crypto lib

author: amjuarez <amjuarez@users.noreply.github.com> 2013-11-15 02:28:17 +0400
committer: amjuarez <amjuarez@users.noreply.github.com> 2013-11-15 02:28:17 +0400
commit: 175d06e75e05aa4a42269dd048516e13b5bd585e (patch)
tree: 6828038a2d86174c6041f65187d7521c719606b3 /src/crypto
parent: Initial commit (diff)
download: monero-175d06e75e05aa4a42269dd048516e13b5bd585e.tar.xz
11 files changed, 4627 insertions, 0 deletions
diff --git a/src/crypto/crypto-ops-data.c b/src/crypto/crypto-ops-data.c
new file mode 100644
index 000000000..8eb2fbb0b
--- /dev/null
+++ b/src/crypto/crypto-ops-data.c
@@ -0,0 +1,842 @@
+#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},
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+     {-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)) */
+\ No newline at end of file
diff --git a/src/crypto/crypto-ops.c b/src/crypto/crypto-ops.c
new file mode 100644
index 000000000..dc2c7092c
--- /dev/null
+++ b/src/crypto/crypto-ops.c
@@ -0,0 +1,2893 @@
+#include <assert.h>
+#include <stdint.h>
+
+#include "crypto-ops.h"
+
+/* 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 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);
+
+/* Common functions */
+
+static uint64_t load_3(const unsigned char *in) {
+  uint64_t result;
+  result = (uint64_t) in[0];
+  result |= ((uint64_t) in[1]) << 8;
+  result |= ((uint64_t) in[2]) << 16;
+  return result;
+}
+
+static uint64_t load_4(const unsigned char *in)
+{
+  uint64_t result;
+  result = (uint64_t) in[0];
+  result |= ((uint64_t) in[1]) << 8;
+  result |= ((uint64_t) in[2]) << 16;
+  result |= ((uint64_t) in[3]) << 24;
+  return result;
+}
+
+/* From fe_0.c */
+
+/*
+h = 0
+*/
+
+static void fe_0(fe h) {
+  h[0] = 0;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}
+
+/* From fe_1.c */
+
+/*
+h = 1
+*/
+
+static void fe_1(fe h) {
+  h[0] = 1;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}
+
+/* From fe_add.c */
+
+/*
+h = f + g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+static void fe_add(fe h, const fe f, const fe g) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t g0 = g[0];
+  int32_t g1 = g[1];
+  int32_t g2 = g[2];
+  int32_t g3 = g[3];
+  int32_t g4 = g[4];
+  int32_t g5 = g[5];
+  int32_t g6 = g[6];
+  int32_t g7 = g[7];
+  int32_t g8 = g[8];
+  int32_t g9 = g[9];
+  int32_t h0 = f0 + g0;
+  int32_t h1 = f1 + g1;
+  int32_t h2 = f2 + g2;
+  int32_t h3 = f3 + g3;
+  int32_t h4 = f4 + g4;
+  int32_t h5 = f5 + g5;
+  int32_t h6 = f6 + g6;
+  int32_t h7 = f7 + g7;
+  int32_t h8 = f8 + g8;
+  int32_t h9 = f9 + g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/* From fe_cmov.c */
+
+/*
+Replace (f,g) with (g,g) if b == 1;
+replace (f,g) with (f,g) if b == 0.
+
+Preconditions: b in {0,1}.
+*/
+
+static void fe_cmov(fe f, const fe g, unsigned int b) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t g0 = g[0];
+  int32_t g1 = g[1];
+  int32_t g2 = g[2];
+  int32_t g3 = g[3];
+  int32_t g4 = g[4];
+  int32_t g5 = g[5];
+  int32_t g6 = g[6];
+  int32_t g7 = g[7];
+  int32_t g8 = g[8];
+  int32_t g9 = g[9];
+  int32_t x0 = f0 ^ g0;
+  int32_t x1 = f1 ^ g1;
+  int32_t x2 = f2 ^ g2;
+  int32_t x3 = f3 ^ g3;
+  int32_t x4 = f4 ^ g4;
+  int32_t x5 = f5 ^ g5;
+  int32_t x6 = f6 ^ g6;
+  int32_t x7 = f7 ^ g7;
+  int32_t x8 = f8 ^ g8;
+  int32_t x9 = f9 ^ g9;
+  assert((((b - 1) & ~b) | ((b - 2) & ~(b - 1))) == (unsigned int) -1);
+  b = -b;
+  x0 &= b;
+  x1 &= b;
+  x2 &= b;
+  x3 &= b;
+  x4 &= b;
+  x5 &= b;
+  x6 &= b;
+  x7 &= b;
+  x8 &= b;
+  x9 &= b;
+  f[0] = f0 ^ x0;
+  f[1] = f1 ^ x1;
+  f[2] = f2 ^ x2;
+  f[3] = f3 ^ x3;
+  f[4] = f4 ^ x4;
+  f[5] = f5 ^ x5;
+  f[6] = f6 ^ x6;
+  f[7] = f7 ^ x7;
+  f[8] = f8 ^ x8;
+  f[9] = f9 ^ x9;
+}
+
+/* From fe_copy.c */
+
+/*
+h = f
+*/
+
+static void fe_copy(fe h, const fe f) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  h[0] = f0;
+  h[1] = f1;
+  h[2] = f2;
+  h[3] = f3;
+  h[4] = f4;
+  h[5] = f5;
+  h[6] = f6;
+  h[7] = f7;
+  h[8] = f8;
+  h[9] = f9;
+}
+
+/* From fe_invert.c */
+
+static void fe_invert(fe out, const fe z) {
+  fe t0;
+  fe t1;
+  fe t2;
+  fe t3;
+  int i;
+
+  fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+  fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
+  fe_mul(t1,z,t1);
+  fe_mul(t0,t0,t1);
+  fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2);
+  fe_mul(t1,t1,t2);
+  fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2);
+  fe_mul(t1,t2,t1);
+  fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+  fe_mul(t2,t2,t1);
+  fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3);
+  fe_mul(t2,t3,t2);
+  fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+  fe_mul(t1,t2,t1);
+  fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+  fe_mul(t2,t2,t1);
+  fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3);
+  fe_mul(t2,t3,t2);
+  fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+  fe_mul(t1,t2,t1);
+  fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1);
+  fe_mul(out,t1,t0);
+
+  return;
+}
+
+/* From fe_isnegative.c */
+
+/*
+return 1 if f is in {1,3,5,...,q-2}
+return 0 if f is in {0,2,4,...,q-1}
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+static int fe_isnegative(const fe f) {
+  unsigned char s[32];
+  fe_tobytes(s, f);
+  return s[0] & 1;
+}
+
+/* From fe_isnonzero.c, modified */
+
+static int fe_isnonzero(const fe f) {
+  unsigned char s[32];
+  fe_tobytes(s, f);
+  return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] |
+    s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] |
+    s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] |
+    s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1;
+}
+
+/* From fe_mul.c */
+
+/*
+h = f * g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+   |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+Notes on implementation strategy:
+
+Using schoolbook multiplication.
+Karatsuba would save a little in some cost models.
+
+Most multiplications by 2 and 19 are 32-bit precomputations;
+cheaper than 64-bit postcomputations.
+
+There is one remaining multiplication by 19 in the carry chain;
+one *19 precomputation can be merged into this,
+but the resulting data flow is considerably less clean.
+
+There are 12 carries below.
+10 of them are 2-way parallelizable and vectorizable.
+Can get away with 11 carries, but then data flow is much deeper.
+
+With tighter constraints on inputs can squeeze carries into int32.
+*/
+
+static void fe_mul(fe h, const fe f, const fe g) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t g0 = g[0];
+  int32_t g1 = g[1];
+  int32_t g2 = g[2];
+  int32_t g3 = g[3];
+  int32_t g4 = g[4];
+  int32_t g5 = g[5];
+  int32_t g6 = g[6];
+  int32_t g7 = g[7];
+  int32_t g8 = g[8];
+  int32_t g9 = g[9];
+  int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
+  int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+  int32_t g3_19 = 19 * g3;
+  int32_t g4_19 = 19 * g4;
+  int32_t g5_19 = 19 * g5;
+  int32_t g6_19 = 19 * g6;
+  int32_t g7_19 = 19 * g7;
+  int32_t g8_19 = 19 * g8;
+  int32_t g9_19 = 19 * g9;
+  int32_t f1_2 = 2 * f1;
+  int32_t f3_2 = 2 * f3;
+  int32_t f5_2 = 2 * f5;
+  int32_t f7_2 = 2 * f7;
+  int32_t f9_2 = 2 * f9;
+  int64_t f0g0    = f0   * (int64_t) g0;
+  int64_t f0g1    = f0   * (int64_t) g1;
+  int64_t f0g2    = f0   * (int64_t) g2;
+  int64_t f0g3    = f0   * (int64_t) g3;
+  int64_t f0g4    = f0   * (int64_t) g4;
+  int64_t f0g5    = f0   * (int64_t) g5;
+  int64_t f0g6    = f0   * (int64_t) g6;
+  int64_t f0g7    = f0   * (int64_t) g7;
+  int64_t f0g8    = f0   * (int64_t) g8;
+  int64_t f0g9    = f0   * (int64_t) g9;
+  int64_t f1g0    = f1   * (int64_t) g0;
+  int64_t f1g1_2  = f1_2 * (int64_t) g1;
+  int64_t f1g2    = f1   * (int64_t) g2;
+  int64_t f1g3_2  = f1_2 * (int64_t) g3;
+  int64_t f1g4    = f1   * (int64_t) g4;
+  int64_t f1g5_2  = f1_2 * (int64_t) g5;
+  int64_t f1g6    = f1   * (int64_t) g6;
+  int64_t f1g7_2  = f1_2 * (int64_t) g7;
+  int64_t f1g8    = f1   * (int64_t) g8;
+  int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
+  int64_t f2g0    = f2   * (int64_t) g0;
+  int64_t f2g1    = f2   * (int64_t) g1;
+  int64_t f2g2    = f2   * (int64_t) g2;
+  int64_t f2g3    = f2   * (int64_t) g3;
+  int64_t f2g4    = f2   * (int64_t) g4;
+  int64_t f2g5    = f2   * (int64_t) g5;
+  int64_t f2g6    = f2   * (int64_t) g6;
+  int64_t f2g7    = f2   * (int64_t) g7;
+  int64_t f2g8_19 = f2   * (int64_t) g8_19;
+  int64_t f2g9_19 = f2   * (int64_t) g9_19;
+  int64_t f3g0    = f3   * (int64_t) g0;
+  int64_t f3g1_2  = f3_2 * (int64_t) g1;
+  int64_t f3g2    = f3   * (int64_t) g2;
+  int64_t f3g3_2  = f3_2 * (int64_t) g3;
+  int64_t f3g4    = f3   * (int64_t) g4;
+  int64_t f3g5_2  = f3_2 * (int64_t) g5;
+  int64_t f3g6    = f3   * (int64_t) g6;
+  int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
+  int64_t f3g8_19 = f3   * (int64_t) g8_19;
+  int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
+  int64_t f4g0    = f4   * (int64_t) g0;
+  int64_t f4g1    = f4   * (int64_t) g1;
+  int64_t f4g2    = f4   * (int64_t) g2;
+  int64_t f4g3    = f4   * (int64_t) g3;
+  int64_t f4g4    = f4   * (int64_t) g4;
+  int64_t f4g5    = f4   * (int64_t) g5;
+  int64_t f4g6_19 = f4   * (int64_t) g6_19;
+  int64_t f4g7_19 = f4   * (int64_t) g7_19;
+  int64_t f4g8_19 = f4   * (int64_t) g8_19;
+  int64_t f4g9_19 = f4   * (int64_t) g9_19;
+  int64_t f5g0    = f5   * (int64_t) g0;
+  int64_t f5g1_2  = f5_2 * (int64_t) g1;
+  int64_t f5g2    = f5   * (int64_t) g2;
+  int64_t f5g3_2  = f5_2 * (int64_t) g3;
+  int64_t f5g4    = f5   * (int64_t) g4;
+  int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
+  int64_t f5g6_19 = f5   * (int64_t) g6_19;
+  int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
+  int64_t f5g8_19 = f5   * (int64_t) g8_19;
+  int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
+  int64_t f6g0    = f6   * (int64_t) g0;
+  int64_t f6g1    = f6   * (int64_t) g1;
+  int64_t f6g2    = f6   * (int64_t) g2;
+  int64_t f6g3    = f6   * (int64_t) g3;
+  int64_t f6g4_19 = f6   * (int64_t) g4_19;
+  int64_t f6g5_19 = f6   * (int64_t) g5_19;
+  int64_t f6g6_19 = f6   * (int64_t) g6_19;
+  int64_t f6g7_19 = f6   * (int64_t) g7_19;
+  int64_t f6g8_19 = f6   * (int64_t) g8_19;
+  int64_t f6g9_19 = f6   * (int64_t) g9_19;
+  int64_t f7g0    = f7   * (int64_t) g0;
+  int64_t f7g1_2  = f7_2 * (int64_t) g1;
+  int64_t f7g2    = f7   * (int64_t) g2;
+  int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
+  int64_t f7g4_19 = f7   * (int64_t) g4_19;
+  int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
+  int64_t f7g6_19 = f7   * (int64_t) g6_19;
+  int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
+  int64_t f7g8_19 = f7   * (int64_t) g8_19;
+  int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
+  int64_t f8g0    = f8   * (int64_t) g0;
+  int64_t f8g1    = f8   * (int64_t) g1;
+  int64_t f8g2_19 = f8   * (int64_t) g2_19;
+  int64_t f8g3_19 = f8   * (int64_t) g3_19;
+  int64_t f8g4_19 = f8   * (int64_t) g4_19;
+  int64_t f8g5_19 = f8   * (int64_t) g5_19;
+  int64_t f8g6_19 = f8   * (int64_t) g6_19;
+  int64_t f8g7_19 = f8   * (int64_t) g7_19;
+  int64_t f8g8_19 = f8   * (int64_t) g8_19;
+  int64_t f8g9_19 = f8   * (int64_t) g9_19;
+  int64_t f9g0    = f9   * (int64_t) g0;
+  int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
+  int64_t f9g2_19 = f9   * (int64_t) g2_19;
+  int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
+  int64_t f9g4_19 = f9   * (int64_t) g4_19;
+  int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
+  int64_t f9g6_19 = f9   * (int64_t) g6_19;
+  int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
+  int64_t f9g8_19 = f9   * (int64_t) g8_19;
+  int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
+  int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
+  int64_t h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
+  int64_t h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
+  int64_t h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
+  int64_t h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
+  int64_t h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
+  int64_t h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
+  int64_t h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
+  int64_t h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
+  int64_t h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  /*
+  |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
+    i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
+  |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
+    i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
+  */
+
+  carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  /* |h0| <= 2^25 */
+  /* |h4| <= 2^25 */
+  /* |h1| <= 1.71*2^59 */
+  /* |h5| <= 1.71*2^59 */
+
+  carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  /* |h1| <= 2^24; from now on fits into int32 */
+  /* |h5| <= 2^24; from now on fits into int32 */
+  /* |h2| <= 1.41*2^60 */
+  /* |h6| <= 1.41*2^60 */
+
+  carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  /* |h2| <= 2^25; from now on fits into int32 unchanged */
+  /* |h6| <= 2^25; from now on fits into int32 unchanged */
+  /* |h3| <= 1.71*2^59 */
+  /* |h7| <= 1.71*2^59 */
+
+  carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+  /* |h3| <= 2^24; from now on fits into int32 unchanged */
+  /* |h7| <= 2^24; from now on fits into int32 unchanged */
+  /* |h4| <= 1.72*2^34 */
+  /* |h8| <= 1.41*2^60 */
+
+  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+  /* |h4| <= 2^25; from now on fits into int32 unchanged */
+  /* |h8| <= 2^25; from now on fits into int32 unchanged */
+  /* |h5| <= 1.01*2^24 */
+  /* |h9| <= 1.71*2^59 */
+
+  carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  /* |h9| <= 2^24; from now on fits into int32 unchanged */
+  /* |h0| <= 1.1*2^39 */
+
+  carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  /* |h0| <= 2^25; from now on fits into int32 unchanged */
+  /* |h1| <= 1.01*2^24 */
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/* From fe_neg.c */
+
+/*
+h = -f
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+static void fe_neg(fe h, const fe f) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t h0 = -f0;
+  int32_t h1 = -f1;
+  int32_t h2 = -f2;
+  int32_t h3 = -f3;
+  int32_t h4 = -f4;
+  int32_t h5 = -f5;
+  int32_t h6 = -f6;
+  int32_t h7 = -f7;
+  int32_t h8 = -f8;
+  int32_t h9 = -f9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/* From fe_sq.c */
+
+/*
+h = f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+static void fe_sq(fe h, const fe f) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t f0_2 = 2 * f0;
+  int32_t f1_2 = 2 * f1;
+  int32_t f2_2 = 2 * f2;
+  int32_t f3_2 = 2 * f3;
+  int32_t f4_2 = 2 * f4;
+  int32_t f5_2 = 2 * f5;
+  int32_t f6_2 = 2 * f6;
+  int32_t f7_2 = 2 * f7;
+  int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+  int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+  int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+  int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+  int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+  int64_t f0f0    = f0   * (int64_t) f0;
+  int64_t f0f1_2  = f0_2 * (int64_t) f1;
+  int64_t f0f2_2  = f0_2 * (int64_t) f2;
+  int64_t f0f3_2  = f0_2 * (int64_t) f3;
+  int64_t f0f4_2  = f0_2 * (int64_t) f4;
+  int64_t f0f5_2  = f0_2 * (int64_t) f5;
+  int64_t f0f6_2  = f0_2 * (int64_t) f6;
+  int64_t f0f7_2  = f0_2 * (int64_t) f7;
+  int64_t f0f8_2  = f0_2 * (int64_t) f8;
+  int64_t f0f9_2  = f0_2 * (int64_t) f9;
+  int64_t f1f1_2  = f1_2 * (int64_t) f1;
+  int64_t f1f2_2  = f1_2 * (int64_t) f2;
+  int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+  int64_t f1f4_2  = f1_2 * (int64_t) f4;
+  int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+  int64_t f1f6_2  = f1_2 * (int64_t) f6;
+  int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+  int64_t f1f8_2  = f1_2 * (int64_t) f8;
+  int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+  int64_t f2f2    = f2   * (int64_t) f2;
+  int64_t f2f3_2  = f2_2 * (int64_t) f3;
+  int64_t f2f4_2  = f2_2 * (int64_t) f4;
+  int64_t f2f5_2  = f2_2 * (int64_t) f5;
+  int64_t f2f6_2  = f2_2 * (int64_t) f6;
+  int64_t f2f7_2  = f2_2 * (int64_t) f7;
+  int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+  int64_t f2f9_38 = f2   * (int64_t) f9_38;
+  int64_t f3f3_2  = f3_2 * (int64_t) f3;
+  int64_t f3f4_2  = f3_2 * (int64_t) f4;
+  int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+  int64_t f3f6_2  = f3_2 * (int64_t) f6;
+  int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+  int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+  int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+  int64_t f4f4    = f4   * (int64_t) f4;
+  int64_t f4f5_2  = f4_2 * (int64_t) f5;
+  int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+  int64_t f4f7_38 = f4   * (int64_t) f7_38;
+  int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+  int64_t f4f9_38 = f4   * (int64_t) f9_38;
+  int64_t f5f5_38 = f5   * (int64_t) f5_38;
+  int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+  int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+  int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+  int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+  int64_t f6f6_19 = f6   * (int64_t) f6_19;
+  int64_t f6f7_38 = f6   * (int64_t) f7_38;
+  int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+  int64_t f6f9_38 = f6   * (int64_t) f9_38;
+  int64_t f7f7_38 = f7   * (int64_t) f7_38;
+  int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+  int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+  int64_t f8f8_19 = f8   * (int64_t) f8_19;
+  int64_t f8f9_38 = f8   * (int64_t) f9_38;
+  int64_t f9f9_38 = f9   * (int64_t) f9_38;
+  int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+  carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+  carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+  carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+  carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/* From fe_sq2.c */
+
+/*
+h = 2 * f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+static void fe_sq2(fe h, const fe f) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t f0_2 = 2 * f0;
+  int32_t f1_2 = 2 * f1;
+  int32_t f2_2 = 2 * f2;
+  int32_t f3_2 = 2 * f3;
+  int32_t f4_2 = 2 * f4;
+  int32_t f5_2 = 2 * f5;
+  int32_t f6_2 = 2 * f6;
+  int32_t f7_2 = 2 * f7;
+  int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+  int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+  int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+  int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+  int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+  int64_t f0f0    = f0   * (int64_t) f0;
+  int64_t f0f1_2  = f0_2 * (int64_t) f1;
+  int64_t f0f2_2  = f0_2 * (int64_t) f2;
+  int64_t f0f3_2  = f0_2 * (int64_t) f3;
+  int64_t f0f4_2  = f0_2 * (int64_t) f4;
+  int64_t f0f5_2  = f0_2 * (int64_t) f5;
+  int64_t f0f6_2  = f0_2 * (int64_t) f6;
+  int64_t f0f7_2  = f0_2 * (int64_t) f7;
+  int64_t f0f8_2  = f0_2 * (int64_t) f8;
+  int64_t f0f9_2  = f0_2 * (int64_t) f9;
+  int64_t f1f1_2  = f1_2 * (int64_t) f1;
+  int64_t f1f2_2  = f1_2 * (int64_t) f2;
+  int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+  int64_t f1f4_2  = f1_2 * (int64_t) f4;
+  int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+  int64_t f1f6_2  = f1_2 * (int64_t) f6;
+  int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+  int64_t f1f8_2  = f1_2 * (int64_t) f8;
+  int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+  int64_t f2f2    = f2   * (int64_t) f2;
+  int64_t f2f3_2  = f2_2 * (int64_t) f3;
+  int64_t f2f4_2  = f2_2 * (int64_t) f4;
+  int64_t f2f5_2  = f2_2 * (int64_t) f5;
+  int64_t f2f6_2  = f2_2 * (int64_t) f6;
+  int64_t f2f7_2  = f2_2 * (int64_t) f7;
+  int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+  int64_t f2f9_38 = f2   * (int64_t) f9_38;
+  int64_t f3f3_2  = f3_2 * (int64_t) f3;
+  int64_t f3f4_2  = f3_2 * (int64_t) f4;
+  int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+  int64_t f3f6_2  = f3_2 * (int64_t) f6;
+  int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+  int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+  int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+  int64_t f4f4    = f4   * (int64_t) f4;
+  int64_t f4f5_2  = f4_2 * (int64_t) f5;
+  int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+  int64_t f4f7_38 = f4   * (int64_t) f7_38;
+  int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+  int64_t f4f9_38 = f4   * (int64_t) f9_38;
+  int64_t f5f5_38 = f5   * (int64_t) f5_38;
+  int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+  int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+  int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+  int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+  int64_t f6f6_19 = f6   * (int64_t) f6_19;
+  int64_t f6f7_38 = f6   * (int64_t) f7_38;
+  int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+  int64_t f6f9_38 = f6   * (int64_t) f9_38;
+  int64_t f7f7_38 = f7   * (int64_t) f7_38;
+  int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+  int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+  int64_t f8f8_19 = f8   * (int64_t) f8_19;
+  int64_t f8f9_38 = f8   * (int64_t) f9_38;
+  int64_t f9f9_38 = f9   * (int64_t) f9_38;
+  int64_t h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  int64_t h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  h0 += h0;
+  h1 += h1;
+  h2 += h2;
+  h3 += h3;
+  h4 += h4;
+  h5 += h5;
+  h6 += h6;
+  h7 += h7;
+  h8 += h8;
+  h9 += h9;
+
+  carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+  carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+  carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+  carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+  carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/* From fe_sub.c */
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+static void fe_sub(fe h, const fe f, const fe g) {
+  int32_t f0 = f[0];
+  int32_t f1 = f[1];
+  int32_t f2 = f[2];
+  int32_t f3 = f[3];
+  int32_t f4 = f[4];
+  int32_t f5 = f[5];
+  int32_t f6 = f[6];
+  int32_t f7 = f[7];
+  int32_t f8 = f[8];
+  int32_t f9 = f[9];
+  int32_t g0 = g[0];
+  int32_t g1 = g[1];
+  int32_t g2 = g[2];
+  int32_t g3 = g[3];
+  int32_t g4 = g[4];
+  int32_t g5 = g[5];
+  int32_t g6 = g[6];
+  int32_t g7 = g[7];
+  int32_t g8 = g[8];
+  int32_t g9 = g[9];
+  int32_t h0 = f0 - g0;
+  int32_t h1 = f1 - g1;
+  int32_t h2 = f2 - g2;
+  int32_t h3 = f3 - g3;
+  int32_t h4 = f4 - g4;
+  int32_t h5 = f5 - g5;
+  int32_t h6 = f6 - g6;
+  int32_t h7 = f7 - g7;
+  int32_t h8 = f8 - g8;
+  int32_t h9 = f9 - g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/* From fe_tobytes.c */
+
+/*
+Preconditions:
+  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Write p=2^255-19; q=floor(h/p).
+Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+Proof:
+  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+  Then 0<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.
+*/
+
+static void fe_tobytes(unsigned char *s, const fe h) {
+  int32_t h0 = h[0];
+  int32_t h1 = h[1];
+  int32_t h2 = h[2];
+  int32_t h3 = h[3];
+  int32_t h4 = h[4];
+  int32_t h5 = h[5];
+  int32_t h6 = h[6];
+  int32_t h7 = h[7];
+  int32_t h8 = h[8];
+  int32_t h9 = h[9];
+  int32_t q;
+  int32_t carry0;
+  int32_t carry1;
+  int32_t carry2;
+  int32_t carry3;
+  int32_t carry4;
+  int32_t carry5;
+  int32_t carry6;
+  int32_t carry7;
+  int32_t carry8;
+  int32_t carry9;
+
+  q = (19 * h9 + (((int32_t) 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;
+}
+
+/* From ge_add.c */
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+  fe t0;
+  fe_add(r->X, p->Y, p->X);
+  fe_sub(r->Y, p->Y, p->X);
+  fe_mul(r->Z, r->X, q->YplusX);
+  fe_mul(r->Y, r->Y, q->YminusX);
+  fe_mul(r->T, q->T2d, p->T);
+  fe_mul(r->X, p->Z, q->Z);
+  fe_add(t0, r->X, r->X);
+  fe_sub(r->X, r->Z, r->Y);
+  fe_add(r->Y, r->Z, r->Y);
+  fe_add(r->Z, t0, r->T);
+  fe_sub(r->T, t0, r->T);
+}
+
+/* From ge_double_scalarmult.c, modified */
+
+static void slide(signed char *r, const unsigned char *a) {
+  int i;
+  int b;
+  int k;
+
+  for (i = 0; i < 256; ++i)
+    r[i] = 1 & (a[i >> 3] >> (i & 7));
+
+  for (i = 0; i < 256; ++i) {
+    if (r[i]) {
+      for (b = 1; b <= 6 && i + b < 256; ++b) {
+        if (r[i + b]) {
+          if (r[i] + (r[i + b] << b) <= 15) {
+            r[i] += r[i + b] << b; r[i + b] = 0;
+          } else if (r[i] - (r[i + b] << b) >= -15) {
+            r[i] -= r[i + b] << b;
+            for (k = i + b; k < 256; ++k) {
+              if (!r[k]) {
+                r[k] = 1;
+                break;
+              }
+              r[k] = 0;
+            }
+          } else
+            break;
+        }
+      }
+    }
+  }
+}
+
+void ge_dsm_precomp(ge_dsmp r, const ge_p3 *s) {
+  ge_p1p1 t;
+  ge_p3 s2, u;
+  ge_p3_to_cached(&r[0], s);
+  ge_p3_dbl(&t, s); ge_p1p1_to_p3(&s2, &t);
+  ge_add(&t, &s2, &r[0]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[1], &u);
+  ge_add(&t, &s2, &r[1]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[2], &u);
+  ge_add(&t, &s2, &r[2]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[3], &u);
+  ge_add(&t, &s2, &r[3]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[4], &u);
+  ge_add(&t, &s2, &r[4]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[5], &u);
+  ge_add(&t, &s2, &r[5]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[6], &u);
+  ge_add(&t, &s2, &r[6]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[7], &u);
+}
+
+/*
+r = a * A + b * B
+where a = a[0]+256*a[1]+...+256^31 a[31].
+and b = b[0]+256*b[1]+...+256^31 b[31].
+B is the Ed25519 base point (x,4/5) with x positive.
+*/
+
+void ge_double_scalarmult_base_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) {
+  signed char aslide[256];
+  signed char bslide[256];
+  ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */
+  ge_p1p1 t;
+  ge_p3 u;
+  int i;
+
+  slide(aslide, a);
+  slide(bslide, b);
+  ge_dsm_precomp(Ai, A);
+
+  ge_p2_0(r);
+
+  for (i = 255; i >= 0; --i) {
+    if (aslide[i] || bslide[i]) break;
+  }
+
+  for (; i >= 0; --i) {
+    ge_p2_dbl(&t, r);
+
+    if (aslide[i] > 0) {
+      ge_p1p1_to_p3(&u, &t);
+      ge_add(&t, &u, &Ai[aslide[i]/2]);
+    } else if (aslide[i] < 0) {
+      ge_p1p1_to_p3(&u, &t);
+      ge_sub(&t, &u, &Ai[(-aslide[i])/2]);
+    }
+
+    if (bslide[i] > 0) {
+      ge_p1p1_to_p3(&u, &t);
+      ge_madd(&t, &u, &ge_Bi[bslide[i]/2]);
+    } else if (bslide[i] < 0) {
+      ge_p1p1_to_p3(&u, &t);
+      ge_msub(&t, &u, &ge_Bi[(-bslide[i])/2]);
+    }
+
+    ge_p1p1_to_p2(r, &t);
+  }
+}
+
+/* From ge_frombytes.c, modified */
+
+int ge_frombytes_vartime(ge_p3 *h, const unsigned char *s) {
+  fe u;
+  fe v;
+  fe vxx;
+  fe check;
+
+  /* From fe_frombytes.c */
+
+  int64_t h0 = load_4(s);
+  int64_t h1 = load_3(s + 4) << 6;
+  int64_t h2 = load_3(s + 7) << 5;
+  int64_t h3 = load_3(s + 10) << 3;
+  int64_t h4 = load_3(s + 13) << 2;
+  int64_t h5 = load_4(s + 16);
+  int64_t h6 = load_3(s + 20) << 7;
+  int64_t h7 = load_3(s + 23) << 5;
+  int64_t h8 = load_3(s + 26) << 4;
+  int64_t h9 = (load_3(s + 29) & 8388607) << 2;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  /* Validate the number to be canonical */
+  if (h9 == 33554428 && h8 == 268435440 && h7 == 536870880 && h6 == 2147483520 &&
+    h5 == 4294967295 && h4 == 67108860 && h3 == 134217720 && h2 == 536870880 &&
+    h1 == 1073741760 && h0 >= 4294967277) {
+    return -1;
+  }
+
+  carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  h->Y[0] = h0;
+  h->Y[1] = h1;
+  h->Y[2] = h2;
+  h->Y[3] = h3;
+  h->Y[4] = h4;
+  h->Y[5] = h5;
+  h->Y[6] = h6;
+  h->Y[7] = h7;
+  h->Y[8] = h8;
+  h->Y[9] = h9;
+
+  /* End fe_frombytes.c */
+
+  fe_1(h->Z);
+  fe_sq(u, h->Y);
+  fe_mul(v, u, fe_d);
+  fe_sub(u, u, h->Z);       /* u = y^2-1 */
+  fe_add(v, v, h->Z);       /* v = dy^2+1 */
+
+  fe_divpowm1(h->X, u, v); /* x = uv^3(uv^7)^((q-5)/8) */
+
+  fe_sq(vxx, h->X);
+  fe_mul(vxx, vxx, v);
+  fe_sub(check, vxx, u);    /* vx^2-u */
+  if (fe_isnonzero(check)) {
+    fe_add(check, vxx, u);  /* vx^2+u */
+    if (fe_isnonzero(check)) {
+      return -1;
+    }
+    fe_mul(h->X, h->X, fe_sqrtm1);
+  }
+
+  if (fe_isnegative(h->X) != (s[31] >> 7)) {
+    /* If x = 0, the sign must be positive */
+    if (!fe_isnonzero(h->X)) {
+      return -1;
+    }
+    fe_neg(h->X, h->X);
+  }
+
+  fe_mul(h->T, h->X, h->Y);
+  return 0;
+}
+
+/* From ge_madd.c */
+
+/*
+r = p + q
+*/
+
+static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+  fe t0;
+  fe_add(r->X, p->Y, p->X);
+  fe_sub(r->Y, p->Y, p->X);
+  fe_mul(r->Z, r->X, q->yplusx);
+  fe_mul(r->Y, r->Y, q->yminusx);
+  fe_mul(r->T, q->xy2d, p->T);
+  fe_add(t0, p->Z, p->Z);
+  fe_sub(r->X, r->Z, r->Y);
+  fe_add(r->Y, r->Z, r->Y);
+  fe_add(r->Z, t0, r->T);
+  fe_sub(r->T, t0, r->T);
+}
+
+/* From ge_msub.c */
+
+/*
+r = p - q
+*/
+
+static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+  fe t0;
+  fe_add(r->X, p->Y, p->X);
+  fe_sub(r->Y, p->Y, p->X);
+  fe_mul(r->Z, r->X, q->yminusx);
+  fe_mul(r->Y, r->Y, q->yplusx);
+  fe_mul(r->T, q->xy2d, p->T);
+  fe_add(t0, p->Z, p->Z);
+  fe_sub(r->X, r->Z, r->Y);
+  fe_add(r->Y, r->Z, r->Y);
+  fe_sub(r->Z, t0, r->T);
+  fe_add(r->T, t0, r->T);
+}
+
+/* From ge_p1p1_to_p2.c */
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
+  fe_mul(r->X, p->X, p->T);
+  fe_mul(r->Y, p->Y, p->Z);
+  fe_mul(r->Z, p->Z, p->T);
+}
+
+/* From ge_p1p1_to_p3.c */
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
+  fe_mul(r->X, p->X, p->T);
+  fe_mul(r->Y, p->Y, p->Z);
+  fe_mul(r->Z, p->Z, p->T);
+  fe_mul(r->T, p->X, p->Y);
+}
+
+/* From ge_p2_0.c */
+
+static void ge_p2_0(ge_p2 *h) {
+  fe_0(h->X);
+  fe_1(h->Y);
+  fe_1(h->Z);
+}
+
+/* From ge_p2_dbl.c */
+
+/*
+r = 2 * p
+*/
+
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
+  fe t0;
+  fe_sq(r->X, p->X);
+  fe_sq(r->Z, p->Y);
+  fe_sq2(r->T, p->Z);
+  fe_add(r->Y, p->X, p->Y);
+  fe_sq(t0, r->Y);
+  fe_add(r->Y, r->Z, r->X);
+  fe_sub(r->Z, r->Z, r->X);
+  fe_sub(r->X, t0, r->Y);
+  fe_sub(r->T, r->T, r->Z);
+}
+
+/* From ge_p3_0.c */
+
+static void ge_p3_0(ge_p3 *h) {
+  fe_0(h->X);
+  fe_1(h->Y);
+  fe_1(h->Z);
+  fe_0(h->T);
+}
+
+/* From ge_p3_dbl.c */
+
+/*
+r = 2 * p
+*/
+
+static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
+  ge_p2 q;
+  ge_p3_to_p2(&q, p);
+  ge_p2_dbl(r, &q);
+}
+
+/* From ge_p3_to_cached.c */
+
+/*
+r = p
+*/
+
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
+  fe_add(r->YplusX, p->Y, p->X);
+  fe_sub(r->YminusX, p->Y, p->X);
+  fe_copy(r->Z, p->Z);
+  fe_mul(r->T2d, p->T, fe_d2);
+}
+
+/* From ge_p3_to_p2.c */
+
+/*
+r = p
+*/
+
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
+  fe_copy(r->X, p->X);
+  fe_copy(r->Y, p->Y);
+  fe_copy(r->Z, p->Z);
+}
+
+/* From ge_p3_tobytes.c */
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) {
+  fe recip;
+  fe x;
+  fe y;
+
+  fe_invert(recip, h->Z);
+  fe_mul(x,h->X, recip);
+  fe_mul(y,h->Y, recip);
+  fe_tobytes(s, y);
+  s[31] ^= fe_isnegative(x) << 7;
+}
+
+/* From ge_precomp_0.c */
+
+static void ge_precomp_0(ge_precomp *h) {
+  fe_1(h->yplusx);
+  fe_1(h->yminusx);
+  fe_0(h->xy2d);
+}
+
+/* From ge_scalarmult_base.c */
+
+static unsigned char equal(signed char b, signed char c) {
+  unsigned char ub = b;
+  unsigned char uc = c;
+  unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
+  uint32_t y = x; /* 0: yes; 1..255: no */
+  y -= 1; /* 4294967295: yes; 0..254: no */
+  y >>= 31; /* 1: yes; 0: no */
+  return y;
+}
+
+static unsigned char negative(signed char b) {
+  unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+  x >>= 63; /* 1: yes; 0: no */
+  return x;
+}
+
+static void ge_precomp_cmov(ge_precomp *t, const ge_precomp *u, unsigned char b) {
+  fe_cmov(t->yplusx, u->yplusx, b);
+  fe_cmov(t->yminusx, u->yminusx, b);
+  fe_cmov(t->xy2d, u->xy2d, b);
+}
+
+static void select(ge_precomp *t, int pos, signed char b) {
+  ge_precomp minust;
+  unsigned char bnegative = negative(b);
+  unsigned char babs = b - (((-bnegative) & b) << 1);
+
+  ge_precomp_0(t);
+  ge_precomp_cmov(t, &ge_base[pos][0], equal(babs, 1));
+  ge_precomp_cmov(t, &ge_base[pos][1], equal(babs, 2));
+  ge_precomp_cmov(t, &ge_base[pos][2], equal(babs, 3));
+  ge_precomp_cmov(t, &ge_base[pos][3], equal(babs, 4));
+  ge_precomp_cmov(t, &ge_base[pos][4], equal(babs, 5));
+  ge_precomp_cmov(t, &ge_base[pos][5], equal(babs, 6));
+  ge_precomp_cmov(t, &ge_base[pos][6], equal(babs, 7));
+  ge_precomp_cmov(t, &ge_base[pos][7], equal(babs, 8));
+  fe_copy(minust.yplusx, t->yminusx);
+  fe_copy(minust.yminusx, t->yplusx);
+  fe_neg(minust.xy2d, t->xy2d);
+  ge_precomp_cmov(t, &minust, bnegative);
+}
+
+/*
+h = a * B
+where a = a[0]+256*a[1]+...+256^31 a[31]
+B is the Ed25519 base point (x,4/5) with x positive.
+
+Preconditions:
+  a[31] <= 127
+*/
+
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) {
+  signed char e[64];
+  signed char carry;
+  ge_p1p1 r;
+  ge_p2 s;
+  ge_precomp t;
+  int i;
+
+  for (i = 0;i < 32;++i) {
+    e[2 * i + 0] = (a[i] >> 0) & 15;
+    e[2 * i + 1] = (a[i] >> 4) & 15;
+  }
+  /* each e[i] is between 0 and 15 */
+  /* e[63] is between 0 and 7 */
+
+  carry = 0;
+  for (i = 0;i < 63;++i) {
+    e[i] += carry;
+    carry = e[i] + 8;
+    carry >>= 4;
+    e[i] -= carry << 4;
+  }
+  e[63] += carry;
+  /* each e[i] is between -8 and 8 */
+
+  ge_p3_0(h);
+  for (i = 1;i < 64;i += 2) {
+    select(&t, i / 2, e[i]);
+    ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r);
+  }
+
+  ge_p3_dbl(&r, h);  ge_p1p1_to_p2(&s, &r);
+  ge_p2_dbl(&r, &s); ge_p1p1_to_p2(&s, &r);
+  ge_p2_dbl(&r, &s); ge_p1p1_to_p2(&s, &r);
+  ge_p2_dbl(&r, &s); ge_p1p1_to_p3(h, &r);
+
+  for (i = 0;i < 64;i += 2) {
+    select(&t, i / 2, e[i]);
+    ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r);
+  }
+}
+
+/* From ge_sub.c */
+
+/*
+r = p - q
+*/
+
+static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+  fe t0;
+  fe_add(r->X, p->Y, p->X);
+  fe_sub(r->Y, p->Y, p->X);
+  fe_mul(r->Z, r->X, q->YminusX);
+  fe_mul(r->Y, r->Y, q->YplusX);
+  fe_mul(r->T, q->T2d, p->T);
+  fe_mul(r->X, p->Z, q->Z);
+  fe_add(t0, r->X, r->X);
+  fe_sub(r->X, r->Z, r->Y);
+  fe_add(r->Y, r->Z, r->Y);
+  fe_sub(r->Z, t0, r->T);
+  fe_add(r->T, t0, r->T);
+}
+
+/* From ge_tobytes.c */
+
+void ge_tobytes(unsigned char *s, const ge_p2 *h) {
+  fe recip;
+  fe x;
+  fe y;
+
+  fe_invert(recip, h->Z);
+  fe_mul(x, h->X, recip);
+  fe_mul(y, h->Y, recip);
+  fe_tobytes(s, y);
+  s[31] ^= fe_isnegative(x) << 7;
+}
+
+/* From sc_reduce.c */
+
+/*
+Input:
+  s[0]+256*s[1]+...+256^63*s[63] = s
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = s mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+  Overwrites s in place.
+*/
+
+void sc_reduce(unsigned char *s) {
+  int64_t s0 = 2097151 & load_3(s);
+  int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
+  int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
+  int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
+  int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
+  int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
+  int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
+  int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
+  int64_t s8 = 2097151 & load_3(s + 21);
+  int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
+  int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
+  int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
+  int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
+  int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
+  int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
+  int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
+  int64_t s16 = 2097151 & load_3(s + 42);
+  int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
+  int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
+  int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
+  int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
+  int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
+  int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
+  int64_t s23 = (load_4(s + 60) >> 3);
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+  int64_t carry10;
+  int64_t carry11;
+  int64_t carry12;
+  int64_t carry13;
+  int64_t carry14;
+  int64_t carry15;
+  int64_t carry16;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+  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;
+}
+
+/* New code */
+
+static void fe_divpowm1(fe r, const fe u, const fe v) {
+  fe v3, uv7, t0, t1, t2;
+  int i;
+
+  fe_sq(v3, v);
+  fe_mul(v3, v3, v); /* v3 = v^3 */
+  fe_sq(uv7, v3);
+  fe_mul(uv7, uv7, v);
+  fe_mul(uv7, uv7, u); /* uv7 = uv^7 */
+
+  /*fe_pow22523(uv7, uv7);*/
+
+  /* From fe_pow22523.c */
+
+  fe_sq(t0, uv7);
+  fe_sq(t1, t0);
+  fe_sq(t1, t1);
+  fe_mul(t1, uv7, t1);
+  fe_mul(t0, t0, t1);
+  fe_sq(t0, t0);
+  fe_mul(t0, t1, t0);
+  fe_sq(t1, t0);
+  for (i = 0; i < 4; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t0, t1, t0);
+  fe_sq(t1, t0);
+  for (i = 0; i < 9; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t1, t1, t0);
+  fe_sq(t2, t1);
+  for (i = 0; i < 19; ++i) {
+    fe_sq(t2, t2);
+  }
+  fe_mul(t1, t2, t1);
+  for (i = 0; i < 10; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t0, t1, t0);
+  fe_sq(t1, t0);
+  for (i = 0; i < 49; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t1, t1, t0);
+  fe_sq(t2, t1);
+  for (i = 0; i < 99; ++i) {
+    fe_sq(t2, t2);
+  }
+  fe_mul(t1, t2, t1);
+  for (i = 0; i < 50; ++i) {
+    fe_sq(t1, t1);
+  }
+  fe_mul(t0, t1, t0);
+  fe_sq(t0, t0);
+  fe_sq(t0, t0);
+  fe_mul(t0, t0, uv7);
+
+  /* End fe_pow22523.c */
+  /* t0 = (uv^7)^((q-5)/8) */
+  fe_mul(t0, t0, v3);
+  fe_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */
+}
+
+static void ge_cached_0(ge_cached *r) {
+  fe_1(r->YplusX);
+  fe_1(r->YminusX);
+  fe_1(r->Z);
+  fe_0(r->T2d);
+}
+
+static void ge_cached_cmov(ge_cached *t, const ge_cached *u, unsigned char b) {
+  fe_cmov(t->YplusX, u->YplusX, b);
+  fe_cmov(t->YminusX, u->YminusX, b);
+  fe_cmov(t->Z, u->Z, b);
+  fe_cmov(t->T2d, u->T2d, b);
+}
+
+/* Assumes that a[31] <= 127 */
+void ge_scalarmult(ge_p2 *r, const unsigned char *a, const ge_p3 *A) {
+  signed char e[64];
+  int carry, carry2, i;
+  ge_cached Ai[8]; /* 1 * A, 2 * A, ..., 8 * A */
+  ge_p1p1 t;
+  ge_p3 u;
+
+  carry = 0; /* 0..1 */
+  for (i = 0; i < 31; i++) {
+    carry += a[i]; /* 0..256 */
+    carry2 = (carry + 8) >> 4; /* 0..16 */
+    e[2 * i] = carry - (carry2 << 4); /* -8..7 */
+    carry = (carry2 + 8) >> 4; /* 0..1 */
+    e[2 * i + 1] = carry2 - (carry << 4); /* -8..7 */
+  }
+  carry += a[31]; /* 0..128 */
+  carry2 = (carry + 8) >> 4; /* 0..8 */
+  e[62] = carry - (carry2 << 4); /* -8..7 */
+  e[63] = carry2; /* 0..8 */
+
+  ge_p3_to_cached(&Ai[0], A);
+  for (i = 0; i < 7; i++) {
+    ge_add(&t, A, &Ai[i]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[i + 1], &u);
+  }
+
+  ge_p2_0(r);
+  for (i = 63; i >= 0; i--) {
+    signed char b = e[i];
+    unsigned char bnegative = negative(b);
+    unsigned char babs = b - (((-bnegative) & b) << 1);
+    ge_cached cur, minuscur;
+    ge_p2_dbl(&t, r);
+    ge_p1p1_to_p2(r, &t);
+    ge_p2_dbl(&t, r);
+    ge_p1p1_to_p2(r, &t);
+    ge_p2_dbl(&t, r);
+    ge_p1p1_to_p2(r, &t);
+    ge_p2_dbl(&t, r);
+    ge_p1p1_to_p3(&u, &t);
+    ge_cached_0(&cur);
+    ge_cached_cmov(&cur, &Ai[0], equal(babs, 1));
+    ge_cached_cmov(&cur, &Ai[1], equal(babs, 2));
+    ge_cached_cmov(&cur, &Ai[2], equal(babs, 3));
+    ge_cached_cmov(&cur, &Ai[3], equal(babs, 4));
+    ge_cached_cmov(&cur, &Ai[4], equal(babs, 5));
+    ge_cached_cmov(&cur, &Ai[5], equal(babs, 6));
+    ge_cached_cmov(&cur, &Ai[6], equal(babs, 7));
+    ge_cached_cmov(&cur, &Ai[7], equal(babs, 8));
+    fe_copy(minuscur.YplusX, cur.YminusX);
+    fe_copy(minuscur.YminusX, cur.YplusX);
+    fe_copy(minuscur.Z, cur.Z);
+    fe_neg(minuscur.T2d, cur.T2d);
+    ge_cached_cmov(&cur, &minuscur, bnegative);
+    ge_add(&t, &u, &cur);
+    ge_p1p1_to_p2(r, &t);
+  }
+}
+
+void ge_double_scalarmult_precomp_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b, const ge_dsmp Bi) {
+  signed char aslide[256];
+  signed char bslide[256];
+  ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */
+  ge_p1p1 t;
+  ge_p3 u;
+  int i;
+
+  slide(aslide, a);
+  slide(bslide, b);
+  ge_dsm_precomp(Ai, A);
+
+  ge_p2_0(r);
+
+  for (i = 255; i >= 0; --i) {
+    if (aslide[i] || bslide[i]) break;
+  }
+
+  for (; i >= 0; --i) {
+    ge_p2_dbl(&t, r);
+
+    if (aslide[i] > 0) {
+      ge_p1p1_to_p3(&u, &t);
+      ge_add(&t, &u, &Ai[aslide[i]/2]);
+    } else if (aslide[i] < 0) {
+      ge_p1p1_to_p3(&u, &t);
+      ge_sub(&t, &u, &Ai[(-aslide[i])/2]);
+    }
+
+    if (bslide[i] > 0) {
+      ge_p1p1_to_p3(&u, &t);
+      ge_add(&t, &u, &Bi[bslide[i]/2]);
+    } else if (bslide[i] < 0) {
+      ge_p1p1_to_p3(&u, &t);
+      ge_sub(&t, &u, &Bi[(-bslide[i])/2]);
+    }
+
+    ge_p1p1_to_p2(r, &t);
+  }
+}
+
+void ge_mul8(ge_p1p1 *r, const ge_p2 *t) {
+  ge_p2 u;
+  ge_p2_dbl(r, t);
+  ge_p1p1_to_p2(&u, r);
+  ge_p2_dbl(r, &u);
+  ge_p1p1_to_p2(&u, r);
+  ge_p2_dbl(r, &u);
+}
+
+void ge_fromfe_frombytes_vartime(ge_p2 *r, const unsigned char *s) {
+  fe u, v, w, x, y, z;
+  unsigned char sign;
+
+  /* From fe_frombytes.c */
+
+  int64_t h0 = load_4(s);
+  int64_t h1 = load_3(s + 4) << 6;
+  int64_t h2 = load_3(s + 7) << 5;
+  int64_t h3 = load_3(s + 10) << 3;
+  int64_t h4 = load_3(s + 13) << 2;
+  int64_t h5 = load_4(s + 16);
+  int64_t h6 = load_3(s + 20) << 7;
+  int64_t h7 = load_3(s + 23) << 5;
+  int64_t h8 = load_3(s + 26) << 4;
+  int64_t h9 = load_3(s + 29) << 2;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+
+  carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  u[0] = h0;
+  u[1] = h1;
+  u[2] = h2;
+  u[3] = h3;
+  u[4] = h4;
+  u[5] = h5;
+  u[6] = h6;
+  u[7] = h7;
+  u[8] = h8;
+  u[9] = h9;
+
+  /* End fe_frombytes.c */
+
+  fe_sq2(v, u); /* 2 * u^2 */
+  fe_1(w);
+  fe_add(w, v, w); /* w = 2 * u^2 + 1 */
+  fe_sq(x, w); /* w^2 */
+  fe_mul(y, fe_ma2, v); /* -2 * A^2 * u^2 */
+  fe_add(x, x, y); /* x = w^2 - 2 * A^2 * u^2 */
+  fe_divpowm1(r->X, w, x); /* (w / x)^(m + 1) */
+  fe_sq(y, r->X);
+  fe_mul(x, y, x);
+  fe_sub(y, w, x);
+  fe_copy(z, fe_ma);
+  if (fe_isnonzero(y)) {
+    fe_add(y, w, x);
+    if (fe_isnonzero(y)) {
+      goto negative;
+    } else {
+      fe_mul(r->X, r->X, fe_fffb1);
+    }
+  } else {
+    fe_mul(r->X, r->X, fe_fffb2);
+  }
+  fe_mul(r->X, r->X, u); /* u * sqrt(2 * A * (A + 2) * w / x) */
+  fe_mul(z, z, v); /* -2 * A * u^2 */
+  sign = 0;
+  goto setsign;
+negative:
+  fe_mul(x, x, fe_sqrtm1);
+  fe_sub(y, w, x);
+  if (fe_isnonzero(y)) {
+    assert((fe_add(y, w, x), !fe_isnonzero(y)));
+    fe_mul(r->X, r->X, fe_fffb3);
+  } else {
+    fe_mul(r->X, r->X, fe_fffb4);
+  }
+  /* r->X = sqrt(A * (A + 2) * w / x) */
+  /* z = -A */
+  sign = 1;
+setsign:
+  if (fe_isnegative(r->X) != sign) {
+    assert(fe_isnonzero(r->X));
+    fe_neg(r->X, r->X);
+  }
+  fe_add(r->Z, z, w);
+  fe_sub(r->Y, z, w);
+  fe_mul(r->X, r->X, r->Z);
+#if !defined(NDEBUG)
+  {
+    fe check_x, check_y, check_iz, check_v;
+    fe_invert(check_iz, r->Z);
+    fe_mul(check_x, r->X, check_iz);
+    fe_mul(check_y, r->Y, check_iz);
+    fe_sq(check_x, check_x);
+    fe_sq(check_y, check_y);
+    fe_mul(check_v, check_x, check_y);
+    fe_mul(check_v, fe_d, check_v);
+    fe_add(check_v, check_v, check_x);
+    fe_sub(check_v, check_v, check_y);
+    fe_1(check_x);
+    fe_add(check_v, check_v, check_x);
+    assert(!fe_isnonzero(check_v));
+  }
+#endif
+}
+
+void sc_0(unsigned char *s) {
+  int i;
+  for (i = 0; i < 32; i++) {
+    s[i] = 0;
+  }
+}
+
+void sc_reduce32(unsigned char *s) {
+  int64_t s0 = 2097151 & load_3(s);
+  int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
+  int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
+  int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
+  int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
+  int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
+  int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
+  int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
+  int64_t s8 = 2097151 & load_3(s + 21);
+  int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
+  int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
+  int64_t s11 = (load_4(s + 28) >> 7);
+  int64_t s12 = 0;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+  int64_t carry10;
+  int64_t carry11;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  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;
+}
+
+void sc_add(unsigned char *s, const unsigned char *a, const unsigned char *b) {
+  int64_t a0 = 2097151 & load_3(a);
+  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+  int64_t a8 = 2097151 & load_3(a + 21);
+  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+  int64_t a11 = (load_4(a + 28) >> 7);
+  int64_t b0 = 2097151 & load_3(b);
+  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+  int64_t b8 = 2097151 & load_3(b + 21);
+  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+  int64_t b11 = (load_4(b + 28) >> 7);
+  int64_t s0 = a0 + b0;
+  int64_t s1 = a1 + b1;
+  int64_t s2 = a2 + b2;
+  int64_t s3 = a3 + b3;
+  int64_t s4 = a4 + b4;
+  int64_t s5 = a5 + b5;
+  int64_t s6 = a6 + b6;
+  int64_t s7 = a7 + b7;
+  int64_t s8 = a8 + b8;
+  int64_t s9 = a9 + b9;
+  int64_t s10 = a10 + b10;
+  int64_t s11 = a11 + b11;
+  int64_t s12 = 0;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+  int64_t carry10;
+  int64_t carry11;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  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;
+}
+
+void sc_sub(unsigned char *s, const unsigned char *a, const unsigned char *b) {
+  int64_t a0 = 2097151 & load_3(a);
+  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+  int64_t a8 = 2097151 & load_3(a + 21);
+  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+  int64_t a11 = (load_4(a + 28) >> 7);
+  int64_t b0 = 2097151 & load_3(b);
+  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+  int64_t b8 = 2097151 & load_3(b + 21);
+  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+  int64_t b11 = (load_4(b + 28) >> 7);
+  int64_t s0 = a0 - b0;
+  int64_t s1 = a1 - b1;
+  int64_t s2 = a2 - b2;
+  int64_t s3 = a3 - b3;
+  int64_t s4 = a4 - b4;
+  int64_t s5 = a5 - b5;
+  int64_t s6 = a6 - b6;
+  int64_t s7 = a7 - b7;
+  int64_t s8 = a8 - b8;
+  int64_t s9 = a9 - b9;
+  int64_t s10 = a10 - b10;
+  int64_t s11 = a11 - b11;
+  int64_t s12 = 0;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+  int64_t carry10;
+  int64_t carry11;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  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;
+}
+
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+  c[0]+256*c[1]+...+256^31*c[31] = c
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (c-ab) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_mulsub(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) {
+  int64_t a0 = 2097151 & load_3(a);
+  int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+  int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+  int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+  int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+  int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+  int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+  int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+  int64_t a8 = 2097151 & load_3(a + 21);
+  int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+  int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+  int64_t a11 = (load_4(a + 28) >> 7);
+  int64_t b0 = 2097151 & load_3(b);
+  int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+  int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+  int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+  int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+  int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+  int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+  int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+  int64_t b8 = 2097151 & load_3(b + 21);
+  int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+  int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+  int64_t b11 = (load_4(b + 28) >> 7);
+  int64_t c0 = 2097151 & load_3(c);
+  int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
+  int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
+  int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
+  int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
+  int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
+  int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
+  int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
+  int64_t c8 = 2097151 & load_3(c + 21);
+  int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
+  int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
+  int64_t c11 = (load_4(c + 28) >> 7);
+  int64_t s0;
+  int64_t s1;
+  int64_t s2;
+  int64_t s3;
+  int64_t s4;
+  int64_t s5;
+  int64_t s6;
+  int64_t s7;
+  int64_t s8;
+  int64_t s9;
+  int64_t s10;
+  int64_t s11;
+  int64_t s12;
+  int64_t s13;
+  int64_t s14;
+  int64_t s15;
+  int64_t s16;
+  int64_t s17;
+  int64_t s18;
+  int64_t s19;
+  int64_t s20;
+  int64_t s21;
+  int64_t s22;
+  int64_t s23;
+  int64_t carry0;
+  int64_t carry1;
+  int64_t carry2;
+  int64_t carry3;
+  int64_t carry4;
+  int64_t carry5;
+  int64_t carry6;
+  int64_t carry7;
+  int64_t carry8;
+  int64_t carry9;
+  int64_t carry10;
+  int64_t carry11;
+  int64_t carry12;
+  int64_t carry13;
+  int64_t carry14;
+  int64_t carry15;
+  int64_t carry16;
+  int64_t carry17;
+  int64_t carry18;
+  int64_t carry19;
+  int64_t carry20;
+  int64_t carry21;
+  int64_t carry22;
+
+  s0 = c0 - a0*b0;
+  s1 = c1 - (a0*b1 + a1*b0);
+  s2 = c2 - (a0*b2 + a1*b1 + a2*b0);
+  s3 = c3 - (a0*b3 + a1*b2 + a2*b1 + a3*b0);
+  s4 = c4 - (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0);
+  s5 = c5 - (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0);
+  s6 = c6 - (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0);
+  s7 = c7 - (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0);
+  s8 = c8 - (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0);
+  s9 = c9 - (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0);
+  s10 = c10 - (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0);
+  s11 = c11 - (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0);
+  s12 = -(a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1);
+  s13 = -(a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2);
+  s14 = -(a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3);
+  s15 = -(a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4);
+  s16 = -(a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5);
+  s17 = -(a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6);
+  s18 = -(a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7);
+  s19 = -(a8*b11 + a9*b10 + a10*b9 + a11*b8);
+  s20 = -(a9*b11 + a10*b10 + a11*b9);
+  s21 = -(a10*b11 + a11*b10);
+  s22 = -a11*b11;
+  s23 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+  carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
+  carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
+  carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+  carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
+  carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
+  carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+  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;
+}
+
+/* Assumes that a != INT64_MIN */
+static int64_t signum(int64_t a) {
+  return (a >> 63) - ((-a) >> 63);
+}
+
+int sc_check(const unsigned char *s) {
+  int64_t s0 = load_4(s);
+  int64_t s1 = load_4(s + 4);
+  int64_t s2 = load_4(s + 8);
+  int64_t s3 = load_4(s + 12);
+  int64_t s4 = load_4(s + 16);
+  int64_t s5 = load_4(s + 20);
+  int64_t s6 = load_4(s + 24);
+  int64_t s7 = load_4(s + 28);
+  return (signum(1559614444 - s0) + (signum(1477600026 - s1) << 1) + (signum(2734136534 - s2) << 2) + (signum(350157278 - s3) << 3) + (signum(-s4) << 4) + (signum(-s5) << 5) + (signum(-s6) << 6) + (signum(268435456 - s7) << 7)) >> 8;
+}
+
+int sc_isnonzero(const unsigned char *s) {
+  return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] |
+    s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] |
+    s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] |
+    s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1;
+}
+\ No newline at end of file
diff --git a/src/crypto/crypto-ops.h b/src/crypto/crypto-ops.h
new file mode 100644
index 000000000..3c253bb5e
--- /dev/null
+++ b/src/crypto/crypto-ops.h
@@ -0,0 +1,115 @@
+#pragma once
+
+/* From fe.h */
+
+typedef int32_t fe[10];
+
+/* From ge.h */
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+} ge_p2;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p3;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p1p1;
+
+typedef struct {
+  fe yplusx;
+  fe yminusx;
+  fe xy2d;
+} ge_precomp;
+
+typedef struct {
+  fe YplusX;
+  fe YminusX;
+  fe Z;
+  fe T2d;
+} ge_cached;
+
+/* From ge_add.c */
+
+void ge_add(ge_p1p1 *, const ge_p3 *, const ge_cached *);
+
+/* From ge_double_scalarmult.c, modified */
+
+typedef ge_cached ge_dsmp[8];
+extern const ge_precomp ge_Bi[8];
+void ge_dsm_precomp(ge_dsmp r, const ge_p3 *s);
+void ge_double_scalarmult_base_vartime(ge_p2 *, const unsigned char *, const ge_p3 *, const unsigned char *);
+
+/* 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 */
+\ No newline at end of file
diff --git a/src/crypto/crypto.cpp b/src/crypto/crypto.cpp
new file mode 100644
index 000000000..020e413e9
--- /dev/null
+++ b/src/crypto/crypto.cpp
@@ -0,0 +1,245 @@
+#include <alloca.h>
+#include <cassert>
+#include <cstddef>
+#include <cstdint>
+#include <cstdlib>
+#include <cstring>
+#include <memory>
+
+#include "crypto.h"
+#include "random.h"
+
+namespace crypto {
+
+  using std::abort;
+  using std::int32_t;
+  using std::int64_t;
+  using std::size_t;
+  using std::uint32_t;
+  using std::uint64_t;
+
+  extern "C" {
+#include "crypto-ops.h"
+  }
+
+  static inline unsigned char *operator &(ec_point &point) {
+    return &reinterpret_cast<unsigned char &>(point);
+  }
+
+  static inline const unsigned char *operator &(const ec_point &point) {
+    return &reinterpret_cast<const unsigned char &>(point);
+  }
+
+  static inline unsigned char *operator &(ec_scalar &scalar) {
+    return &reinterpret_cast<unsigned char &>(scalar);
+  }
+
+  static inline const unsigned char *operator &(const ec_scalar &scalar) {
+    return &reinterpret_cast<const unsigned char &>(scalar);
+  }
+
+  static inline void random_scalar(ec_scalar &res) {
+    unsigned char tmp[64];
+    generate_random_bytes(64, tmp);
+    sc_reduce(tmp);
+    memcpy(&res, tmp, 32);
+  }
+
+  static inline void hash_to_scalar(const void *data, size_t length, ec_scalar &res) {
+    keccak(data, length, reinterpret_cast<hash &>(res));
+    sc_reduce32(&res);
+  }
+
+  void crypto_ops::generate_keys(public_key &pub, secret_key &sec) {
+    ge_p3 point;
+    random_scalar(sec);
+    ge_scalarmult_base(&point, &sec);
+    ge_p3_tobytes(&pub, &point);
+  }
+
+  bool crypto_ops::check_key(const public_key &key) {
+    ge_p3 point;
+    return ge_frombytes_vartime(&point, &key) == 0;
+  }
+
+  struct s_comm {
+    hash h;
+    ec_point key;
+    ec_point comm;
+  };
+
+  void crypto_ops::generate_signature(const hash &message_hash, const public_key &pub, const secret_key &sec, signature &sig) {
+    ge_p3 tmp3;
+    ec_scalar k;
+    s_comm buf;
+#if !defined(NDEBUG)
+    {
+      ge_p3 t;
+      public_key t2;
+      assert(sc_check(&sec) == 0);
+      ge_scalarmult_base(&t, &sec);
+      ge_p3_tobytes(&t2, &t);
+      assert(pub == t2);
+    }
+#endif
+    buf.h = message_hash;
+    buf.key = pub;
+    random_scalar(k);
+    ge_scalarmult_base(&tmp3, &k);
+    ge_p3_tobytes(&buf.comm, &tmp3);
+    hash_to_scalar(&buf, sizeof(s_comm), sig.c);
+    sc_mulsub(&sig.r, &sig.c, &sec, &k);
+  }
+
+  bool crypto_ops::check_signature(const hash &message_hash, const public_key &pub, const signature &sig) {
+    ge_p2 tmp2;
+    ge_p3 tmp3;
+    ec_scalar c;
+    s_comm buf;
+    assert(check_key(pub));
+    buf.h = message_hash;
+    buf.key = pub;
+    if (ge_frombytes_vartime(&tmp3, &pub) != 0) {
+      abort();
+    }
+    if (sc_check(&sig.c) != 0 || sc_check(&sig.r) != 0) {
+      return false;
+    }
+    ge_double_scalarmult_base_vartime(&tmp2, &sig.c, &tmp3, &sig.r);
+    ge_tobytes(&buf.comm, &tmp2);
+    hash_to_scalar(&buf, sizeof(s_comm), c);
+    sc_sub(&c, &c, &sig.c);
+    return sc_isnonzero(&c) == 0;
+  }
+
+  static void hash_to_ec(const public_key &key, ge_p3 &res) {
+    hash h;
+    ge_p2 point;
+    ge_p1p1 point2;
+    keccak(std::addressof(key), sizeof(public_key), h);
+    ge_fromfe_frombytes_vartime(&point, reinterpret_cast<const unsigned char *>(&h));
+    ge_mul8(&point2, &point);
+    ge_p1p1_to_p3(&res, &point2);
+  }
+
+  void crypto_ops::generate_key_image(const public_key &pub, const secret_key &sec, key_image &image) {
+    ge_p3 point;
+    ge_p2 point2;
+    assert(sc_check(&sec) == 0);
+    hash_to_ec(pub, point);
+    ge_scalarmult(&point2, &sec, &point);
+    ge_tobytes(&image, &point2);
+  }
+
+  struct rs_comm {
+    hash h;
+    struct {
+      ec_point a, b;
+    } ab[];
+  };
+
+  static inline size_t rs_comm_size(size_t pubs_count) {
+    return sizeof(rs_comm) + pubs_count * sizeof(rs_comm().ab[0]);
+  }
+
+  void crypto_ops::generate_ring_signature(const hash &message_hash, const key_image &image,
+    const public_key *const *pubs, size_t pubs_count,
+    const secret_key &sec, size_t sec_index,
+    signature *sig) {
+    size_t i;
+    ge_p3 image_unp;
+    ge_dsmp image_pre;
+    ec_scalar sum, k, h;
+    rs_comm *const buf = reinterpret_cast<rs_comm *>(alloca(rs_comm_size(pubs_count)));
+    assert(sec_index < pubs_count);
+#if !defined(NDEBUG)
+    {
+      ge_p3 t;
+      public_key t2;
+      key_image t3;
+      assert(sc_check(&sec) == 0);
+      ge_scalarmult_base(&t, &sec);
+      ge_p3_tobytes(&t2, &t);
+      assert(*pubs[sec_index] == t2);
+      generate_key_image(*pubs[sec_index], sec, t3);
+      assert(image == t3);
+      for (i = 0; i < pubs_count; i++) {
+        assert(check_key(*pubs[i]));
+      }
+    }
+#endif
+    if (ge_frombytes_vartime(&image_unp, &image) != 0) {
+      abort();
+    }
+    ge_dsm_precomp(image_pre, &image_unp);
+    sc_0(&sum);
+    buf->h = message_hash;
+    for (i = 0; i < pubs_count; i++) {
+      ge_p2 tmp2;
+      ge_p3 tmp3;
+      if (i == sec_index) {
+        random_scalar(k);
+        ge_scalarmult_base(&tmp3, &k);
+        ge_p3_tobytes(&buf->ab[i].a, &tmp3);
+        hash_to_ec(*pubs[i], tmp3);
+        ge_scalarmult(&tmp2, &k, &tmp3);
+        ge_tobytes(&buf->ab[i].b, &tmp2);
+      } else {
+        random_scalar(sig[i].c);
+        random_scalar(sig[i].r);
+        if (ge_frombytes_vartime(&tmp3, &*pubs[i]) != 0) {
+          abort();
+        }
+        ge_double_scalarmult_base_vartime(&tmp2, &sig[i].c, &tmp3, &sig[i].r);
+        ge_tobytes(&buf->ab[i].a, &tmp2);
+        hash_to_ec(*pubs[i], tmp3);
+        ge_double_scalarmult_precomp_vartime(&tmp2, &sig[i].r, &tmp3, &sig[i].c, image_pre);
+        ge_tobytes(&buf->ab[i].b, &tmp2);
+        sc_add(&sum, &sum, &sig[i].c);
+      }
+    }
+    hash_to_scalar(buf, rs_comm_size(pubs_count), h);
+    sc_sub(&sig[sec_index].c, &h, &sum);
+    sc_mulsub(&sig[sec_index].r, &sig[sec_index].c, &sec, &k);
+  }
+
+  bool crypto_ops::check_ring_signature(const hash &message_hash, const key_image &image,
+    const public_key *const *pubs, size_t pubs_count,
+    const signature *sig) {
+    size_t i;
+    ge_p3 image_unp;
+    ge_dsmp image_pre;
+    ec_scalar sum, h;
+    rs_comm *const buf = reinterpret_cast<rs_comm *>(alloca(rs_comm_size(pubs_count)));
+#if !defined(NDEBUG)
+    for (i = 0; i < pubs_count; i++) {
+      assert(check_key(*pubs[i]));
+    }
+#endif
+    if (ge_frombytes_vartime(&image_unp, &image) != 0) {
+      return false;
+    }
+    ge_dsm_precomp(image_pre, &image_unp);
+    sc_0(&sum);
+    buf->h = message_hash;
+    for (i = 0; i < pubs_count; i++) {
+      ge_p2 tmp2;
+      ge_p3 tmp3;
+      if (sc_check(&sig[i].c) != 0 || sc_check(&sig[i].r) != 0) {
+        return false;
+      }
+      if (ge_frombytes_vartime(&tmp3, &*pubs[i]) != 0) {
+        abort();
+      }
+      ge_double_scalarmult_base_vartime(&tmp2, &sig[i].c, &tmp3, &sig[i].r);
+      ge_tobytes(&buf->ab[i].a, &tmp2);
+      hash_to_ec(*pubs[i], tmp3);
+      ge_double_scalarmult_precomp_vartime(&tmp2, &sig[i].r, &tmp3, &sig[i].c, image_pre);
+      ge_tobytes(&buf->ab[i].b, &tmp2);
+      sc_add(&sum, &sum, &sig[i].c);
+    }
+    hash_to_scalar(buf, rs_comm_size(pubs_count), h);
+    sc_sub(&h, &h, &sum);
+    return sc_isnonzero(&h) == 0;
+  }
+}
+\ No newline at end of file
diff --git a/src/crypto/crypto.h b/src/crypto/crypto.h
new file mode 100644
index 000000000..2dd2085ce
--- /dev/null
+++ b/src/crypto/crypto.h
@@ -0,0 +1,166 @@
+#pragma once
+
+#include <cstddef>
+#include <cstring>
+
+namespace crypto {
+
+#pragma pack(push, 1)
+  class hash {
+    char data[32];
+  };
+
+  class ec_point {
+    char data[32];
+  };
+
+  class ec_scalar {
+    char data[32];
+  };
+
+  class public_key: ec_point {
+    friend class crypto_ops;
+  };
+
+  class secret_key: ec_scalar {
+    friend class crypto_ops;
+  };
+
+  class key_image: ec_point {
+    friend class crypto_ops;
+  };
+
+  class signature {
+    ec_scalar c, r;
+    friend class crypto_ops;
+  };
+#pragma pack(pop)
+
+  static_assert(sizeof(hash) == 32 && sizeof(ec_point) == 32 &&
+    sizeof(ec_scalar) == 32 && sizeof(public_key) == 32 &&
+    sizeof(secret_key) == 32 && sizeof(key_image) == 32 &&
+    sizeof(signature) == 64, "Invalid structure size");
+
+  extern "C" {
+    void keccak(const void *data, std::size_t length, char *hash);
+  }
+
+  inline void keccak(const void *data, std::size_t length, hash &hash) {
+    keccak(data, length, reinterpret_cast<char *>(&hash));
+  }
+
+  inline bool operator==(const hash &a, const hash &b) {
+    return std::memcmp(&a, &b, sizeof(struct hash)) == 0;
+  }
+
+  inline bool operator==(const public_key &a, const public_key &b) {
+    return std::memcmp(&a, &b, sizeof(struct public_key)) == 0;
+  }
+
+  inline bool operator==(const key_image &a, const key_image &b) {
+    return std::memcmp(&a, &b, sizeof(struct key_image)) == 0;
+  }
+
+  class crypto_ops {
+    crypto_ops();
+    crypto_ops(const crypto_ops &);
+    void operator=(const crypto_ops &);
+    ~crypto_ops();
+
+    static void generate_keys(public_key &, secret_key &);
+    friend void generate_keys(public_key &, secret_key &);
+    static bool check_key(const public_key &);
+    friend bool check_key(const public_key &);
+    static void generate_signature(const hash &, const public_key &, const secret_key &, signature &);
+    friend void generate_signature(const hash &, const public_key &, const secret_key &, signature &);
+    static bool check_signature(const hash &, const public_key &, const signature &);
+    friend bool check_signature(const hash &, const public_key &, const signature &);
+    static void generate_key_image(const public_key &, const secret_key &, key_image &);
+    friend void generate_key_image(const public_key &, const secret_key &, key_image &);
+    static void generate_ring_signature(const hash &, const key_image &,
+      const public_key *const *, std::size_t, const secret_key &, std::size_t, signature *);
+    friend void generate_ring_signature(const hash &, const key_image &,
+      const public_key *const *, std::size_t, const secret_key &, std::size_t, signature *);
+    static bool check_ring_signature(const hash &, const key_image &,
+      const public_key *const *, std::size_t, const signature *);
+    friend bool check_ring_signature(const hash &, const key_image &,
+      const public_key *const *, std::size_t, const signature *);
+  };
+
+  /* Generate a new key pair.
+   * pub: a newly generated public key.
+   * sec: a newly generated secret key.
+   */
+  inline void generate_keys(public_key &pub, secret_key &sec) {
+    crypto_ops::generate_keys(pub, sec);
+  }
+
+  /* Check a public key.
+   * key: a key to check.
+   * returns: true if the key is valid, false otherwise.
+   */
+  inline bool check_key(const public_key &key) {
+    return crypto_ops::check_key(key);
+  }
+
+  /* Sign a message.
+   * message_hash: hash of a message.
+   * pub: public key used for signing. Assumed to be valid.
+   * sec: secret key used for signing. Assumed to correspond to pub.
+   * sig: the resulting signature.
+   */
+  inline void generate_signature(const hash &message_hash, const public_key &pub, const secret_key &sec, signature &sig) {
+    crypto_ops::generate_signature(message_hash, pub, sec, sig);
+  }
+
+  /* Verify a signature.
+   * message_hash: hash of a message.
+   * pub: public key used for signing. Assumed to be valid, use check_key to check it first.
+   * sig: a signature.
+   * returns: true if the signature is valid, false otherwise.
+   */
+  inline bool check_signature(const hash &message_hash, const public_key &pub, const signature &sig) {
+    return crypto_ops::check_signature(message_hash, pub, sig);
+  }
+
+  /* Generate the image of a key.
+   * pub: public key used for signing. Assumed to be valid.
+   * sec: secret key used for signing. Assumed to correspond to pub.
+   * image: the resulting key image.
+   */
+  inline void generate_key_image(const public_key &pub, const secret_key &sec, key_image &image) {
+    crypto_ops::generate_key_image(pub, sec, image);
+  }
+
+  /* Sign a message using linkable ring signature.
+   * message_hash: hash of a message.
+   * image: image of the key used for signing. Use generate_key_image to create it. Assumed to correspond to the key used for signing.
+   * pubs: pointer to an array of pointers to public keys of a ring. All keys are assumed to be valid, use check_key to check them first.
+   * pubs_count: number of keys in a ring.
+   * sec: secret key used for signing.
+   * sec_index: index of the key used for signing in pubs. It is assumed that 0 <= sec_index < pubs_count and that sec corresponds to *pubs[sec_index].
+   * sig: the resulting signature (occupies pubs_count elements). To verify it, image of the key is also necessary.
+   */
+  inline void generate_ring_signature(const hash &message_hash, const key_image &image,
+    const public_key *const *pubs, std::size_t pubs_count,
+    const secret_key &sec, std::size_t sec_index,
+    signature *sig) {
+    crypto_ops::generate_ring_signature(message_hash, image, pubs, pubs_count, sec, sec_index, sig);
+  }
+
+  /* Verify a linkable ring signature.
+   * message_hash: hash of a message.
+   * image: image of the key used for signing.
+   * pubs: pointer to an array of pointers to public keys of a ring. All keys are assumed to be valid, use check_key to check them first.
+   * pubs_count: number of keys in a ring.
+   * sig: a signature (occupies pubs_count elements).
+   * returns: true if the signature is valid, false otherwise.
+   */
+  inline bool check_ring_signature(const hash &message_hash, const key_image &image,
+    const public_key *const *pubs, std::size_t pubs_count,
+    const signature *sig) {
+    return crypto_ops::check_ring_signature(message_hash, image, pubs, pubs_count, sig);
+  }
+
+  /* To check whether two signatures are linked, compare their key images. */
+}
+\ No newline at end of file
diff --git a/src/crypto/example.cpp b/src/crypto/example.cpp
new file mode 100644
index 000000000..a8b6b7462
--- /dev/null
+++ b/src/crypto/example.cpp
@@ -0,0 +1,42 @@
+#include <assert.h>
+
+#include "crypto.h"
+#include "random.h"
+
+using namespace crypto;
+
+int main(int argc, char *argv[]) {
+  char message[10];
+  hash mh;
+  public_key pk1, pk2;
+  secret_key sk1, sk2;
+  key_image ki;
+  public_key *ppk[2];
+  signature sig[2];
+  bool res;
+  /* Call this before using functions that depend on randomness. */
+  init_random();
+  /* Generate a random message. */
+  generate_random_bytes(sizeof message, message);
+  /* Find its hash */
+  keccak(message, sizeof message, mh);
+  /* Generate some keys */
+  generate_keys(pk1, sk1);
+  generate_keys(pk2, sk2);
+  /* Sign the message */
+  generate_signature(mh, pk1, sk1, sig[0]);
+  /* Check the signature */
+  res = check_signature(mh, pk1, sig[0]);
+  assert(res);
+  /* Sign the message using ring signature */
+  /* First, generate a key image */
+  generate_key_image(pk2, sk2, ki);
+  /* Then, generate the signature */
+  ppk[0] = &pk1;
+  ppk[1] = &pk2;
+  generate_ring_signature(mh, ki, ppk, 2, sk2, 1, sig);
+  /* Check it */
+  res = check_ring_signature(mh, ki, ppk, 2, sig);
+  assert(res);
+  return 0;
+}
+\ No newline at end of file
diff --git a/src/crypto/hash.c b/src/crypto/hash.c
new file mode 100644
index 000000000..f07ffd661
--- /dev/null
+++ b/src/crypto/hash.c
@@ -0,0 +1,82 @@
+#include <stddef.h>
+#include <stdint.h>
+#include <string.h>
+
+#include "int-util.h"
+#include "hash.h"
+
+static const uint64_t round_constants[] = {
+  0x0000000000000001, 0x0000000000008082, 0x800000000000808a, 0x8000000080008000,
+  0x000000000000808b, 0x0000000080000001, 0x8000000080008081, 0x8000000000008009,
+  0x000000000000008a, 0x0000000000000088, 0x0000000080008009, 0x000000008000000a,
+  0x000000008000808b, 0x800000000000008b, 0x8000000000008089, 0x8000000000008003,
+  0x8000000000008002, 0x8000000000000080, 0x000000000000800a, 0x800000008000000a,
+  0x8000000080008081, 0x8000000000008080, 0x0000000080000001, 0x8000000080008008
+};
+
+static const uint8_t rho_offsets[] = {
+  0, 1, 62, 28, 27,
+  36, 44, 6, 55, 20,
+  3, 10, 43, 25, 39,
+  41, 45, 15, 21, 8,
+  18, 2, 61, 56, 14
+};
+
+static void keccak_round(uint64_t *state, unsigned int i) {
+  unsigned int j, k;
+  uint64_t tmp[25];
+  for(j = 0; j < 5; j++) {
+    tmp[j] = state[j] ^ state[j + 5] ^ state[j + 10] ^ state[j + 15] ^ state[j + 20];
+  }
+  for(j = 0; j < 5; j++) {
+    uint64_t t = rol64(tmp[(j + 1) % 5], 1) ^ tmp[(j + 4) % 5];
+    state[j] ^= t;
+    state[j + 5] ^= t;
+    state[j + 10] ^= t;
+    state[j + 15] ^= t;
+    state[j + 20] ^= t;
+  }
+  for(j = 0; j < 25; j++) {
+    state[j] = rol64(state[j], rho_offsets[j]);
+  }
+#define index(x, y) (((x) % 5) + 5 * ((y) % 5))
+  for(j = 0; j < 5; j++) {
+    for(k = 0; k < 5; k++) {
+      tmp[index(0 * k + 1 * j, 2 * k + 3 * j)] = state[index(k, j)];
+    }
+  }
+  for(j = 0; j < 5; j++) {
+    for(k = 0; k < 5; k++) {
+      state[index(k, j)] = tmp[index(k, j)] ^ ((~tmp[index(k + 1, j)]) & tmp[index(k + 2, j)]);
+    }
+  }
+#undef index
+  state[0] ^= round_constants[i];
+}
+
+void keccak_permutation(struct keccak_state *state) {
+  unsigned int i;
+  mem_inplace_swap64le(&state, 25);
+  for (i = 0; i < 24; i++) {
+    keccak_round(state->w, i);
+  }
+  mem_inplace_swap64le(&state, 25);
+}
+
+void keccak(const void *data, size_t length, char *hash) {
+  struct keccak_state state;
+  const void *limit = cpadd(data, length);
+  size_t i;
+  memset(&state, 0, sizeof(struct keccak_state));
+  for (i = 0; data != limit; ++data) {
+    state.b[i] ^= *(char *) data;
+    if (++i == 136) {
+      keccak_permutation(&state);
+      i = 0;
+    }
+  }
+  state.b[i] ^= 1;
+  state.b[135] ^= 0x80;
+  keccak_permutation(&state);
+  memcpy(hash, &state, 32);
+}
+\ No newline at end of file
diff --git a/src/crypto/hash.h b/src/crypto/hash.h
new file mode 100644
index 000000000..32e8f4701
--- /dev/null
+++ b/src/crypto/hash.h
@@ -0,0 +1,40 @@
+#pragma once
+
+#include <assert.h>
+#include <stdbool.h>
+#include <stddef.h>
+#include <stdint.h>
+
+#include "int-util.h"
+
+static inline void *padd(void *p, size_t i) {
+  return (char *) p + i;
+}
+
+static inline const void *cpadd(const void *p, size_t i) {
+  return (const char *) p + i;
+}
+
+static_assert(sizeof(size_t) == 4 || sizeof(size_t) == 8, "size_t must be 4 or 8 bytes long");
+static inline void place_length(uint8_t *buffer, size_t bufsize, size_t length) {
+  if (sizeof(size_t) == 4) {
+    *(uint32_t *) padd(buffer, bufsize - 4) = swap32be(length);
+  } else {
+    *(uint64_t *) padd(buffer, bufsize - 8) = swap64be(length);
+  }
+}
+
+struct keccak_state {
+  union {
+    uint8_t b[200];
+    uint64_t w[25];
+  };
+};
+
+enum {
+  HASH_SIZE = 32,
+  HASH_DATA_AREA = 136
+};
+
+void keccak(const void *data, size_t length, char *hash);
+void keccak_permutation(struct keccak_state *state);
+\ No newline at end of file
diff --git a/src/crypto/int-util.h b/src/crypto/int-util.h
new file mode 100644
index 000000000..933f2e784
--- /dev/null
+++ b/src/crypto/int-util.h
@@ -0,0 +1,121 @@
+#pragma once
+
+#include <stdint.h>
+#include <string.h>
+#include <sys/param.h>
+
+static inline uint32_t rol32(uint32_t x, int r) {
+	return (x << (r & 31)) | (x >> (-r & 31));
+}
+
+static inline uint64_t rol64(uint64_t x, int r) {
+	return (x << (r & 63)) | (x >> (-r & 63));
+}
+
+#define IDENT32(x) ((uint32_t) (x))
+#define IDENT64(x) ((uint64_t) (x))
+
+#define SWAP32(x) ((((uint32_t) (x) & 0x000000ff) << 24) | \
+                   (((uint32_t) (x) & 0x0000ff00) <<  8) | \
+                   (((uint32_t) (x) & 0x00ff0000) >>  8) | \
+                   (((uint32_t) (x) & 0xff000000) >> 24))
+#define SWAP64(x) ((((uint64_t) (x) & 0x00000000000000ff) << 56) | \
+                   (((uint64_t) (x) & 0x000000000000ff00) << 40) | \
+                   (((uint64_t) (x) & 0x0000000000ff0000) << 24) | \
+                   (((uint64_t) (x) & 0x00000000ff000000) <<  8) | \
+                   (((uint64_t) (x) & 0x000000ff00000000) >>  8) | \
+                   (((uint64_t) (x) & 0x0000ff0000000000) >> 24) | \
+                   (((uint64_t) (x) & 0x00ff000000000000) >> 40) | \
+                   (((uint64_t) (x) & 0xff00000000000000) >> 56))
+
+static inline uint32_t ident32(uint32_t x) { return x; }
+static inline uint64_t ident64(uint64_t x) { return x; }
+
+static inline uint32_t swap32(uint32_t x) {
+	x = ((x & 0x00ff00ff) << 8) | ((x & 0xff00ff00) >> 8);
+	return (x << 16) | (x >> 16);
+}
+static inline uint64_t swap64(uint64_t x) {
+	x = ((x & 0x00ff00ff00ff00ff) <<  8) | ((x & 0xff00ff00ff00ff00) >>  8);
+	x = ((x & 0x0000ffff0000ffff) << 16) | ((x & 0xffff0000ffff0000) >> 16);
+	return (x << 32) | (x >> 32);
+}
+
+#if defined(__GNUC__)
+#define UNUSED __attribute__((unused))
+#else
+#define UNUSED
+#endif
+static inline void mem_inplace_ident(void *mem UNUSED, size_t n UNUSED) { }
+#undef UNUSED
+
+static inline void mem_inplace_swap32(void *mem, size_t n) {
+	size_t i;
+	for (i = 0; i < n; i++) {
+		((uint32_t *) mem)[i] = swap32(((const uint32_t *) mem)[i]);
+	}
+}
+static inline void mem_inplace_swap64(void *mem, size_t n) {
+	size_t i;
+	for (i = 0; i < n; i++) {
+		((uint64_t *) mem)[i] = swap64(((const uint64_t *) mem)[i]);
+	}
+}
+
+static inline void memcpy_ident32(void *dst, const void *src, size_t n) {
+	memcpy(dst, src, 4 * n);
+}
+static inline void memcpy_ident64(void *dst, const void *src, size_t n) {
+	memcpy(dst, src, 8 * n);
+}
+
+static inline void memcpy_swap32(void *dst, const void *src, size_t n) {
+	size_t i;
+	for (i = 0; i < n; i++) {
+		((uint32_t *) dst)[i] = swap32(((const uint32_t *) src)[i]);
+	}
+}
+static inline void memcpy_swap64(void *dst, const void *src, size_t n) {
+	size_t i;
+	for (i = 0; i < n; i++) {
+		((uint64_t *) dst)[i] = swap64(((const uint64_t *) src)[i]);
+	}
+}
+
+#if BYTE_ORDER == LITTLE_ENDIAN
+#define SWAP32LE IDENT32
+#define SWAP32BE SWAP32
+#define swap32le ident32
+#define swap32be swap32
+#define mem_inplace_swap32le mem_inplace_ident
+#define mem_inplace_swap32be mem_inplace_swap32
+#define memcpy_swap32le memcpy_ident32
+#define memcpy_swap32be memcpy_swap32
+#define SWAP64LE IDENT64
+#define SWAP64BE SWAP64
+#define swap64le ident64
+#define swap64be swap64
+#define mem_inplace_swap64le mem_inplace_ident
+#define mem_inplace_swap64be mem_inplace_swap64
+#define memcpy_swap64le memcpy_ident64
+#define memcpy_swap64be memcpy_swap64
+#endif
+
+#if BYTE_ORDER == BIG_ENDIAN
+#define SWAP32BE IDENT32
+#define SWAP32LE SWAP32
+#define swap32be ident32
+#define swap32le swap32
+#define mem_inplace_swap32be mem_inplace_ident
+#define mem_inplace_swap32le mem_inplace_swap32
+#define memcpy_swap32be memcpy_ident32
+#define memcpy_swap32le memcpy_swap32
+#define SWAP64BE IDENT64
+#define SWAP64LE SWAP64
+#define swap64be ident64
+#define swap64le swap64
+#define mem_inplace_swap64be mem_inplace_ident
+#define mem_inplace_swap64le mem_inplace_swap64
+#define memcpy_swap64be memcpy_ident64
+#define memcpy_swap64le memcpy_swap64
+#endif
+\ No newline at end of file
diff --git a/src/crypto/random.c b/src/crypto/random.c
new file mode 100644
index 000000000..582d0b8f6
--- /dev/null
+++ b/src/crypto/random.c
@@ -0,0 +1,62 @@
+#include <assert.h>
+#include <err.h>
+#include <errno.h>
+#include <fcntl.h>
+#include <stddef.h>
+#include <stdlib.h>
+#include <string.h>
+#include <sys/stat.h>
+#include <sys/types.h>
+#include <unistd.h>
+
+#include "hash.h"
+#include "random.h"
+
+static void generate_system_random_bytes(size_t n, void *result) {
+  int fd;
+  if ((fd = open("/dev/urandom", O_RDONLY | O_NOCTTY | O_CLOEXEC)) < 0) {
+    err(EXIT_FAILURE, "open /dev/urandom");
+  }
+  for (;;) {
+    ssize_t res = read(fd, result, n);
+    if ((size_t) res == n) {
+      break;
+    }
+    if (res < 0) {
+      if (errno != EINTR) {
+        err(EXIT_FAILURE, "read /dev/urandom");
+      }
+    } else if (res == 0) {
+      errx(EXIT_FAILURE, "read /dev/urandom: end of file");
+    } else {
+      result = padd(result, (size_t) res);
+      n -= (size_t) res;
+    }
+  }
+  if (close(fd) < 0) {
+    err(EXIT_FAILURE, "close /dev/urandom");
+  }
+}
+
+static struct keccak_state state;
+
+void init_random(void) {
+  generate_system_random_bytes(32, &state);
+}
+
+void generate_random_bytes(size_t n, void *result) {
+  if (n == 0) {
+    return;
+  }
+  for (;;) {
+    keccak_permutation(&state);
+    if (n <= HASH_DATA_AREA) {
+      memcpy(result, &state, n);
+      return;
+    } else {
+      memcpy(result, &state, HASH_DATA_AREA);
+      result = padd(result, HASH_DATA_AREA);
+      n -= HASH_DATA_AREA;
+    }
+  }
+}
+\ No newline at end of file
diff --git a/src/crypto/random.h b/src/crypto/random.h
new file mode 100644
index 000000000..b37963c0f
--- /dev/null
+++ b/src/crypto/random.h
@@ -0,0 +1,19 @@
+#pragma once
+
+#include <stddef.h>
+
+#if defined(__cplusplus)
+#include <type_traits>
+
+namespace crypto {
+
+  extern "C" {
+#endif
+
+  void init_random(void);
+  void generate_random_bytes(size_t n, void *result);
+
+#if defined(__cplusplus)
+  }
+}
+#endif
+\ No newline at end of file
author	amjuarez <amjuarez@users.noreply.github.com>	2013-11-15 02:28:17 +0400
committer	amjuarez <amjuarez@users.noreply.github.com>	2013-11-15 02:28:17 +0400
commit	175d06e75e05aa4a42269dd048516e13b5bd585e (patch)
tree	6828038a2d86174c6041f65187d7521c719606b3 /src/crypto
parent	Initial commit (diff)
download	monero-175d06e75e05aa4a42269dd048516e13b5bd585e.tar.xz