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
x[i] -= carry * 2**bits[i]
x[i + 1] += carry
result = ""
for i in range(9):
result = result+str(x[i])+","
result = result+str(x[9])
return result
Bi = B
for i in range(32):
print "{"
Bij = Bi
for j in range(8):
print " {"
print " {",radix255(Bij[1]+Bij[0]),"},"
print " {",radix255(Bij[1]-Bij[0]),"},"
print " {",radix255(2*d*Bij[0]*Bij[1]),"},"
Bij = edwards(Bij,Bi)
print " },"
print "},"
for k in range(8):
Bi = edwards(Bi,Bi)

40
src/crypto/shen_ed25519_ref/ref10CommentedCombined/base2.h Normal file
View File

@ -0,0 +1,40 @@
{
{ 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 },
},

60
src/crypto/shen_ed25519_ref/ref10CommentedCombined/base2.py Normal file
View File

@ -0,0 +1,60 @@
b = 256
q = 2**255 - 19
l = 2**252 + 27742317777372353535851937790883648493
def expmod(b,e,m):
if e == 0: return 1
t = expmod(b,e/2,m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x,q-2,q)
d = -121665 * inv(121666)
I = expmod(2,(q-1)/4,q)
def xrecover(y):
xx = (y*y-1) * inv(d*y*y+1)
x = expmod(xx,(q+3)/8,q)
if (x*x - xx) % q != 0: x = (x*I) % q
if x % 2 != 0: x = q-x
return x
By = 4 * inv(5)
Bx = xrecover(By)
B = [Bx % q,By % q]
def edwards(P,Q):
x1 = P[0]
y1 = P[1]
x2 = Q[0]
y2 = Q[1]
x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
return [x3 % q,y3 % q]
def radix255(x):
x = x % q
if x + x > q: x -= q
x = [x,0,0,0,0,0,0,0,0,0]
bits = [26,25,26,25,26,25,26,25,26,25]
for i in range(9):
carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
x[i] -= carry * 2**bits[i]
x[i + 1] += carry
result = ""
for i in range(9):
result = result+str(x[i])+","
result = result+str(x[9])
return result
Bi = B
for i in range(8):
print " {"
print " {",radix255(Bi[1]+Bi[0]),"},"
print " {",radix255(Bi[1]-Bi[0]),"},"
print " {",radix255(2*d*Bi[0]*Bi[1]),"},"
print " },"
Bi = edwards(B,edwards(B,Bi))

4830
src/crypto/shen_ed25519_ref/ref10CommentedCombined/crypto-ops.c Normal file
View File

File diff suppressed because it is too large Load Diff

Some files were not shown because too many files have changed in this diff Show More