Update vendor (whatsapp)

2 files changed, 0 insertions, 3215 deletions

diff --git a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go
deleted file mode 100644
index e39f086c..00000000
--- a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/const.go
+++ /dev/null
@@ -1,1422 +0,0 @@
-// Copyright 2016 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package edwards25519
-
-// These values are from the public domain, “ref10” implementation of ed25519
-// from SUPERCOP.
-
-// d is a constant in the Edwards curve equation.
-var d = FieldElement{
-	-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116,
-}
-
-// d2 is 2*d.
-var d2 = FieldElement{
-	-21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199,
-}
-
-// SqrtM1 is the square-root of -1 in the field.
-var SqrtM1 = FieldElement{
-	-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482,
-}
-
-// A is a constant in the Montgomery-form of curve25519.
-var A = FieldElement{
-	486662, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-}
-
-// bi contains precomputed multiples of the base-point. See the Ed25519 paper
-// for a discussion about how these values are used.
-var bi = [8]PreComputedGroupElement{
-	{
-		FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
-		FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
-		FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546},
-	},
-	{
-		FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
-		FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
-		FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357},
-	},
-	{
-		FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
-		FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
-		FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942},
-	},
-	{
-		FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
-		FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
-		FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300},
-	},
-	{
-		FieldElement{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877},
-		FieldElement{-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951},
-		FieldElement{4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784},
-	},
-	{
-		FieldElement{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436},
-		FieldElement{25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918},
-		FieldElement{23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877},
-	},
-	{
-		FieldElement{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800},
-		FieldElement{-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305},
-		FieldElement{-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300},
-	},
-	{
-		FieldElement{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876},
-		FieldElement{-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619},
-		FieldElement{-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683},
-	},
-}
-
-// base contains precomputed multiples of the base-point. See the Ed25519 paper
-// for a discussion about how these values are used.
-var base = [32][8]PreComputedGroupElement{
-	{
-		{
-			FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
-			FieldElement{-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
-			FieldElement{-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546},
-		},
-		{
-			FieldElement{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303},
-			FieldElement{-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081},
-			FieldElement{26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697},
-		},
-		{
-			FieldElement{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
-			FieldElement{16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
-			FieldElement{30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357},
-		},
-		{
-			FieldElement{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540},
-			FieldElement{23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397},
-			FieldElement{7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325},
-		},
-		{
-			FieldElement{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
-			FieldElement{4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
-			FieldElement{19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942},
-		},
-		{
-			FieldElement{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777},
-			FieldElement{-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737},
-			FieldElement{-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652},
-		},
-		{
-			FieldElement{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
-			FieldElement{-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
-			FieldElement{28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300},
-		},
-		{
-			FieldElement{14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726},
-			FieldElement{-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955},
-			FieldElement{27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425},
-		},
-	},
-	{
-		{
-			FieldElement{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171},
-			FieldElement{27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510},
-			FieldElement{17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660},
-		},
-		{
-			FieldElement{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639},
-			FieldElement{29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963},
-			FieldElement{5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950},
-		},
-		{
-			FieldElement{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568},
-			FieldElement{12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335},
-			FieldElement{25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628},
-		},
-		{
-			FieldElement{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007},
-			FieldElement{-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772},
-			FieldElement{-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653},
-		},
-		{
-			FieldElement{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567},
-			FieldElement{13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686},
-			FieldElement{21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372},
-		},
-		{
-			FieldElement{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887},
-			FieldElement{-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954},
-			FieldElement{-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953},
-		},
-		{
-			FieldElement{24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833},
-			FieldElement{-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532},
-			FieldElement{-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876},
-		},
-		{
-			FieldElement{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268},
-			FieldElement{33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214},
-			FieldElement{1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038},
-		},
-	},
-	{
-		{
-			FieldElement{6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800},
-			FieldElement{4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645},
-			FieldElement{-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664},
-		},
-		{
-			FieldElement{1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933},
-			FieldElement{-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182},
-			FieldElement{-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222},
-		},
-		{
-			FieldElement{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991},
-			FieldElement{20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880},
-			FieldElement{9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092},
-		},
-		{
-			FieldElement{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295},
-			FieldElement{19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788},
-			FieldElement{8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553},
-		},
-		{
-			FieldElement{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026},
-			FieldElement{11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347},
-			FieldElement{-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033},
-		},
-		{
-			FieldElement{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395},
-			FieldElement{-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278},
-			FieldElement{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890},
-		},
-		{
-			FieldElement{32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995},
-			FieldElement{-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596},
-			FieldElement{-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891},
-		},
-		{
-			FieldElement{31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060},
-			FieldElement{11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608},
-			FieldElement{-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606},
-		},
-	},
-	{
-		{
-			FieldElement{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389},
-			FieldElement{-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016},
-			FieldElement{-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341},
-		},
-		{
-			FieldElement{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505},
-			FieldElement{14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553},
-			FieldElement{-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655},
-		},
-		{
-			FieldElement{15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220},
-			FieldElement{12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631},
-			FieldElement{-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099},
-		},
-		{
-			FieldElement{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556},
-			FieldElement{14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749},
-			FieldElement{236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930},
-		},
-		{
-			FieldElement{1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391},
-			FieldElement{5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253},
-			FieldElement{20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066},
-		},
-		{
-			FieldElement{24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958},
-			FieldElement{-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082},
-			FieldElement{-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383},
-		},
-		{
-			FieldElement{-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521},
-			FieldElement{-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807},
-			FieldElement{23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948},
-		},
-		{
-			FieldElement{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134},
-			FieldElement{-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455},
-			FieldElement{27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629},
-		},
-	},
-	{
-		{
-			FieldElement{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069},
-			FieldElement{-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746},
-			FieldElement{24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919},
-		},
-		{
-			FieldElement{11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837},
-			FieldElement{8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906},
-			FieldElement{-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771},
-		},
-		{
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-			FieldElement{-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376},
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-			FieldElement{-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958},
-			FieldElement{-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577},
-		},
-		{
-			FieldElement{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743},
-			FieldElement{29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684},
-			FieldElement{-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476},
-		},
-	},
-}
diff --git a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go b/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go
deleted file mode 100644
index fd03c252..00000000
--- a/vendor/golang.org/x/crypto/ed25519/internal/edwards25519/edwards25519.go
+++ /dev/null
@@ -1,1793 +0,0 @@
-// Copyright 2016 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package edwards25519
-
-import "encoding/binary"
-
-// This code is a port of the public domain, “ref10” implementation of ed25519
-// from SUPERCOP.
-
-// FieldElement represents an element of the field GF(2^255 - 19).  An element
-// t, entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
-// t[3]+2^102 t[4]+...+2^230 t[9].  Bounds on each t[i] vary depending on
-// context.
-type FieldElement [10]int32
-
-var zero FieldElement
-
-func FeZero(fe *FieldElement) {
-	copy(fe[:], zero[:])
-}
-
-func FeOne(fe *FieldElement) {
-	FeZero(fe)
-	fe[0] = 1
-}
-
-func FeAdd(dst, a, b *FieldElement) {
-	dst[0] = a[0] + b[0]
-	dst[1] = a[1] + b[1]
-	dst[2] = a[2] + b[2]
-	dst[3] = a[3] + b[3]
-	dst[4] = a[4] + b[4]
-	dst[5] = a[5] + b[5]
-	dst[6] = a[6] + b[6]
-	dst[7] = a[7] + b[7]
-	dst[8] = a[8] + b[8]
-	dst[9] = a[9] + b[9]
-}
-
-func FeSub(dst, a, b *FieldElement) {
-	dst[0] = a[0] - b[0]
-	dst[1] = a[1] - b[1]
-	dst[2] = a[2] - b[2]
-	dst[3] = a[3] - b[3]
-	dst[4] = a[4] - b[4]
-	dst[5] = a[5] - b[5]
-	dst[6] = a[6] - b[6]
-	dst[7] = a[7] - b[7]
-	dst[8] = a[8] - b[8]
-	dst[9] = a[9] - b[9]
-}
-
-func FeCopy(dst, src *FieldElement) {
-	copy(dst[:], src[:])
-}
-
-// Replace (f,g) with (g,g) if b == 1;
-// replace (f,g) with (f,g) if b == 0.
-//
-// Preconditions: b in {0,1}.
-func FeCMove(f, g *FieldElement, b int32) {
-	b = -b
-	f[0] ^= b & (f[0] ^ g[0])
-	f[1] ^= b & (f[1] ^ g[1])
-	f[2] ^= b & (f[2] ^ g[2])
-	f[3] ^= b & (f[3] ^ g[3])
-	f[4] ^= b & (f[4] ^ g[4])
-	f[5] ^= b & (f[5] ^ g[5])
-	f[6] ^= b & (f[6] ^ g[6])
-	f[7] ^= b & (f[7] ^ g[7])
-	f[8] ^= b & (f[8] ^ g[8])
-	f[9] ^= b & (f[9] ^ g[9])
-}
-
-func load3(in []byte) int64 {
-	var r int64
-	r = int64(in[0])
-	r |= int64(in[1]) << 8
-	r |= int64(in[2]) << 16
-	return r
-}
-
-func load4(in []byte) int64 {
-	var r int64
-	r = int64(in[0])
-	r |= int64(in[1]) << 8
-	r |= int64(in[2]) << 16
-	r |= int64(in[3]) << 24
-	return r
-}
-
-func FeFromBytes(dst *FieldElement, src *[32]byte) {
-	h0 := load4(src[:])
-	h1 := load3(src[4:]) << 6
-	h2 := load3(src[7:]) << 5
-	h3 := load3(src[10:]) << 3
-	h4 := load3(src[13:]) << 2
-	h5 := load4(src[16:])
-	h6 := load3(src[20:]) << 7
-	h7 := load3(src[23:]) << 5
-	h8 := load3(src[26:]) << 4
-	h9 := (load3(src[29:]) & 8388607) << 2
-
-	FeCombine(dst, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-// FeToBytes marshals h to s.
-// Preconditions:
-//   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,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|<2^230 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.
-func FeToBytes(s *[32]byte, h *FieldElement) {
-	var carry [10]int32
-
-	q := (19*h[9] + (1 << 24)) >> 25
-	q = (h[0] + q) >> 26
-	q = (h[1] + q) >> 25
-	q = (h[2] + q) >> 26
-	q = (h[3] + q) >> 25
-	q = (h[4] + q) >> 26
-	q = (h[5] + q) >> 25
-	q = (h[6] + q) >> 26
-	q = (h[7] + q) >> 25
-	q = (h[8] + q) >> 26
-	q = (h[9] + q) >> 25
-
-	// Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20.
-	h[0] += 19 * q
-	// Goal: Output h-2^255 q, which is between 0 and 2^255-20.
-
-	carry[0] = h[0] >> 26
-	h[1] += carry[0]
-	h[0] -= carry[0] << 26
-	carry[1] = h[1] >> 25
-	h[2] += carry[1]
-	h[1] -= carry[1] << 25
-	carry[2] = h[2] >> 26
-	h[3] += carry[2]
-	h[2] -= carry[2] << 26
-	carry[3] = h[3] >> 25
-	h[4] += carry[3]
-	h[3] -= carry[3] << 25
-	carry[4] = h[4] >> 26
-	h[5] += carry[4]
-	h[4] -= carry[4] << 26
-	carry[5] = h[5] >> 25
-	h[6] += carry[5]
-	h[5] -= carry[5] << 25
-	carry[6] = h[6] >> 26
-	h[7] += carry[6]
-	h[6] -= carry[6] << 26
-	carry[7] = h[7] >> 25
-	h[8] += carry[7]
-	h[7] -= carry[7] << 25
-	carry[8] = h[8] >> 26
-	h[9] += carry[8]
-	h[8] -= carry[8] << 26
-	carry[9] = h[9] >> 25
-	h[9] -= carry[9] << 25
-	// h10 = carry9
-
-	// Goal: Output h[0]+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
-	// Have h[0]+...+2^230 h[9] between 0 and 2^255-1;
-	// evidently 2^255 h10-2^255 q = 0.
-	// Goal: Output h[0]+...+2^230 h[9].
-
-	s[0] = byte(h[0] >> 0)
-	s[1] = byte(h[0] >> 8)
-	s[2] = byte(h[0] >> 16)
-	s[3] = byte((h[0] >> 24) | (h[1] << 2))
-	s[4] = byte(h[1] >> 6)
-	s[5] = byte(h[1] >> 14)
-	s[6] = byte((h[1] >> 22) | (h[2] << 3))
-	s[7] = byte(h[2] >> 5)
-	s[8] = byte(h[2] >> 13)
-	s[9] = byte((h[2] >> 21) | (h[3] << 5))
-	s[10] = byte(h[3] >> 3)
-	s[11] = byte(h[3] >> 11)
-	s[12] = byte((h[3] >> 19) | (h[4] << 6))
-	s[13] = byte(h[4] >> 2)
-	s[14] = byte(h[4] >> 10)
-	s[15] = byte(h[4] >> 18)
-	s[16] = byte(h[5] >> 0)
-	s[17] = byte(h[5] >> 8)
-	s[18] = byte(h[5] >> 16)
-	s[19] = byte((h[5] >> 24) | (h[6] << 1))
-	s[20] = byte(h[6] >> 7)
-	s[21] = byte(h[6] >> 15)
-	s[22] = byte((h[6] >> 23) | (h[7] << 3))
-	s[23] = byte(h[7] >> 5)
-	s[24] = byte(h[7] >> 13)
-	s[25] = byte((h[7] >> 21) | (h[8] << 4))
-	s[26] = byte(h[8] >> 4)
-	s[27] = byte(h[8] >> 12)
-	s[28] = byte((h[8] >> 20) | (h[9] << 6))
-	s[29] = byte(h[9] >> 2)
-	s[30] = byte(h[9] >> 10)
-	s[31] = byte(h[9] >> 18)
-}
-
-func FeIsNegative(f *FieldElement) byte {
-	var s [32]byte
-	FeToBytes(&s, f)
-	return s[0] & 1
-}
-
-func FeIsNonZero(f *FieldElement) int32 {
-	var s [32]byte
-	FeToBytes(&s, f)
-	var x uint8
-	for _, b := range s {
-		x |= b
-	}
-	x |= x >> 4
-	x |= x >> 2
-	x |= x >> 1
-	return int32(x & 1)
-}
-
-// FeNeg sets 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.
-func FeNeg(h, f *FieldElement) {
-	h[0] = -f[0]
-	h[1] = -f[1]
-	h[2] = -f[2]
-	h[3] = -f[3]
-	h[4] = -f[4]
-	h[5] = -f[5]
-	h[6] = -f[6]
-	h[7] = -f[7]
-	h[8] = -f[8]
-	h[9] = -f[9]
-}
-
-func FeCombine(h *FieldElement, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
-	var c0, c1, c2, c3, c4, c5, c6, c7, c8, c9 int64
-
-	/*
-	  |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
-	    i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
-	  |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
-	    i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
-	*/
-
-	c0 = (h0 + (1 << 25)) >> 26
-	h1 += c0
-	h0 -= c0 << 26
-	c4 = (h4 + (1 << 25)) >> 26
-	h5 += c4
-	h4 -= c4 << 26
-	/* |h0| <= 2^25 */
-	/* |h4| <= 2^25 */
-	/* |h1| <= 1.51*2^58 */
-	/* |h5| <= 1.51*2^58 */
-
-	c1 = (h1 + (1 << 24)) >> 25
-	h2 += c1
-	h1 -= c1 << 25
-	c5 = (h5 + (1 << 24)) >> 25
-	h6 += c5
-	h5 -= c5 << 25
-	/* |h1| <= 2^24; from now on fits into int32 */
-	/* |h5| <= 2^24; from now on fits into int32 */
-	/* |h2| <= 1.21*2^59 */
-	/* |h6| <= 1.21*2^59 */
-
-	c2 = (h2 + (1 << 25)) >> 26
-	h3 += c2
-	h2 -= c2 << 26
-	c6 = (h6 + (1 << 25)) >> 26
-	h7 += c6
-	h6 -= c6 << 26
-	/* |h2| <= 2^25; from now on fits into int32 unchanged */
-	/* |h6| <= 2^25; from now on fits into int32 unchanged */
-	/* |h3| <= 1.51*2^58 */
-	/* |h7| <= 1.51*2^58 */
-
-	c3 = (h3 + (1 << 24)) >> 25
-	h4 += c3
-	h3 -= c3 << 25
-	c7 = (h7 + (1 << 24)) >> 25
-	h8 += c7
-	h7 -= c7 << 25
-	/* |h3| <= 2^24; from now on fits into int32 unchanged */
-	/* |h7| <= 2^24; from now on fits into int32 unchanged */
-	/* |h4| <= 1.52*2^33 */
-	/* |h8| <= 1.52*2^33 */
-
-	c4 = (h4 + (1 << 25)) >> 26
-	h5 += c4
-	h4 -= c4 << 26
-	c8 = (h8 + (1 << 25)) >> 26
-	h9 += c8
-	h8 -= c8 << 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| <= 1.51*2^58 */
-
-	c9 = (h9 + (1 << 24)) >> 25
-	h0 += c9 * 19
-	h9 -= c9 << 25
-	/* |h9| <= 2^24; from now on fits into int32 unchanged */
-	/* |h0| <= 1.8*2^37 */
-
-	c0 = (h0 + (1 << 25)) >> 26
-	h1 += c0
-	h0 -= c0 << 26
-	/* |h0| <= 2^25; from now on fits into int32 unchanged */
-	/* |h1| <= 1.01*2^24 */
-
-	h[0] = int32(h0)
-	h[1] = int32(h1)
-	h[2] = int32(h2)
-	h[3] = int32(h3)
-	h[4] = int32(h4)
-	h[5] = int32(h5)
-	h[6] = int32(h6)
-	h[7] = int32(h7)
-	h[8] = int32(h8)
-	h[9] = int32(h9)
-}
-
-// FeMul calculates h = f * g
-// Can overlap h with f or g.
-//
-// Preconditions:
-//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//    |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*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.
-func FeMul(h, f, g *FieldElement) {
-	f0 := int64(f[0])
-	f1 := int64(f[1])
-	f2 := int64(f[2])
-	f3 := int64(f[3])
-	f4 := int64(f[4])
-	f5 := int64(f[5])
-	f6 := int64(f[6])
-	f7 := int64(f[7])
-	f8 := int64(f[8])
-	f9 := int64(f[9])
-
-	f1_2 := int64(2 * f[1])
-	f3_2 := int64(2 * f[3])
-	f5_2 := int64(2 * f[5])
-	f7_2 := int64(2 * f[7])
-	f9_2 := int64(2 * f[9])
-
-	g0 := int64(g[0])
-	g1 := int64(g[1])
-	g2 := int64(g[2])
-	g3 := int64(g[3])
-	g4 := int64(g[4])
-	g5 := int64(g[5])
-	g6 := int64(g[6])
-	g7 := int64(g[7])
-	g8 := int64(g[8])
-	g9 := int64(g[9])
-
-	g1_19 := int64(19 * g[1]) /* 1.4*2^29 */
-	g2_19 := int64(19 * g[2]) /* 1.4*2^30; still ok */
-	g3_19 := int64(19 * g[3])
-	g4_19 := int64(19 * g[4])
-	g5_19 := int64(19 * g[5])
-	g6_19 := int64(19 * g[6])
-	g7_19 := int64(19 * g[7])
-	g8_19 := int64(19 * g[8])
-	g9_19 := int64(19 * g[9])
-
-	h0 := f0*g0 + f1_2*g9_19 + f2*g8_19 + f3_2*g7_19 + f4*g6_19 + f5_2*g5_19 + f6*g4_19 + f7_2*g3_19 + f8*g2_19 + f9_2*g1_19
-	h1 := f0*g1 + f1*g0 + f2*g9_19 + f3*g8_19 + f4*g7_19 + f5*g6_19 + f6*g5_19 + f7*g4_19 + f8*g3_19 + f9*g2_19
-	h2 := f0*g2 + f1_2*g1 + f2*g0 + f3_2*g9_19 + f4*g8_19 + f5_2*g7_19 + f6*g6_19 + f7_2*g5_19 + f8*g4_19 + f9_2*g3_19
-	h3 := f0*g3 + f1*g2 + f2*g1 + f3*g0 + f4*g9_19 + f5*g8_19 + f6*g7_19 + f7*g6_19 + f8*g5_19 + f9*g4_19
-	h4 := f0*g4 + f1_2*g3 + f2*g2 + f3_2*g1 + f4*g0 + f5_2*g9_19 + f6*g8_19 + f7_2*g7_19 + f8*g6_19 + f9_2*g5_19
-	h5 := f0*g5 + f1*g4 + f2*g3 + f3*g2 + f4*g1 + f5*g0 + f6*g9_19 + f7*g8_19 + f8*g7_19 + f9*g6_19
-	h6 := f0*g6 + f1_2*g5 + f2*g4 + f3_2*g3 + f4*g2 + f5_2*g1 + f6*g0 + f7_2*g9_19 + f8*g8_19 + f9_2*g7_19
-	h7 := f0*g7 + f1*g6 + f2*g5 + f3*g4 + f4*g3 + f5*g2 + f6*g1 + f7*g0 + f8*g9_19 + f9*g8_19
-	h8 := f0*g8 + f1_2*g7 + f2*g6 + f3_2*g5 + f4*g4 + f5_2*g3 + f6*g2 + f7_2*g1 + f8*g0 + f9_2*g9_19
-	h9 := f0*g9 + f1*g8 + f2*g7 + f3*g6 + f4*g5 + f5*g4 + f6*g3 + f7*g2 + f8*g1 + f9*g0
-
-	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-func feSquare(f *FieldElement) (h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 int64) {
-	f0 := int64(f[0])
-	f1 := int64(f[1])
-	f2 := int64(f[2])
-	f3 := int64(f[3])
-	f4 := int64(f[4])
-	f5 := int64(f[5])
-	f6 := int64(f[6])
-	f7 := int64(f[7])
-	f8 := int64(f[8])
-	f9 := int64(f[9])
-	f0_2 := int64(2 * f[0])
-	f1_2 := int64(2 * f[1])
-	f2_2 := int64(2 * f[2])
-	f3_2 := int64(2 * f[3])
-	f4_2 := int64(2 * f[4])
-	f5_2 := int64(2 * f[5])
-	f6_2 := int64(2 * f[6])
-	f7_2 := int64(2 * f[7])
-	f5_38 := 38 * f5 // 1.31*2^30
-	f6_19 := 19 * f6 // 1.31*2^30
-	f7_38 := 38 * f7 // 1.31*2^30
-	f8_19 := 19 * f8 // 1.31*2^30
-	f9_38 := 38 * f9 // 1.31*2^30
-
-	h0 = f0*f0 + f1_2*f9_38 + f2_2*f8_19 + f3_2*f7_38 + f4_2*f6_19 + f5*f5_38
-	h1 = f0_2*f1 + f2*f9_38 + f3_2*f8_19 + f4*f7_38 + f5_2*f6_19
-	h2 = f0_2*f2 + f1_2*f1 + f3_2*f9_38 + f4_2*f8_19 + f5_2*f7_38 + f6*f6_19
-	h3 = f0_2*f3 + f1_2*f2 + f4*f9_38 + f5_2*f8_19 + f6*f7_38
-	h4 = f0_2*f4 + f1_2*f3_2 + f2*f2 + f5_2*f9_38 + f6_2*f8_19 + f7*f7_38
-	h5 = f0_2*f5 + f1_2*f4 + f2_2*f3 + f6*f9_38 + f7_2*f8_19
-	h6 = f0_2*f6 + f1_2*f5_2 + f2_2*f4 + f3_2*f3 + f7_2*f9_38 + f8*f8_19
-	h7 = f0_2*f7 + f1_2*f6 + f2_2*f5 + f3_2*f4 + f8*f9_38
-	h8 = f0_2*f8 + f1_2*f7_2 + f2_2*f6 + f3_2*f5_2 + f4*f4 + f9*f9_38
-	h9 = f0_2*f9 + f1_2*f8 + f2_2*f7 + f3_2*f6 + f4_2*f5
-
-	return
-}
-
-// FeSquare calculates h = f*f. Can overlap h with f.
-//
-// Preconditions:
-//    |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
-//
-// Postconditions:
-//    |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
-func FeSquare(h, f *FieldElement) {
-	h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
-	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-// FeSquare2 sets 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.
-func FeSquare2(h, f *FieldElement) {
-	h0, h1, h2, h3, h4, h5, h6, h7, h8, h9 := feSquare(f)
-
-	h0 += h0
-	h1 += h1
-	h2 += h2
-	h3 += h3
-	h4 += h4
-	h5 += h5
-	h6 += h6
-	h7 += h7
-	h8 += h8
-	h9 += h9
-
-	FeCombine(h, h0, h1, h2, h3, h4, h5, h6, h7, h8, h9)
-}
-
-func FeInvert(out, z *FieldElement) {
-	var t0, t1, t2, t3 FieldElement
-	var i int
-
-	FeSquare(&t0, z)        // 2^1
-	FeSquare(&t1, &t0)      // 2^2
-	for i = 1; i < 2; i++ { // 2^3
-		FeSquare(&t1, &t1)
-	}
-	FeMul(&t1, z, &t1)      // 2^3 + 2^0
-	FeMul(&t0, &t0, &t1)    // 2^3 + 2^1 + 2^0
-	FeSquare(&t2, &t0)      // 2^4 + 2^2 + 2^1
-	FeMul(&t1, &t1, &t2)    // 2^4 + 2^3 + 2^2 + 2^1 + 2^0
-	FeSquare(&t2, &t1)      // 5,4,3,2,1
-	for i = 1; i < 5; i++ { // 9,8,7,6,5
-		FeSquare(&t2, &t2)
-	}
-	FeMul(&t1, &t2, &t1)     // 9,8,7,6,5,4,3,2,1,0
-	FeSquare(&t2, &t1)       // 10..1
-	for i = 1; i < 10; i++ { // 19..10
-		FeSquare(&t2, &t2)
-	}
-	FeMul(&t2, &t2, &t1)     // 19..0
-	FeSquare(&t3, &t2)       // 20..1
-	for i = 1; i < 20; i++ { // 39..20
-		FeSquare(&t3, &t3)
-	}
-	FeMul(&t2, &t3, &t2)     // 39..0
-	FeSquare(&t2, &t2)       // 40..1
-	for i = 1; i < 10; i++ { // 49..10
-		FeSquare(&t2, &t2)
-	}
-	FeMul(&t1, &t2, &t1)     // 49..0
-	FeSquare(&t2, &t1)       // 50..1
-	for i = 1; i < 50; i++ { // 99..50
-		FeSquare(&t2, &t2)
-	}
-	FeMul(&t2, &t2, &t1)      // 99..0
-	FeSquare(&t3, &t2)        // 100..1
-	for i = 1; i < 100; i++ { // 199..100
-		FeSquare(&t3, &t3)
-	}
-	FeMul(&t2, &t3, &t2)     // 199..0
-	FeSquare(&t2, &t2)       // 200..1
-	for i = 1; i < 50; i++ { // 249..50
-		FeSquare(&t2, &t2)
-	}
-	FeMul(&t1, &t2, &t1)    // 249..0
-	FeSquare(&t1, &t1)      // 250..1
-	for i = 1; i < 5; i++ { // 254..5
-		FeSquare(&t1, &t1)
-	}
-	FeMul(out, &t1, &t0) // 254..5,3,1,0
-}
-
-func fePow22523(out, z *FieldElement) {
-	var t0, t1, t2 FieldElement
-	var i int
-
-	FeSquare(&t0, z)
-	for i = 1; i < 1; i++ {
-		FeSquare(&t0, &t0)
-	}
-	FeSquare(&t1, &t0)
-	for i = 1; i < 2; i++ {
-		FeSquare(&t1, &t1)
-	}
-	FeMul(&t1, z, &t1)
-	FeMul(&t0, &t0, &t1)
-	FeSquare(&t0, &t0)
-	for i = 1; i < 1; i++ {
-		FeSquare(&t0, &t0)
-	}
-	FeMul(&t0, &t1, &t0)
-	FeSquare(&t1, &t0)
-	for i = 1; i < 5; i++ {
-		FeSquare(&t1, &t1)
-	}
-	FeMul(&t0, &t1, &t0)
-	FeSquare(&t1, &t0)
-	for i = 1; i < 10; i++ {
-		FeSquare(&t1, &t1)
-	}
-	FeMul(&t1, &t1, &t0)
-	FeSquare(&t2, &t1)
-	for i = 1; i < 20; i++ {
-		FeSquare(&t2, &t2)
-	}
-	FeMul(&t1, &t2, &t1)
-	FeSquare(&t1, &t1)
-	for i = 1; i < 10; i++ {
-		FeSquare(&t1, &t1)
-	}
-	FeMul(&t0, &t1, &t0)
-	FeSquare(&t1, &t0)
-	for i = 1; i < 50; i++ {
-		FeSquare(&t1, &t1)
-	}
-	FeMul(&t1, &t1, &t0)
-	FeSquare(&t2, &t1)
-	for i = 1; i < 100; i++ {
-		FeSquare(&t2, &t2)
-	}
-	FeMul(&t1, &t2, &t1)
-	FeSquare(&t1, &t1)
-	for i = 1; i < 50; i++ {
-		FeSquare(&t1, &t1)
-	}
-	FeMul(&t0, &t1, &t0)
-	FeSquare(&t0, &t0)
-	for i = 1; i < 2; i++ {
-		FeSquare(&t0, &t0)
-	}
-	FeMul(out, &t0, z)
-}
-
-// Group elements are members of the elliptic curve -x^2 + y^2 = 1 + d * x^2 *
-// y^2 where d = -121665/121666.
-//
-// Several representations are used:
-//   ProjectiveGroupElement: (X:Y:Z) satisfying x=X/Z, y=Y/Z
-//   ExtendedGroupElement: (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
-//   CompletedGroupElement: ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
-//   PreComputedGroupElement: (y+x,y-x,2dxy)
-
-type ProjectiveGroupElement struct {
-	X, Y, Z FieldElement
-}
-
-type ExtendedGroupElement struct {
-	X, Y, Z, T FieldElement
-}
-
-type CompletedGroupElement struct {
-	X, Y, Z, T FieldElement
-}
-
-type PreComputedGroupElement struct {
-	yPlusX, yMinusX, xy2d FieldElement
-}
-
-type CachedGroupElement struct {
-	yPlusX, yMinusX, Z, T2d FieldElement
-}
-
-func (p *ProjectiveGroupElement) Zero() {
-	FeZero(&p.X)
-	FeOne(&p.Y)
-	FeOne(&p.Z)
-}
-
-func (p *ProjectiveGroupElement) Double(r *CompletedGroupElement) {
-	var t0 FieldElement
-
-	FeSquare(&r.X, &p.X)
-	FeSquare(&r.Z, &p.Y)
-	FeSquare2(&r.T, &p.Z)
-	FeAdd(&r.Y, &p.X, &p.Y)
-	FeSquare(&t0, &r.Y)
-	FeAdd(&r.Y, &r.Z, &r.X)
-	FeSub(&r.Z, &r.Z, &r.X)
-	FeSub(&r.X, &t0, &r.Y)
-	FeSub(&r.T, &r.T, &r.Z)
-}
-
-func (p *ProjectiveGroupElement) ToBytes(s *[32]byte) {
-	var recip, x, y FieldElement
-
-	FeInvert(&recip, &p.Z)
-	FeMul(&x, &p.X, &recip)
-	FeMul(&y, &p.Y, &recip)
-	FeToBytes(s, &y)
-	s[31] ^= FeIsNegative(&x) << 7
-}
-
-func (p *ExtendedGroupElement) Zero() {
-	FeZero(&p.X)
-	FeOne(&p.Y)
-	FeOne(&p.Z)
-	FeZero(&p.T)
-}
-
-func (p *ExtendedGroupElement) Double(r *CompletedGroupElement) {
-	var q ProjectiveGroupElement
-	p.ToProjective(&q)
-	q.Double(r)
-}
-
-func (p *ExtendedGroupElement) ToCached(r *CachedGroupElement) {
-	FeAdd(&r.yPlusX, &p.Y, &p.X)
-	FeSub(&r.yMinusX, &p.Y, &p.X)
-	FeCopy(&r.Z, &p.Z)
-	FeMul(&r.T2d, &p.T, &d2)
-}
-
-func (p *ExtendedGroupElement) ToProjective(r *ProjectiveGroupElement) {
-	FeCopy(&r.X, &p.X)
-	FeCopy(&r.Y, &p.Y)
-	FeCopy(&r.Z, &p.Z)
-}
-
-func (p *ExtendedGroupElement) ToBytes(s *[32]byte) {
-	var recip, x, y FieldElement
-
-	FeInvert(&recip, &p.Z)
-	FeMul(&x, &p.X, &recip)
-	FeMul(&y, &p.Y, &recip)
-	FeToBytes(s, &y)
-	s[31] ^= FeIsNegative(&x) << 7
-}
-
-func (p *ExtendedGroupElement) FromBytes(s *[32]byte) bool {
-	var u, v, v3, vxx, check FieldElement
-
-	FeFromBytes(&p.Y, s)
-	FeOne(&p.Z)
-	FeSquare(&u, &p.Y)
-	FeMul(&v, &u, &d)
-	FeSub(&u, &u, &p.Z) // y = y^2-1
-	FeAdd(&v, &v, &p.Z) // v = dy^2+1
-
-	FeSquare(&v3, &v)
-	FeMul(&v3, &v3, &v) // v3 = v^3
-	FeSquare(&p.X, &v3)
-	FeMul(&p.X, &p.X, &v)
-	FeMul(&p.X, &p.X, &u) // x = uv^7
-
-	fePow22523(&p.X, &p.X) // x = (uv^7)^((q-5)/8)
-	FeMul(&p.X, &p.X, &v3)
-	FeMul(&p.X, &p.X, &u) // x = uv^3(uv^7)^((q-5)/8)
-
-	var tmpX, tmp2 [32]byte
-
-	FeSquare(&vxx, &p.X)
-	FeMul(&vxx, &vxx, &v)
-	FeSub(&check, &vxx, &u) // vx^2-u
-	if FeIsNonZero(&check) == 1 {
-		FeAdd(&check, &vxx, &u) // vx^2+u
-		if FeIsNonZero(&check) == 1 {
-			return false
-		}
-		FeMul(&p.X, &p.X, &SqrtM1)
-
-		FeToBytes(&tmpX, &p.X)
-		for i, v := range tmpX {
-			tmp2[31-i] = v
-		}
-	}
-
-	if FeIsNegative(&p.X) != (s[31] >> 7) {
-		FeNeg(&p.X, &p.X)
-	}
-
-	FeMul(&p.T, &p.X, &p.Y)
-	return true
-}
-
-func (p *CompletedGroupElement) ToProjective(r *ProjectiveGroupElement) {
-	FeMul(&r.X, &p.X, &p.T)
-	FeMul(&r.Y, &p.Y, &p.Z)
-	FeMul(&r.Z, &p.Z, &p.T)
-}
-
-func (p *CompletedGroupElement) ToExtended(r *ExtendedGroupElement) {
-	FeMul(&r.X, &p.X, &p.T)
-	FeMul(&r.Y, &p.Y, &p.Z)
-	FeMul(&r.Z, &p.Z, &p.T)
-	FeMul(&r.T, &p.X, &p.Y)
-}
-
-func (p *PreComputedGroupElement) Zero() {
-	FeOne(&p.yPlusX)
-	FeOne(&p.yMinusX)
-	FeZero(&p.xy2d)
-}
-
-func geAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
-	var t0 FieldElement
-
-	FeAdd(&r.X, &p.Y, &p.X)
-	FeSub(&r.Y, &p.Y, &p.X)
-	FeMul(&r.Z, &r.X, &q.yPlusX)
-	FeMul(&r.Y, &r.Y, &q.yMinusX)
-	FeMul(&r.T, &q.T2d, &p.T)
-	FeMul(&r.X, &p.Z, &q.Z)
-	FeAdd(&t0, &r.X, &r.X)
-	FeSub(&r.X, &r.Z, &r.Y)
-	FeAdd(&r.Y, &r.Z, &r.Y)
-	FeAdd(&r.Z, &t0, &r.T)
-	FeSub(&r.T, &t0, &r.T)
-}
-
-func geSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *CachedGroupElement) {
-	var t0 FieldElement
-
-	FeAdd(&r.X, &p.Y, &p.X)
-	FeSub(&r.Y, &p.Y, &p.X)
-	FeMul(&r.Z, &r.X, &q.yMinusX)
-	FeMul(&r.Y, &r.Y, &q.yPlusX)
-	FeMul(&r.T, &q.T2d, &p.T)
-	FeMul(&r.X, &p.Z, &q.Z)
-	FeAdd(&t0, &r.X, &r.X)
-	FeSub(&r.X, &r.Z, &r.Y)
-	FeAdd(&r.Y, &r.Z, &r.Y)
-	FeSub(&r.Z, &t0, &r.T)
-	FeAdd(&r.T, &t0, &r.T)
-}
-
-func geMixedAdd(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
-	var t0 FieldElement
-
-	FeAdd(&r.X, &p.Y, &p.X)
-	FeSub(&r.Y, &p.Y, &p.X)
-	FeMul(&r.Z, &r.X, &q.yPlusX)
-	FeMul(&r.Y, &r.Y, &q.yMinusX)
-	FeMul(&r.T, &q.xy2d, &p.T)
-	FeAdd(&t0, &p.Z, &p.Z)
-	FeSub(&r.X, &r.Z, &r.Y)
-	FeAdd(&r.Y, &r.Z, &r.Y)
-	FeAdd(&r.Z, &t0, &r.T)
-	FeSub(&r.T, &t0, &r.T)
-}
-
-func geMixedSub(r *CompletedGroupElement, p *ExtendedGroupElement, q *PreComputedGroupElement) {
-	var t0 FieldElement
-
-	FeAdd(&r.X, &p.Y, &p.X)
-	FeSub(&r.Y, &p.Y, &p.X)
-	FeMul(&r.Z, &r.X, &q.yMinusX)
-	FeMul(&r.Y, &r.Y, &q.yPlusX)
-	FeMul(&r.T, &q.xy2d, &p.T)
-	FeAdd(&t0, &p.Z, &p.Z)
-	FeSub(&r.X, &r.Z, &r.Y)
-	FeAdd(&r.Y, &r.Z, &r.Y)
-	FeSub(&r.Z, &t0, &r.T)
-	FeAdd(&r.T, &t0, &r.T)
-}
-
-func slide(r *[256]int8, a *[32]byte) {
-	for i := range r {
-		r[i] = int8(1 & (a[i>>3] >> uint(i&7)))
-	}
-
-	for i := range r {
-		if r[i] != 0 {
-			for b := 1; b <= 6 && i+b < 256; b++ {
-				if r[i+b] != 0 {
-					if r[i]+(r[i+b]<<uint(b)) <= 15 {
-						r[i] += r[i+b] << uint(b)
-						r[i+b] = 0
-					} else if r[i]-(r[i+b]<<uint(b)) >= -15 {
-						r[i] -= r[i+b] << uint(b)
-						for k := i + b; k < 256; k++ {
-							if r[k] == 0 {
-								r[k] = 1
-								break
-							}
-							r[k] = 0
-						}
-					} else {
-						break
-					}
-				}
-			}
-		}
-	}
-}
-
-// GeDoubleScalarMultVartime sets 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.
-func GeDoubleScalarMultVartime(r *ProjectiveGroupElement, a *[32]byte, A *ExtendedGroupElement, b *[32]byte) {
-	var aSlide, bSlide [256]int8
-	var Ai [8]CachedGroupElement // A,3A,5A,7A,9A,11A,13A,15A
-	var t CompletedGroupElement
-	var u, A2 ExtendedGroupElement
-	var i int
-
-	slide(&aSlide, a)
-	slide(&bSlide, b)
-
-	A.ToCached(&Ai[0])
-	A.Double(&t)
-	t.ToExtended(&A2)
-
-	for i := 0; i < 7; i++ {
-		geAdd(&t, &A2, &Ai[i])
-		t.ToExtended(&u)
-		u.ToCached(&Ai[i+1])
-	}
-
-	r.Zero()
-
-	for i = 255; i >= 0; i-- {
-		if aSlide[i] != 0 || bSlide[i] != 0 {
-			break
-		}
-	}
-
-	for ; i >= 0; i-- {
-		r.Double(&t)
-
-		if aSlide[i] > 0 {
-			t.ToExtended(&u)
-			geAdd(&t, &u, &Ai[aSlide[i]/2])
-		} else if aSlide[i] < 0 {
-			t.ToExtended(&u)
-			geSub(&t, &u, &Ai[(-aSlide[i])/2])
-		}
-
-		if bSlide[i] > 0 {
-			t.ToExtended(&u)
-			geMixedAdd(&t, &u, &bi[bSlide[i]/2])
-		} else if bSlide[i] < 0 {
-			t.ToExtended(&u)
-			geMixedSub(&t, &u, &bi[(-bSlide[i])/2])
-		}
-
-		t.ToProjective(r)
-	}
-}
-
-// equal returns 1 if b == c and 0 otherwise, assuming that b and c are
-// non-negative.
-func equal(b, c int32) int32 {
-	x := uint32(b ^ c)
-	x--
-	return int32(x >> 31)
-}
-
-// negative returns 1 if b < 0 and 0 otherwise.
-func negative(b int32) int32 {
-	return (b >> 31) & 1
-}
-
-func PreComputedGroupElementCMove(t, u *PreComputedGroupElement, b int32) {
-	FeCMove(&t.yPlusX, &u.yPlusX, b)
-	FeCMove(&t.yMinusX, &u.yMinusX, b)
-	FeCMove(&t.xy2d, &u.xy2d, b)
-}
-
-func selectPoint(t *PreComputedGroupElement, pos int32, b int32) {
-	var minusT PreComputedGroupElement
-	bNegative := negative(b)
-	bAbs := b - (((-bNegative) & b) << 1)
-
-	t.Zero()
-	for i := int32(0); i < 8; i++ {
-		PreComputedGroupElementCMove(t, &base[pos][i], equal(bAbs, i+1))
-	}
-	FeCopy(&minusT.yPlusX, &t.yMinusX)
-	FeCopy(&minusT.yMinusX, &t.yPlusX)
-	FeNeg(&minusT.xy2d, &t.xy2d)
-	PreComputedGroupElementCMove(t, &minusT, bNegative)
-}
-
-// GeScalarMultBase computes 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
-func GeScalarMultBase(h *ExtendedGroupElement, a *[32]byte) {
-	var e [64]int8
-
-	for i, v := range a {
-		e[2*i] = int8(v & 15)
-		e[2*i+1] = int8((v >> 4) & 15)
-	}
-
-	// each e[i] is between 0 and 15 and e[63] is between 0 and 7.
-
-	carry := int8(0)
-	for i := 0; i < 63; i++ {
-		e[i] += carry
-		carry = (e[i] + 8) >> 4
-		e[i] -= carry << 4
-	}
-	e[63] += carry
-	// each e[i] is between -8 and 8.
-
-	h.Zero()
-	var t PreComputedGroupElement
-	var r CompletedGroupElement
-	for i := int32(1); i < 64; i += 2 {
-		selectPoint(&t, i/2, int32(e[i]))
-		geMixedAdd(&r, h, &t)
-		r.ToExtended(h)
-	}
-
-	var s ProjectiveGroupElement
-
-	h.Double(&r)
-	r.ToProjective(&s)
-	s.Double(&r)
-	r.ToProjective(&s)
-	s.Double(&r)
-	r.ToProjective(&s)
-	s.Double(&r)
-	r.ToExtended(h)
-
-	for i := int32(0); i < 64; i += 2 {
-		selectPoint(&t, i/2, int32(e[i]))
-		geMixedAdd(&r, h, &t)
-		r.ToExtended(h)
-	}
-}
-
-// The scalars are GF(2^252 + 27742317777372353535851937790883648493).
-
-// Input:
-//   a[0]+256*a[1]+...+256^31*a[31] = a
-//   b[0]+256*b[1]+...+256^31*b[31] = b
-//   c[0]+256*c[1]+...+256^31*c[31] = c
-//
-// Output:
-//   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
-//   where l = 2^252 + 27742317777372353535851937790883648493.
-func ScMulAdd(s, a, b, c *[32]byte) {
-	a0 := 2097151 & load3(a[:])
-	a1 := 2097151 & (load4(a[2:]) >> 5)
-	a2 := 2097151 & (load3(a[5:]) >> 2)
-	a3 := 2097151 & (load4(a[7:]) >> 7)
-	a4 := 2097151 & (load4(a[10:]) >> 4)
-	a5 := 2097151 & (load3(a[13:]) >> 1)
-	a6 := 2097151 & (load4(a[15:]) >> 6)
-	a7 := 2097151 & (load3(a[18:]) >> 3)
-	a8 := 2097151 & load3(a[21:])
-	a9 := 2097151 & (load4(a[23:]) >> 5)
-	a10 := 2097151 & (load3(a[26:]) >> 2)
-	a11 := (load4(a[28:]) >> 7)
-	b0 := 2097151 & load3(b[:])
-	b1 := 2097151 & (load4(b[2:]) >> 5)
-	b2 := 2097151 & (load3(b[5:]) >> 2)
-	b3 := 2097151 & (load4(b[7:]) >> 7)
-	b4 := 2097151 & (load4(b[10:]) >> 4)
-	b5 := 2097151 & (load3(b[13:]) >> 1)
-	b6 := 2097151 & (load4(b[15:]) >> 6)
-	b7 := 2097151 & (load3(b[18:]) >> 3)
-	b8 := 2097151 & load3(b[21:])
-	b9 := 2097151 & (load4(b[23:]) >> 5)
-	b10 := 2097151 & (load3(b[26:]) >> 2)
-	b11 := (load4(b[28:]) >> 7)
-	c0 := 2097151 & load3(c[:])
-	c1 := 2097151 & (load4(c[2:]) >> 5)
-	c2 := 2097151 & (load3(c[5:]) >> 2)
-	c3 := 2097151 & (load4(c[7:]) >> 7)
-	c4 := 2097151 & (load4(c[10:]) >> 4)
-	c5 := 2097151 & (load3(c[13:]) >> 1)
-	c6 := 2097151 & (load4(c[15:]) >> 6)
-	c7 := 2097151 & (load3(c[18:]) >> 3)
-	c8 := 2097151 & load3(c[21:])
-	c9 := 2097151 & (load4(c[23:]) >> 5)
-	c10 := 2097151 & (load3(c[26:]) >> 2)
-	c11 := (load4(c[28:]) >> 7)
-	var carry [23]int64
-
-	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 := int64(0)
-
-	carry[0] = (s0 + (1 << 20)) >> 21
-	s1 += carry[0]
-	s0 -= carry[0] << 21
-	carry[2] = (s2 + (1 << 20)) >> 21
-	s3 += carry[2]
-	s2 -= carry[2] << 21
-	carry[4] = (s4 + (1 << 20)) >> 21
-	s5 += carry[4]
-	s4 -= carry[4] << 21
-	carry[6] = (s6 + (1 << 20)) >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[8] = (s8 + (1 << 20)) >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[10] = (s10 + (1 << 20)) >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-	carry[12] = (s12 + (1 << 20)) >> 21
-	s13 += carry[12]
-	s12 -= carry[12] << 21
-	carry[14] = (s14 + (1 << 20)) >> 21
-	s15 += carry[14]
-	s14 -= carry[14] << 21
-	carry[16] = (s16 + (1 << 20)) >> 21
-	s17 += carry[16]
-	s16 -= carry[16] << 21
-	carry[18] = (s18 + (1 << 20)) >> 21
-	s19 += carry[18]
-	s18 -= carry[18] << 21
-	carry[20] = (s20 + (1 << 20)) >> 21
-	s21 += carry[20]
-	s20 -= carry[20] << 21
-	carry[22] = (s22 + (1 << 20)) >> 21
-	s23 += carry[22]
-	s22 -= carry[22] << 21
-
-	carry[1] = (s1 + (1 << 20)) >> 21
-	s2 += carry[1]
-	s1 -= carry[1] << 21
-	carry[3] = (s3 + (1 << 20)) >> 21
-	s4 += carry[3]
-	s3 -= carry[3] << 21
-	carry[5] = (s5 + (1 << 20)) >> 21
-	s6 += carry[5]
-	s5 -= carry[5] << 21
-	carry[7] = (s7 + (1 << 20)) >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[9] = (s9 + (1 << 20)) >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[11] = (s11 + (1 << 20)) >> 21
-	s12 += carry[11]
-	s11 -= carry[11] << 21
-	carry[13] = (s13 + (1 << 20)) >> 21
-	s14 += carry[13]
-	s13 -= carry[13] << 21
-	carry[15] = (s15 + (1 << 20)) >> 21
-	s16 += carry[15]
-	s15 -= carry[15] << 21
-	carry[17] = (s17 + (1 << 20)) >> 21
-	s18 += carry[17]
-	s17 -= carry[17] << 21
-	carry[19] = (s19 + (1 << 20)) >> 21
-	s20 += carry[19]
-	s19 -= carry[19] << 21
-	carry[21] = (s21 + (1 << 20)) >> 21
-	s22 += carry[21]
-	s21 -= carry[21] << 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
-
-	carry[6] = (s6 + (1 << 20)) >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[8] = (s8 + (1 << 20)) >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[10] = (s10 + (1 << 20)) >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-	carry[12] = (s12 + (1 << 20)) >> 21
-	s13 += carry[12]
-	s12 -= carry[12] << 21
-	carry[14] = (s14 + (1 << 20)) >> 21
-	s15 += carry[14]
-	s14 -= carry[14] << 21
-	carry[16] = (s16 + (1 << 20)) >> 21
-	s17 += carry[16]
-	s16 -= carry[16] << 21
-
-	carry[7] = (s7 + (1 << 20)) >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[9] = (s9 + (1 << 20)) >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[11] = (s11 + (1 << 20)) >> 21
-	s12 += carry[11]
-	s11 -= carry[11] << 21
-	carry[13] = (s13 + (1 << 20)) >> 21
-	s14 += carry[13]
-	s13 -= carry[13] << 21
-	carry[15] = (s15 + (1 << 20)) >> 21
-	s16 += carry[15]
-	s15 -= carry[15] << 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
-
-	carry[0] = (s0 + (1 << 20)) >> 21
-	s1 += carry[0]
-	s0 -= carry[0] << 21
-	carry[2] = (s2 + (1 << 20)) >> 21
-	s3 += carry[2]
-	s2 -= carry[2] << 21
-	carry[4] = (s4 + (1 << 20)) >> 21
-	s5 += carry[4]
-	s4 -= carry[4] << 21
-	carry[6] = (s6 + (1 << 20)) >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[8] = (s8 + (1 << 20)) >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[10] = (s10 + (1 << 20)) >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-
-	carry[1] = (s1 + (1 << 20)) >> 21
-	s2 += carry[1]
-	s1 -= carry[1] << 21
-	carry[3] = (s3 + (1 << 20)) >> 21
-	s4 += carry[3]
-	s3 -= carry[3] << 21
-	carry[5] = (s5 + (1 << 20)) >> 21
-	s6 += carry[5]
-	s5 -= carry[5] << 21
-	carry[7] = (s7 + (1 << 20)) >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[9] = (s9 + (1 << 20)) >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[11] = (s11 + (1 << 20)) >> 21
-	s12 += carry[11]
-	s11 -= carry[11] << 21
-
-	s0 += s12 * 666643
-	s1 += s12 * 470296
-	s2 += s12 * 654183
-	s3 -= s12 * 997805
-	s4 += s12 * 136657
-	s5 -= s12 * 683901
-	s12 = 0
-
-	carry[0] = s0 >> 21
-	s1 += carry[0]
-	s0 -= carry[0] << 21
-	carry[1] = s1 >> 21
-	s2 += carry[1]
-	s1 -= carry[1] << 21
-	carry[2] = s2 >> 21
-	s3 += carry[2]
-	s2 -= carry[2] << 21
-	carry[3] = s3 >> 21
-	s4 += carry[3]
-	s3 -= carry[3] << 21
-	carry[4] = s4 >> 21
-	s5 += carry[4]
-	s4 -= carry[4] << 21
-	carry[5] = s5 >> 21
-	s6 += carry[5]
-	s5 -= carry[5] << 21
-	carry[6] = s6 >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[7] = s7 >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[8] = s8 >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[9] = s9 >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[10] = s10 >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-	carry[11] = s11 >> 21
-	s12 += carry[11]
-	s11 -= carry[11] << 21
-
-	s0 += s12 * 666643
-	s1 += s12 * 470296
-	s2 += s12 * 654183
-	s3 -= s12 * 997805
-	s4 += s12 * 136657
-	s5 -= s12 * 683901
-	s12 = 0
-
-	carry[0] = s0 >> 21
-	s1 += carry[0]
-	s0 -= carry[0] << 21
-	carry[1] = s1 >> 21
-	s2 += carry[1]
-	s1 -= carry[1] << 21
-	carry[2] = s2 >> 21
-	s3 += carry[2]
-	s2 -= carry[2] << 21
-	carry[3] = s3 >> 21
-	s4 += carry[3]
-	s3 -= carry[3] << 21
-	carry[4] = s4 >> 21
-	s5 += carry[4]
-	s4 -= carry[4] << 21
-	carry[5] = s5 >> 21
-	s6 += carry[5]
-	s5 -= carry[5] << 21
-	carry[6] = s6 >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[7] = s7 >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[8] = s8 >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[9] = s9 >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[10] = s10 >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-
-	s[0] = byte(s0 >> 0)
-	s[1] = byte(s0 >> 8)
-	s[2] = byte((s0 >> 16) | (s1 << 5))
-	s[3] = byte(s1 >> 3)
-	s[4] = byte(s1 >> 11)
-	s[5] = byte((s1 >> 19) | (s2 << 2))
-	s[6] = byte(s2 >> 6)
-	s[7] = byte((s2 >> 14) | (s3 << 7))
-	s[8] = byte(s3 >> 1)
-	s[9] = byte(s3 >> 9)
-	s[10] = byte((s3 >> 17) | (s4 << 4))
-	s[11] = byte(s4 >> 4)
-	s[12] = byte(s4 >> 12)
-	s[13] = byte((s4 >> 20) | (s5 << 1))
-	s[14] = byte(s5 >> 7)
-	s[15] = byte((s5 >> 15) | (s6 << 6))
-	s[16] = byte(s6 >> 2)
-	s[17] = byte(s6 >> 10)
-	s[18] = byte((s6 >> 18) | (s7 << 3))
-	s[19] = byte(s7 >> 5)
-	s[20] = byte(s7 >> 13)
-	s[21] = byte(s8 >> 0)
-	s[22] = byte(s8 >> 8)
-	s[23] = byte((s8 >> 16) | (s9 << 5))
-	s[24] = byte(s9 >> 3)
-	s[25] = byte(s9 >> 11)
-	s[26] = byte((s9 >> 19) | (s10 << 2))
-	s[27] = byte(s10 >> 6)
-	s[28] = byte((s10 >> 14) | (s11 << 7))
-	s[29] = byte(s11 >> 1)
-	s[30] = byte(s11 >> 9)
-	s[31] = byte(s11 >> 17)
-}
-
-// 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.
-func ScReduce(out *[32]byte, s *[64]byte) {
-	s0 := 2097151 & load3(s[:])
-	s1 := 2097151 & (load4(s[2:]) >> 5)
-	s2 := 2097151 & (load3(s[5:]) >> 2)
-	s3 := 2097151 & (load4(s[7:]) >> 7)
-	s4 := 2097151 & (load4(s[10:]) >> 4)
-	s5 := 2097151 & (load3(s[13:]) >> 1)
-	s6 := 2097151 & (load4(s[15:]) >> 6)
-	s7 := 2097151 & (load3(s[18:]) >> 3)
-	s8 := 2097151 & load3(s[21:])
-	s9 := 2097151 & (load4(s[23:]) >> 5)
-	s10 := 2097151 & (load3(s[26:]) >> 2)
-	s11 := 2097151 & (load4(s[28:]) >> 7)
-	s12 := 2097151 & (load4(s[31:]) >> 4)
-	s13 := 2097151 & (load3(s[34:]) >> 1)
-	s14 := 2097151 & (load4(s[36:]) >> 6)
-	s15 := 2097151 & (load3(s[39:]) >> 3)
-	s16 := 2097151 & load3(s[42:])
-	s17 := 2097151 & (load4(s[44:]) >> 5)
-	s18 := 2097151 & (load3(s[47:]) >> 2)
-	s19 := 2097151 & (load4(s[49:]) >> 7)
-	s20 := 2097151 & (load4(s[52:]) >> 4)
-	s21 := 2097151 & (load3(s[55:]) >> 1)
-	s22 := 2097151 & (load4(s[57:]) >> 6)
-	s23 := (load4(s[60:]) >> 3)
-
-	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
-
-	var carry [17]int64
-
-	carry[6] = (s6 + (1 << 20)) >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[8] = (s8 + (1 << 20)) >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[10] = (s10 + (1 << 20)) >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-	carry[12] = (s12 + (1 << 20)) >> 21
-	s13 += carry[12]
-	s12 -= carry[12] << 21
-	carry[14] = (s14 + (1 << 20)) >> 21
-	s15 += carry[14]
-	s14 -= carry[14] << 21
-	carry[16] = (s16 + (1 << 20)) >> 21
-	s17 += carry[16]
-	s16 -= carry[16] << 21
-
-	carry[7] = (s7 + (1 << 20)) >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[9] = (s9 + (1 << 20)) >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[11] = (s11 + (1 << 20)) >> 21
-	s12 += carry[11]
-	s11 -= carry[11] << 21
-	carry[13] = (s13 + (1 << 20)) >> 21
-	s14 += carry[13]
-	s13 -= carry[13] << 21
-	carry[15] = (s15 + (1 << 20)) >> 21
-	s16 += carry[15]
-	s15 -= carry[15] << 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
-
-	carry[0] = (s0 + (1 << 20)) >> 21
-	s1 += carry[0]
-	s0 -= carry[0] << 21
-	carry[2] = (s2 + (1 << 20)) >> 21
-	s3 += carry[2]
-	s2 -= carry[2] << 21
-	carry[4] = (s4 + (1 << 20)) >> 21
-	s5 += carry[4]
-	s4 -= carry[4] << 21
-	carry[6] = (s6 + (1 << 20)) >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[8] = (s8 + (1 << 20)) >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[10] = (s10 + (1 << 20)) >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-
-	carry[1] = (s1 + (1 << 20)) >> 21
-	s2 += carry[1]
-	s1 -= carry[1] << 21
-	carry[3] = (s3 + (1 << 20)) >> 21
-	s4 += carry[3]
-	s3 -= carry[3] << 21
-	carry[5] = (s5 + (1 << 20)) >> 21
-	s6 += carry[5]
-	s5 -= carry[5] << 21
-	carry[7] = (s7 + (1 << 20)) >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[9] = (s9 + (1 << 20)) >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[11] = (s11 + (1 << 20)) >> 21
-	s12 += carry[11]
-	s11 -= carry[11] << 21
-
-	s0 += s12 * 666643
-	s1 += s12 * 470296
-	s2 += s12 * 654183
-	s3 -= s12 * 997805
-	s4 += s12 * 136657
-	s5 -= s12 * 683901
-	s12 = 0
-
-	carry[0] = s0 >> 21
-	s1 += carry[0]
-	s0 -= carry[0] << 21
-	carry[1] = s1 >> 21
-	s2 += carry[1]
-	s1 -= carry[1] << 21
-	carry[2] = s2 >> 21
-	s3 += carry[2]
-	s2 -= carry[2] << 21
-	carry[3] = s3 >> 21
-	s4 += carry[3]
-	s3 -= carry[3] << 21
-	carry[4] = s4 >> 21
-	s5 += carry[4]
-	s4 -= carry[4] << 21
-	carry[5] = s5 >> 21
-	s6 += carry[5]
-	s5 -= carry[5] << 21
-	carry[6] = s6 >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[7] = s7 >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[8] = s8 >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[9] = s9 >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[10] = s10 >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-	carry[11] = s11 >> 21
-	s12 += carry[11]
-	s11 -= carry[11] << 21
-
-	s0 += s12 * 666643
-	s1 += s12 * 470296
-	s2 += s12 * 654183
-	s3 -= s12 * 997805
-	s4 += s12 * 136657
-	s5 -= s12 * 683901
-	s12 = 0
-
-	carry[0] = s0 >> 21
-	s1 += carry[0]
-	s0 -= carry[0] << 21
-	carry[1] = s1 >> 21
-	s2 += carry[1]
-	s1 -= carry[1] << 21
-	carry[2] = s2 >> 21
-	s3 += carry[2]
-	s2 -= carry[2] << 21
-	carry[3] = s3 >> 21
-	s4 += carry[3]
-	s3 -= carry[3] << 21
-	carry[4] = s4 >> 21
-	s5 += carry[4]
-	s4 -= carry[4] << 21
-	carry[5] = s5 >> 21
-	s6 += carry[5]
-	s5 -= carry[5] << 21
-	carry[6] = s6 >> 21
-	s7 += carry[6]
-	s6 -= carry[6] << 21
-	carry[7] = s7 >> 21
-	s8 += carry[7]
-	s7 -= carry[7] << 21
-	carry[8] = s8 >> 21
-	s9 += carry[8]
-	s8 -= carry[8] << 21
-	carry[9] = s9 >> 21
-	s10 += carry[9]
-	s9 -= carry[9] << 21
-	carry[10] = s10 >> 21
-	s11 += carry[10]
-	s10 -= carry[10] << 21
-
-	out[0] = byte(s0 >> 0)
-	out[1] = byte(s0 >> 8)
-	out[2] = byte((s0 >> 16) | (s1 << 5))
-	out[3] = byte(s1 >> 3)
-	out[4] = byte(s1 >> 11)
-	out[5] = byte((s1 >> 19) | (s2 << 2))
-	out[6] = byte(s2 >> 6)
-	out[7] = byte((s2 >> 14) | (s3 << 7))
-	out[8] = byte(s3 >> 1)
-	out[9] = byte(s3 >> 9)
-	out[10] = byte((s3 >> 17) | (s4 << 4))
-	out[11] = byte(s4 >> 4)
-	out[12] = byte(s4 >> 12)
-	out[13] = byte((s4 >> 20) | (s5 << 1))
-	out[14] = byte(s5 >> 7)
-	out[15] = byte((s5 >> 15) | (s6 << 6))
-	out[16] = byte(s6 >> 2)
-	out[17] = byte(s6 >> 10)
-	out[18] = byte((s6 >> 18) | (s7 << 3))
-	out[19] = byte(s7 >> 5)
-	out[20] = byte(s7 >> 13)
-	out[21] = byte(s8 >> 0)
-	out[22] = byte(s8 >> 8)
-	out[23] = byte((s8 >> 16) | (s9 << 5))
-	out[24] = byte(s9 >> 3)
-	out[25] = byte(s9 >> 11)
-	out[26] = byte((s9 >> 19) | (s10 << 2))
-	out[27] = byte(s10 >> 6)
-	out[28] = byte((s10 >> 14) | (s11 << 7))
-	out[29] = byte(s11 >> 1)
-	out[30] = byte(s11 >> 9)
-	out[31] = byte(s11 >> 17)
-}
-
-// order is the order of Curve25519 in little-endian form.
-var order = [4]uint64{0x5812631a5cf5d3ed, 0x14def9dea2f79cd6, 0, 0x1000000000000000}
-
-// ScMinimal returns true if the given scalar is less than the order of the
-// curve.
-func ScMinimal(scalar *[32]byte) bool {
-	for i := 3; ; i-- {
-		v := binary.LittleEndian.Uint64(scalar[i*8:])
-		if v > order[i] {
-			return false
-		} else if v < order[i] {
-			break
-		} else if i == 0 {
-			return false
-		}
-	}
-
-	return true
-}