--- /dev/null
+static const ge_precomp 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 },
+ },
+ {
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+ { -10562541,14895633,26814552,-16673850,-17480754,-2489360,-2781891,6993761,-18093885,10114655 },
+ { -20107055,-929418,31422704,10427861,-7110749,6150669,-29091755,-11529146,25953725,-106158 },
+ },
+ {
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+ },
+ {
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+ },
+ {
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+ { -21327538,13448259,25284571,1143661,20614966,-8849387,2031539,-12391231,-16253183,-13582083 },
+ },
+ {
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+ { -5075835,9368966,-8562079,-4600902,-15249953,6970560,-9189873,16292057,-8867157,3507940 },
+ { 29439664,3537914,23333589,6997794,-17555561,-11018068,-15209202,-15051267,-9164929,6580396 },
+ },
+},
+{
+ {
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+ { -16665533,-10650790,-6160345,-13305760,9192020,-1802462,17271490,12349094,26939669,-3752294 },
+ },
+ {
+ { -12889898,9373458,31595848,16374215,21471720,13221525,-27283495,-12348559,-3698806,117887 },
+ { 22263325,-6560050,3984570,-11174646,-15114008,-566785,28311253,5358056,-23319780,541964 },
+ { 16259219,3261970,2309254,-15534474,-16885711,-4581916,24134070,-16705829,-13337066,-13552195 },
+ },
+ {
+ { 9378160,-13140186,-22845982,-12745264,28198281,-7244098,-2399684,-717351,690426,14876244 },
+ { 24977353,-314384,-8223969,-13465086,28432343,-1176353,-13068804,-12297348,-22380984,6618999 },
+ { -1538174,11685646,12944378,13682314,-24389511,-14413193,8044829,-13817328,32239829,-5652762 },
+ },
+ {
+ { -18603066,4762990,-926250,8885304,-28412480,-3187315,9781647,-10350059,32779359,5095274 },
+ { -33008130,-5214506,-32264887,-3685216,9460461,-9327423,-24601656,14506724,21639561,-2630236 },
+ { -16400943,-13112215,25239338,15531969,3987758,-4499318,-1289502,-6863535,17874574,558605 },
+ },
+ {
+ { -13600129,10240081,9171883,16131053,-20869254,9599700,33499487,5080151,2085892,5119761 },
+ { -22205145,-2519528,-16381601,414691,-25019550,2170430,30634760,-8363614,-31999993,-5759884 },
+ { -6845704,15791202,8550074,-1312654,29928809,-12092256,27534430,-7192145,-22351378,12961482 },
+ },
+ {
+ { -24492060,-9570771,10368194,11582341,-23397293,-2245287,16533930,8206996,-30194652,-5159638 },
+ { -11121496,-3382234,2307366,6362031,-135455,8868177,-16835630,7031275,7589640,8945490 },
+ { -32152748,8917967,6661220,-11677616,-1192060,-15793393,7251489,-11182180,24099109,-14456170 },
+ },
+ {
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+ },
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+ },
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+ },
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+ },
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+ },
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+ { -23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424 },
+ },
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+ },
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+ },
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+ { -26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099 },
+ },
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+ },
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+ { -17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628 },
+ { -13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657 },
+ },
+ {
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+ { 25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616 },
+ { 31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014 },
+ },
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+ { -20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718 },
+ },
+ {
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+ },
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+ },
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+ },
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+ },
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+ },
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+ },
+ {
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+ },
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+ { -185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376 },
+ },
+ {
+ { -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 },
+ { -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 },
+ { -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 },
+ },
+ {
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+ { -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 },
+ },
+},
+};
/*
-version 20081011
-Matthew Dempsky
-Public domain.
-Derived from public domain code by D. J. Bernstein.
-20140216 tweak: Mask top bit of point input.
-*/
+ version 20081011
+ Matthew Dempsky
+ Public domain.
+ Derived from public domain code by D. J. Bernstein.
+ 20140216 tweak: Mask top bit of point input.
+ */
+#include <stddef.h>
+#include <stdint.h>
+#include <string.h>
#include "config.h"
#include "curve25519.h"
+#include "fe.h"
-static void add (unsigned int out[32],
- const unsigned int a[32],
- const unsigned int b[32])
-{
- unsigned int j;
- unsigned int u;
- u = 0;
- for (j = 0; j < 31; ++j) {
- u += a[j] + b[j];
- out[j] = u & 255;
- u >>= 8;
- }
- u += a[31] + b[31];
- out[31] = u;
+
+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 void curve25519_ref_sub (unsigned int out[32],
- const unsigned int a[32],
- const unsigned int b[32])
+static uint64_t load_4(const unsigned char *in)
{
- unsigned int j;
- unsigned int u;
- u = 218;
- for (j = 0; j < 31; ++j) {
- u += a[j] + 65280 - b[j];
- out[j] = u & 255;
- u >>= 8;
- }
- u += a[31] - b[31];
- out[31] = u;
+ 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;
}
-static void curve25519_ref_squeeze (unsigned int a[32])
+/*
+ h = 0
+ */
+
+void fe_0(fe h)
{
- unsigned int j;
- unsigned int u;
- u = 0;
- for (j = 0; j < 31; ++j) {
- u += a[j];
- a[j] = u & 255;
- u >>= 8;
- }
- u += a[31];
- a[31] = u & 127;
- u = 19 * (u >> 7);
- for (j = 0; j < 31; ++j) {
- u += a[j];
- a[j] = u & 255;
- u >>= 8;
+ memset(&h[0], 0, 10 * sizeof h[0]);
+}
+
+/*
+ h = 1
+ */
+
+void fe_1(fe h)
+{
+ h[0] = 1;
+ h[1] = 0;
+ memset(&h[2], 0, 8 * sizeof h[0]);
+}
+
+/*
+ h = f + g
+ Can overlap h with f or g.
+
+ Preconditions:
+ |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+ Postconditions:
+ |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+
+void fe_add(fe h, const fe f, const fe g)
+{
+ int32_t f0 = f[0];
+ int32_t f1 = f[1];
+ int32_t f2 = f[2];
+ int32_t f3 = f[3];
+ int32_t f4 = f[4];
+ int32_t f5 = f[5];
+ int32_t f6 = f[6];
+ int32_t f7 = f[7];
+ int32_t f8 = f[8];
+ int32_t f9 = f[9];
+ int32_t g0 = g[0];
+ int32_t g1 = g[1];
+ int32_t g2 = g[2];
+ int32_t g3 = g[3];
+ int32_t g4 = g[4];
+ int32_t g5 = g[5];
+ int32_t g6 = g[6];
+ int32_t g7 = g[7];
+ int32_t g8 = g[8];
+ int32_t g9 = g[9];
+ int32_t h0 = f0 + g0;
+ int32_t h1 = f1 + g1;
+ int32_t h2 = f2 + g2;
+ int32_t h3 = f3 + g3;
+ int32_t h4 = f4 + g4;
+ int32_t h5 = f5 + g5;
+ int32_t h6 = f6 + g6;
+ int32_t h7 = f7 + g7;
+ int32_t h8 = f8 + g8;
+ int32_t h9 = f9 + g9;
+ h[0] = h0;
+ h[1] = h1;
+ h[2] = h2;
+ h[3] = h3;
+ h[4] = h4;
+ h[5] = h5;
+ h[6] = h6;
+ h[7] = h7;
+ h[8] = h8;
+ h[9] = h9;
+}
+
+/*
+ Replace (f,g) with (g,g) if b == 1;
+ replace (f,g) with (f,g) if b == 0.
+
+ Preconditions: b in {0,1}.
+ */
+
+void fe_cmov(fe f, const fe g, unsigned int b)
+{
+ 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;
+ b = (unsigned int) (-(int) 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;
+}
+
+/*
+ h = f
+ */
+
+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;
+}
+
+/*
+ Ignores top bit of h.
+ */
+
+void fe_frombytes(fe h, const unsigned char *s)
+{
+ 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;
+
+ carry9 = (h9 + (int64_t) (1L << 24)) >> 25;
+ h0 += carry9 * 19;
+ h9 -= carry9 * ((uint64_t) 1L << 25);
+ carry1 = (h1 + (int64_t) (1L << 24)) >> 25;
+ h2 += carry1;
+ h1 -= carry1 * ((uint64_t) 1L << 25);
+ carry3 = (h3 + (int64_t) (1L << 24)) >> 25;
+ h4 += carry3;
+ h3 -= carry3 * ((uint64_t) 1L << 25);
+ carry5 = (h5 + (int64_t) (1L << 24)) >> 25;
+ h6 += carry5;
+ h5 -= carry5 * ((uint64_t) 1L << 25);
+ carry7 = (h7 + (int64_t) (1L << 24)) >> 25;
+ h8 += carry7;
+ h7 -= carry7 * ((uint64_t) 1L << 25);
+
+ carry0 = (h0 + (int64_t) (1L << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 * ((uint64_t) 1L << 26);
+ carry2 = (h2 + (int64_t) (1L << 25)) >> 26;
+ h3 += carry2;
+ h2 -= carry2 * ((uint64_t) 1L << 26);
+ carry4 = (h4 + (int64_t) (1L << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 * ((uint64_t) 1L << 26);
+ carry6 = (h6 + (int64_t) (1L << 25)) >> 26;
+ h7 += carry6;
+ h6 -= carry6 * ((uint64_t) 1L << 26);
+ carry8 = (h8 + (int64_t) (1L << 25)) >> 26;
+ h9 += carry8;
+ h8 -= carry8 * ((uint64_t) 1L << 26);
+
+ h[0] = (int32_t) h0;
+ h[1] = (int32_t) h1;
+ h[2] = (int32_t) h2;
+ h[3] = (int32_t) h3;
+ h[4] = (int32_t) h4;
+ h[5] = (int32_t) h5;
+ h[6] = (int32_t) h6;
+ h[7] = (int32_t) h7;
+ h[8] = (int32_t) h8;
+ h[9] = (int32_t) h9;
+}
+
+/*
+ Preconditions:
+ |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+ Write p=2^255-19; q=floor(h/p).
+ Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+ Proof:
+ Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+ Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+ Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+ Then 0<y<1.
+
+ Write r=h-pq.
+ Have 0<=r<=p-1=2^255-20.
+ Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+
+ Write x=r+19(2^-255)r+y.
+ Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+
+ Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+ so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+ */
+
+void fe_tobytes(unsigned char *s, const fe h)
+{
+ 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 + ((uint32_t) 1L << 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 * ((uint32_t) 1L << 26);
+ carry1 = h1 >> 25;
+ h2 += carry1;
+ h1 -= carry1 * ((uint32_t) 1L << 25);
+ carry2 = h2 >> 26;
+ h3 += carry2;
+ h2 -= carry2 * ((uint32_t) 1L << 26);
+ carry3 = h3 >> 25;
+ h4 += carry3;
+ h3 -= carry3 * ((uint32_t) 1L << 25);
+ carry4 = h4 >> 26;
+ h5 += carry4;
+ h4 -= carry4 * ((uint32_t) 1L << 26);
+ carry5 = h5 >> 25;
+ h6 += carry5;
+ h5 -= carry5 * ((uint32_t) 1L << 25);
+ carry6 = h6 >> 26;
+ h7 += carry6;
+ h6 -= carry6 * ((uint32_t) 1L << 26);
+ carry7 = h7 >> 25;
+ h8 += carry7;
+ h7 -= carry7 * ((uint32_t) 1L << 25);
+ carry8 = h8 >> 26;
+ h9 += carry8;
+ h8 -= carry8 * ((uint32_t) 1L << 26);
+ carry9 = h9 >> 25;
+ h9 -= carry9 * ((uint32_t) 1L << 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 * ((uint32_t) 1 << 2));
+ s[4] = h1 >> 6;
+ s[5] = h1 >> 14;
+ s[6] = (h1 >> 22) | (h2 * ((uint32_t) 1 << 3));
+ s[7] = h2 >> 5;
+ s[8] = h2 >> 13;
+ s[9] = (h2 >> 21) | (h3 * ((uint32_t) 1 << 5));
+ s[10] = h3 >> 3;
+ s[11] = h3 >> 11;
+ s[12] = (h3 >> 19) | (h4 * ((uint32_t) 1 << 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 * ((uint32_t) 1 << 1));
+ s[20] = h6 >> 7;
+ s[21] = h6 >> 15;
+ s[22] = (h6 >> 23) | (h7 * ((uint32_t) 1 << 3));
+ s[23] = h7 >> 5;
+ s[24] = h7 >> 13;
+ s[25] = (h7 >> 21) | (h8 * ((uint32_t) 1 << 4));
+ s[26] = h8 >> 4;
+ s[27] = h8 >> 12;
+ s[28] = (h8 >> 20) | (h9 * ((uint32_t) 1 << 6));
+ s[29] = h9 >> 2;
+ s[30] = h9 >> 10;
+ s[31] = h9 >> 18;
+}
+
+/*
+ return 1 if f is in {1,3,5,...,q-2}
+ return 0 if f is in {0,2,4,...,q-1}
+
+ Preconditions:
+ |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+
+int fe_isnegative(const fe f)
+{
+ unsigned char s[32];
+ fe_tobytes (s, f);
+ return s[0] & 1;
+}
+
+/*
+ return 1 if f == 0
+ return 0 if f != 0
+
+ Preconditions:
+ |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+
+static unsigned char zero[32];
+
+int verify_32(const unsigned char *x, const unsigned char *y)
+{
+ volatile uint_fast16_t d = 0U;
+ int i;
+
+ for (i = 0; i < 32; i++) {
+ d |= x[i] ^ y[i];
}
- u += a[31];
- a[31] = u;
+ return (1 & ((d - 1) >> 8)) - 1;
+}
+
+int fe_isnonzero(const fe f)
+{
+ unsigned char s[32];
+ fe_tobytes (s, f);
+ return verify_32 (s, zero);
}
-static const unsigned int minusp[32] = {
- 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, 0, 0, 128
-};
+/*
+ h = f * g
+ Can overlap h with f or g.
-static void curve25519_ref_freeze (unsigned int a[32])
+ Preconditions:
+ |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+ |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+ Postconditions:
+ |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+ */
+
+/*
+ Notes on implementation strategy:
+
+ Using schoolbook multiplication.
+ Karatsuba would save a little in some cost models.
+
+ Most multiplications by 2 and 19 are 32-bit precomputations;
+ cheaper than 64-bit postcomputations.
+
+ There is one remaining multiplication by 19 in the carry chain;
+ one *19 precomputation can be merged into this,
+ but the resulting data flow is considerably less clean.
+
+ There are 12 carries below.
+ 10 of them are 2-way parallelizable and vectorizable.
+ Can get away with 11 carries, but then data flow is much deeper.
+
+ With tighter constraints on inputs can squeeze carries into int32.
+ */
+
+void fe_mul(fe h, const fe f, const fe g)
{
- unsigned int aorig[32];
- unsigned int j;
- unsigned int negative;
+ 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) (1L << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 * ((uint64_t) 1L << 26);
+ carry4 = (h4 + (int64_t) (1L << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 * ((uint64_t) 1L << 26);
+ /* |h0| <= 2^25 */
+ /* |h4| <= 2^25 */
+ /* |h1| <= 1.71*2^59 */
+ /* |h5| <= 1.71*2^59 */
+
+ carry1 = (h1 + (int64_t) (1L << 24)) >> 25;
+ h2 += carry1;
+ h1 -= carry1 * ((uint64_t) 1L << 25);
+ carry5 = (h5 + (int64_t) (1L << 24)) >> 25;
+ h6 += carry5;
+ h5 -= carry5 * ((uint64_t) 1L << 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 */
- for (j = 0; j < 32; ++j)
- aorig[j] = a[j];
- add (a, a, minusp);
- negative = -((a[31] >> 7) & 1);
- for (j = 0; j < 32; ++j)
- a[j] ^= negative & (aorig[j] ^ a[j]);
+ carry2 = (h2 + (int64_t) (1L << 25)) >> 26;
+ h3 += carry2;
+ h2 -= carry2 * ((uint64_t) 1L << 26);
+ carry6 = (h6 + (int64_t) (1L << 25)) >> 26;
+ h7 += carry6;
+ h6 -= carry6 * ((uint64_t) 1L << 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) (1L << 24)) >> 25;
+ h4 += carry3;
+ h3 -= carry3 * ((uint64_t) 1L << 25);
+ carry7 = (h7 + (int64_t) (1L << 24)) >> 25;
+ h8 += carry7;
+ h7 -= carry7 * ((uint64_t) 1L << 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) (1L << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 * ((uint64_t) 1L << 26);
+ carry8 = (h8 + (int64_t) (1L << 25)) >> 26;
+ h9 += carry8;
+ h8 -= carry8 * ((uint64_t) 1L << 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) (1L << 24)) >> 25;
+ h0 += carry9 * 19;
+ h9 -= carry9 * ((uint64_t) 1L << 25);
+ /* |h9| <= 2^24; from now on fits into int32 unchanged */
+ /* |h0| <= 1.1*2^39 */
+
+ carry0 = (h0 + (int64_t) (1L << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 * ((uint64_t) 1L << 26);
+ /* |h0| <= 2^25; from now on fits into int32 unchanged */
+ /* |h1| <= 1.01*2^24 */
+
+ h[0] = (int32_t) h0;
+ h[1] = (int32_t) h1;
+ h[2] = (int32_t) h2;
+ h[3] = (int32_t) h3;
+ h[4] = (int32_t) h4;
+ h[5] = (int32_t) h5;
+ h[6] = (int32_t) h6;
+ h[7] = (int32_t) h7;
+ h[8] = (int32_t) h8;
+ h[9] = (int32_t) h9;
}
-static void curve25519_ref_mult (unsigned int out[32],
- const unsigned int a[32],
- const unsigned int b[32])
+/*
+ h = -f
+
+ Preconditions:
+ |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+ Postconditions:
+ |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ */
+
+void fe_neg(fe h, const fe f)
{
- unsigned int i;
- unsigned int j;
- unsigned int u;
+ 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;
+}
- for (i = 0; i < 32; ++i) {
- u = 0;
- for (j = 0; j <= i; ++j)
- u += a[j] * b[i - j];
- for (j = i + 1; j < 32; ++j)
- u += 38 * a[j] * b[i + 32 - j];
- out[i] = u;
+/*
+ h = f * f
+ Can overlap h with f.
+
+ Preconditions:
+ |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+ Postconditions:
+ |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+ */
+
+/*
+ See fe_mul.c for discussion of implementation strategy.
+ */
+
+void fe_sq(fe h, const fe f)
+{
+ 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) (1L << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 * ((uint64_t) 1L << 26);
+ carry4 = (h4 + (int64_t) (1L << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 * ((uint64_t) 1L << 26);
+
+ carry1 = (h1 + (int64_t) (1L << 24)) >> 25;
+ h2 += carry1;
+ h1 -= carry1 * ((uint64_t) 1L << 25);
+ carry5 = (h5 + (int64_t) (1L << 24)) >> 25;
+ h6 += carry5;
+ h5 -= carry5 * ((uint64_t) 1L << 25);
+
+ carry2 = (h2 + (int64_t) (1L << 25)) >> 26;
+ h3 += carry2;
+ h2 -= carry2 * ((uint64_t) 1L << 26);
+ carry6 = (h6 + (int64_t) (1L << 25)) >> 26;
+ h7 += carry6;
+ h6 -= carry6 * ((uint64_t) 1L << 26);
+
+ carry3 = (h3 + (int64_t) (1L << 24)) >> 25;
+ h4 += carry3;
+ h3 -= carry3 * ((uint64_t) 1L << 25);
+ carry7 = (h7 + (int64_t) (1L << 24)) >> 25;
+ h8 += carry7;
+ h7 -= carry7 * ((uint64_t) 1L << 25);
+
+ carry4 = (h4 + (int64_t) (1L << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 * ((uint64_t) 1L << 26);
+ carry8 = (h8 + (int64_t) (1L << 25)) >> 26;
+ h9 += carry8;
+ h8 -= carry8 * ((uint64_t) 1L << 26);
+
+ carry9 = (h9 + (int64_t) (1L << 24)) >> 25;
+ h0 += carry9 * 19;
+ h9 -= carry9 * ((uint64_t) 1L << 25);
+
+ carry0 = (h0 + (int64_t) (1L << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 * ((uint64_t) 1L << 26);
+
+ h[0] = (int32_t) h0;
+ h[1] = (int32_t) h1;
+ h[2] = (int32_t) h2;
+ h[3] = (int32_t) h3;
+ h[4] = (int32_t) h4;
+ h[5] = (int32_t) h5;
+ h[6] = (int32_t) h6;
+ h[7] = (int32_t) h7;
+ h[8] = (int32_t) h8;
+ h[9] = (int32_t) h9;
+}
+
+/*
+ h = 2 * f * f
+ Can overlap h with f.
+
+ Preconditions:
+ |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+ Postconditions:
+ |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+ */
+
+/*
+ See fe_mul.c for discussion of implementation strategy.
+ */
+
+void fe_sq2(fe h, const fe f)
+{
+ 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) (1L << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 * ((uint64_t) 1L << 26);
+ carry4 = (h4 + (int64_t) (1L << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 * ((uint64_t) 1L << 26);
+
+ carry1 = (h1 + (int64_t) (1L << 24)) >> 25;
+ h2 += carry1;
+ h1 -= carry1 * ((uint64_t) 1L << 25);
+ carry5 = (h5 + (int64_t) (1L << 24)) >> 25;
+ h6 += carry5;
+ h5 -= carry5 * ((uint64_t) 1L << 25);
+
+ carry2 = (h2 + (int64_t) (1L << 25)) >> 26;
+ h3 += carry2;
+ h2 -= carry2 * ((uint64_t) 1L << 26);
+ carry6 = (h6 + (int64_t) (1L << 25)) >> 26;
+ h7 += carry6;
+ h6 -= carry6 * ((uint64_t) 1L << 26);
+
+ carry3 = (h3 + (int64_t) (1L << 24)) >> 25;
+ h4 += carry3;
+ h3 -= carry3 * ((uint64_t) 1L << 25);
+ carry7 = (h7 + (int64_t) (1L << 24)) >> 25;
+ h8 += carry7;
+ h7 -= carry7 * ((uint64_t) 1L << 25);
+
+ carry4 = (h4 + (int64_t) (1L << 25)) >> 26;
+ h5 += carry4;
+ h4 -= carry4 * ((uint64_t) 1L << 26);
+ carry8 = (h8 + (int64_t) (1L << 25)) >> 26;
+ h9 += carry8;
+ h8 -= carry8 * ((uint64_t) 1L << 26);
+
+ carry9 = (h9 + (int64_t) (1L << 24)) >> 25;
+ h0 += carry9 * 19;
+ h9 -= carry9 * ((uint64_t) 1L << 25);
+
+ carry0 = (h0 + (int64_t) (1L << 25)) >> 26;
+ h1 += carry0;
+ h0 -= carry0 * ((uint64_t) 1L << 26);
+
+ h[0] = (int32_t) h0;
+ h[1] = (int32_t) h1;
+ h[2] = (int32_t) h2;
+ h[3] = (int32_t) h3;
+ h[4] = (int32_t) h4;
+ h[5] = (int32_t) h5;
+ h[6] = (int32_t) h6;
+ h[7] = (int32_t) h7;
+ h[8] = (int32_t) h8;
+ h[9] = (int32_t) h9;
+}
+
+void fe_invert(fe out, const fe z)
+{
+ fe t0;
+ fe t1;
+ fe t2;
+ fe t3;
+ int i;
+
+ fe_sq (t0, z);
+ fe_sq (t1, t0);
+ fe_sq (t1, t1);
+ fe_mul (t1, z, t1);
+ fe_mul (t0, t0, t1);
+ fe_sq (t2, t0);
+ fe_mul (t1, t1, t2);
+ fe_sq (t2, t1);
+ for (i = 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);
}
- curve25519_ref_squeeze (out);
+ 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);
}
-static void curve25519_ref_mult121665 (unsigned int out[32], const unsigned int a[32])
+void fe_pow22523(fe out, const fe z)
{
- unsigned int j;
- unsigned int u;
+ fe t0;
+ fe t1;
+ fe t2;
+ int i;
- u = 0;
- for (j = 0; j < 31; ++j) {
- u += 121665 * a[j];
- out[j] = u & 255;
- u >>= 8;
+ fe_sq (t0, z);
+ fe_sq (t1, t0);
+ fe_sq (t1, t1);
+ fe_mul (t1, z, t1);
+ fe_mul (t0, t0, t1);
+ fe_sq (t0, t0);
+ fe_mul (t0, t1, t0);
+ fe_sq (t1, t0);
+ for (i = 1; i < 5; ++i) {
+ fe_sq (t1, t1);
+ }
+ fe_mul (t0, t1, t0);
+ fe_sq (t1, t0);
+ for (i = 1; i < 10; ++i) {
+ fe_sq (t1, t1);
+ }
+ fe_mul (t1, t1, t0);
+ fe_sq (t2, t1);
+ for (i = 1; i < 20; ++i) {
+ fe_sq (t2, t2);
+ }
+ fe_mul (t1, t2, t1);
+ fe_sq (t1, t1);
+ for (i = 1; i < 10; ++i) {
+ fe_sq (t1, t1);
}
- u += 121665 * a[31];
- out[31] = u & 127;
- u = 19 * (u >> 7);
- for (j = 0; j < 31; ++j) {
- u += out[j];
- out[j] = u & 255;
- u >>= 8;
+ fe_mul (t0, t1, t0);
+ fe_sq (t1, t0);
+ for (i = 1; i < 50; ++i) {
+ fe_sq (t1, t1);
}
- u += out[j];
- out[j] = u;
+ fe_mul (t1, t1, t0);
+ fe_sq (t2, t1);
+ for (i = 1; i < 100; ++i) {
+ fe_sq (t2, t2);
+ }
+ fe_mul (t1, t2, t1);
+ fe_sq (t1, t1);
+ for (i = 1; i < 50; ++i) {
+ fe_sq (t1, t1);
+ }
+ fe_mul (t0, t1, t0);
+ fe_sq (t0, t0);
+ fe_sq (t0, t0);
+ fe_mul (out, t0, z);
}
-static void curve25519_ref_square (unsigned int out[32], const unsigned int a[32])
+/*
+ h = f - g
+ Can overlap h with f or g.
+
+ Preconditions:
+ |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+ |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+ Postconditions:
+ |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+ */
+
+void fe_sub(fe h, const fe f, const fe g)
{
- unsigned int i;
- unsigned int j;
- unsigned int u;
+ 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;
+}
- for (i = 0; i < 32; ++i) {
- u = 0;
- for (j = 0; j < i - j; ++j)
- u += a[j] * a[i - j];
- for (j = i + 1; j < i + 32 - j; ++j)
- u += 38 * a[j] * a[i + 32 - j];
- u *= 2;
- if ((i & 1) == 0) {
- u += a[i / 2] * a[i / 2];
- u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
+/*
+ r = p + q
+ */
+
+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);
+}
+
+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;
+ }
+ }
}
- out[i] = u;
- }
- curve25519_ref_squeeze (out);
+
}
-static void curve25519_ref_select (unsigned int p[64],
- unsigned int q[64],
- const unsigned int r[64],
- const unsigned int s[64],
- unsigned int b)
+#include "base_constants2.h"
+
+/* 37095705934669439343138083508754565189542113879843219016388785533085940283555 */
+static const fe d =
+{ -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719,
+ -18696448, -12055116 };
+
+/* sqrt(-1) */
+static const fe sqrtm1 =
+{ -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654,
+ 326686, 11406482 };
+
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s)
{
- unsigned int j;
- unsigned int t;
- unsigned int bminus1;
+ fe u;
+ fe v;
+ fe v3;
+ fe vxx;
+ fe check;
+
+ fe_frombytes (h->Y, s);
+ fe_1 (h->Z);
+ fe_sq (u, h->Y);
+ fe_mul (v, u, d);
+ fe_sub (u, u, h->Z); /* u = y^2-1 */
+ fe_add (v, v, h->Z); /* v = dy^2+1 */
- bminus1 = b - 1;
- for (j = 0; j < 64; ++j) {
- t = bminus1 & (r[j] ^ s[j]);
- p[j] = s[j] ^ t;
- q[j] = r[j] ^ t;
+ fe_sq (v3, v);
+ fe_mul (v3, v3, v); /* v3 = v^3 */
+ fe_sq (h->X, v3);
+ fe_mul (h->X, h->X, v);
+ fe_mul (h->X, h->X, u); /* x = uv^7 */
+
+ fe_pow22523 (h->X, h->X); /* x = (uv^7)^((q-5)/8) */
+ fe_mul (h->X, h->X, v3);
+ fe_mul (h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
+
+ fe_sq (vxx, h->X);
+ fe_mul (vxx, vxx, v);
+ fe_sub (check, vxx, u); /* vx^2-u */
+ if (fe_isnonzero (check)) {
+ fe_add (check, vxx, u); /* vx^2+u */
+ if (fe_isnonzero (check))
+ return -1;
+ fe_mul (h->X, h->X, sqrtm1);
}
+
+ if (fe_isnegative (h->X) == (s[31] >> 7))
+ fe_neg (h->X, h->X);
+
+ fe_mul (h->T, h->X, h->Y);
+ return 0;
}
-static void mainloop (unsigned int work[64], const unsigned char e[32])
-{
- unsigned int xzm1[64];
- unsigned int xzm[64];
- unsigned int xzmb[64];
- unsigned int xzm1b[64];
- unsigned int xznb[64];
- unsigned int xzn1b[64];
- unsigned int a0[64];
- unsigned int a1[64];
- unsigned int b0[64];
- unsigned int b1[64];
- unsigned int c1[64];
- unsigned int r[32];
- unsigned int s[32];
- unsigned int t[32];
- unsigned int u[32];
- unsigned int j;
- unsigned int b;
- int pos;
+/*
+ r = p + q
+ */
- for (j = 0; j < 32; ++j)
- xzm1[j] = work[j];
- xzm1[32] = 1;
- for (j = 33; j < 64; ++j)
- xzm1[j] = 0;
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
+{
+ fe t0;
- xzm[0] = 1;
- for (j = 1; j < 64; ++j)
- xzm[j] = 0;
+ 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);
+}
- for (pos = 254; pos >= 0; --pos) {
- b = e[pos / 8] >> (pos & 7);
- b &= 1;
- curve25519_ref_select (xzmb, xzm1b, xzm, xzm1, b);
- add (a0, xzmb, xzmb + 32);
- curve25519_ref_sub (a0 + 32, xzmb, xzmb + 32);
- add (a1, xzm1b, xzm1b + 32);
- curve25519_ref_sub (a1 + 32, xzm1b, xzm1b + 32);
- curve25519_ref_square (b0, a0);
- curve25519_ref_square (b0 + 32, a0 + 32);
- curve25519_ref_mult (b1, a1, a0 + 32);
- curve25519_ref_mult (b1 + 32, a1 + 32, a0);
- add (c1, b1, b1 + 32);
- curve25519_ref_sub (c1 + 32, b1, b1 + 32);
- curve25519_ref_square (r, c1 + 32);
- curve25519_ref_sub (s, b0, b0 + 32);
- curve25519_ref_mult121665 (t, s);
- add (u, t, b0);
- curve25519_ref_mult (xznb, b0, b0 + 32);
- curve25519_ref_mult (xznb + 32, s, u);
- curve25519_ref_square (xzn1b, c1);
- curve25519_ref_mult (xzn1b + 32, r, work);
- curve25519_ref_select (xzm, xzm1, xznb, xzn1b, b);
+/*
+ r = p - q
+ */
+
+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);
+}
+
+/*
+ r = p
+ */
+
+extern void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p)
+{
+ fe_mul (r->X, p->X, p->T);
+ fe_mul (r->Y, p->Y, p->Z);
+ fe_mul (r->Z, p->Z, p->T);
+}
+
+/*
+ r = p
+ */
+
+extern void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p)
+{
+ fe_mul (r->X, p->X, p->T);
+ fe_mul (r->Y, p->Y, p->Z);
+ fe_mul (r->Z, p->Z, p->T);
+ fe_mul (r->T, p->X, p->Y);
+}
+
+void ge_p2_0(ge_p2 *h)
+{
+ fe_0 (h->X);
+ fe_1 (h->Y);
+ fe_1 (h->Z);
+}
+
+/*
+ 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);
+}
+
+void ge_p3_0(ge_p3 *h)
+{
+ fe_0 (h->X);
+ fe_1 (h->Y);
+ fe_1 (h->Z);
+ fe_0 (h->T);
+}
+
+/*
+ r = p
+ */
+
+/* 2 * d = 16295367250680780974490674513165176452449235426866156013048779062215315747161 */
+static const fe d2 =
+{ -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817,
+ -6495438, 29715968, 9444199 };
+
+extern void ge_p3_to_cached(ge_cached *r, const ge_p3 *p)
+{
+ fe_add (r->YplusX, p->Y, p->X);
+ fe_sub (r->YminusX, p->Y, p->X);
+ fe_copy (r->Z, p->Z);
+ fe_mul (r->T2d, p->T, d2);
+}
+
+/*
+ r = p
+ */
+
+extern void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p)
+{
+ fe_copy (r->X, p->X);
+ fe_copy (r->Y, p->Y);
+ fe_copy (r->Z, p->Z);
+}
+
+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;
+}
+
+/*
+ r = 2 * p
+ */
+
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p)
+{
+ ge_p2 q;
+ ge_p3_to_p2 (&q, p);
+ ge_p2_dbl (r, &q);
+}
+
+void ge_precomp_0(ge_precomp *h)
+{
+ fe_1 (h->yplusx);
+ fe_1 (h->yminusx);
+ fe_0 (h->xy2d);
+}
+
+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)
+{
+ uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+ x >>= 63; /* 1: yes; 0: no */
+ return x;
+}
+
+static void 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);
+}
+
+/* base[i][j] = (j+1)*256^i*B */
+#include "base_constants.h"
+
+
+static void ge_select(ge_precomp *t, int pos, signed char b)
+{
+ ge_precomp minust;
+ unsigned char bnegative = negative (b);
+ unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1));
+
+ ge_precomp_0 (t);
+ cmov (t, &base[pos][0], equal (babs, 1));
+ cmov (t, &base[pos][1], equal (babs, 2));
+ cmov (t, &base[pos][2], equal (babs, 3));
+ cmov (t, &base[pos][3], equal (babs, 4));
+ cmov (t, &base[pos][4], equal (babs, 5));
+ cmov (t, &base[pos][5], equal (babs, 6));
+ cmov (t, &base[pos][6], equal (babs, 7));
+ cmov (t, &base[pos][7], equal (babs, 8));
+ fe_copy (minust.yplusx, t->yminusx);
+ fe_copy (minust.yminusx, t->yplusx);
+ fe_neg (minust.xy2d, t->xy2d);
+ cmov (t, &minust, bnegative);
+}
+
+/*
+ r = p - q
+ */
+
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
+{
+ fe t0;
+
+ fe_add (r->X, p->Y, p->X);
+ fe_sub (r->Y, p->Y, p->X);
+ fe_mul (r->Z, r->X, q->YminusX);
+ fe_mul (r->Y, r->Y, q->YplusX);
+ fe_mul (r->T, q->T2d, p->T);
+ fe_mul (r->X, p->Z, q->Z);
+ fe_add (t0, r->X, r->X);
+ fe_sub (r->X, r->Z, r->Y);
+ fe_add (r->Y, r->Z, r->Y);
+ fe_sub (r->Z, t0, r->T);
+ fe_add (r->T, t0, r->T);
+}
+
+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;
+}
+
+/*
+ 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
+ */
+
+/*
+ r = a * A + b * B
+ where a = a[0]+256*a[1]+...+256^31 a[31].
+ and b = b[0]+256*b[1]+...+256^31 b[31].
+ B is the Ed25519 base point (x,4/5) with x positive.
+ */
+
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a,
+ const ge_p3 *A, const unsigned char *b)
+{
+ signed char aslide[256];
+ signed char bslide[256];
+ ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+ ge_p1p1 t;
+ ge_p3 u;
+ ge_p3 A2;
+ int i;
+
+ slide (aslide, a);
+ slide (bslide, b);
+
+ ge_p3_to_cached (&Ai[0], A);
+ ge_p3_dbl (&t, A);
+ ge_p1p1_to_p3 (&A2, &t);
+ ge_add (&t, &A2, &Ai[0]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[1], &u);
+ ge_add (&t, &A2, &Ai[1]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[2], &u);
+ ge_add (&t, &A2, &Ai[2]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[3], &u);
+ ge_add (&t, &A2, &Ai[3]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[4], &u);
+ ge_add (&t, &A2, &Ai[4]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[5], &u);
+ ge_add (&t, &A2, &Ai[5]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[6], &u);
+ ge_add (&t, &A2, &Ai[6]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[7], &u);
+
+ ge_p2_0 (r);
+
+ for (i = 255; i >= 0; --i) {
+ if (aslide[i] || bslide[i])
+ break;
}
- for (j = 0; j < 64; ++j)
- work[j] = xzm[j];
+ for (; i >= 0; --i) {
+ ge_p2_dbl (&t, r);
+
+ if (aslide[i] > 0) {
+ ge_p1p1_to_p3 (&u, &t);
+ ge_add (&t, &u, &Ai[aslide[i] / 2]);
+ }
+ else if (aslide[i] < 0) {
+ ge_p1p1_to_p3 (&u, &t);
+ ge_sub (&t, &u, &Ai[(-aslide[i]) / 2]);
+ }
+
+ if (bslide[i] > 0) {
+ ge_p1p1_to_p3 (&u, &t);
+ ge_madd (&t, &u, &Bi[bslide[i] / 2]);
+ }
+ else if (bslide[i] < 0) {
+ ge_p1p1_to_p3 (&u, &t);
+ ge_msub (&t, &u, &Bi[(-bslide[i]) / 2]);
+ }
+
+ ge_p1p1_to_p2 (r, &t);
+ }
}
-static void recip (unsigned int out[32], const unsigned int z[32])
+void ge_scalarmult_vartime(ge_p3 *r, const unsigned char *a, const ge_p3 *A)
{
- unsigned int z2[32];
- unsigned int z9[32];
- unsigned int z11[32];
- unsigned int z2_5_0[32];
- unsigned int z2_10_0[32];
- unsigned int z2_20_0[32];
- unsigned int z2_50_0[32];
- unsigned int z2_100_0[32];
- unsigned int t0[32];
- unsigned int t1[32];
+ signed char aslide[256];
+ ge_cached Ai[8];
+ ge_p1p1 t;
+ ge_p3 u;
+ ge_p3 A2;
int i;
- /* 2 */ curve25519_ref_square (z2, z);
- /* 4 */ curve25519_ref_square (t1, z2);
- /* 8 */ curve25519_ref_square (t0, t1);
- /* 9 */ curve25519_ref_mult (z9, t0, z);
- /* 11 */ curve25519_ref_mult (z11, z9, z2);
- /* 22 */ curve25519_ref_square (t0, z11);
- /* 2^5 - 2^0 = 31 */ curve25519_ref_mult (z2_5_0, t0, z9);
-
- /* 2^6 - 2^1 */ curve25519_ref_square (t0, z2_5_0);
- /* 2^7 - 2^2 */ curve25519_ref_square (t1, t0);
- /* 2^8 - 2^3 */ curve25519_ref_square (t0, t1);
- /* 2^9 - 2^4 */ curve25519_ref_square (t1, t0);
- /* 2^10 - 2^5 */ curve25519_ref_square (t0, t1);
- /* 2^10 - 2^0 */ curve25519_ref_mult (z2_10_0, t0, z2_5_0);
-
- /* 2^11 - 2^1 */ curve25519_ref_square (t0, z2_10_0);
- /* 2^12 - 2^2 */ curve25519_ref_square (t1, t0);
- /* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) {
- curve25519_ref_square (t0, t1);
- curve25519_ref_square (t1, t0);
+ slide (aslide, a);
+
+ ge_p3_to_cached (&Ai[0], A);
+ ge_p3_dbl (&t, A);
+ ge_p1p1_to_p3 (&A2, &t);
+ ge_add (&t, &A2, &Ai[0]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[1], &u);
+ ge_add (&t, &A2, &Ai[1]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[2], &u);
+ ge_add (&t, &A2, &Ai[2]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[3], &u);
+ ge_add (&t, &A2, &Ai[3]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[4], &u);
+ ge_add (&t, &A2, &Ai[4]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[5], &u);
+ ge_add (&t, &A2, &Ai[5]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[6], &u);
+ ge_add (&t, &A2, &Ai[6]);
+ ge_p1p1_to_p3 (&u, &t);
+ ge_p3_to_cached (&Ai[7], &u);
+
+ ge_p3_0 (r);
+
+ for (i = 255; i >= 0; --i) {
+ if (aslide[i])
+ break;
}
- /* 2^20 - 2^0 */ curve25519_ref_mult (z2_20_0, t1, z2_10_0);
- /* 2^21 - 2^1 */ curve25519_ref_square (t0, z2_20_0);
- /* 2^22 - 2^2 */ curve25519_ref_square (t1, t0);
- /* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) {
- curve25519_ref_square (t0, t1);
- curve25519_ref_square (t1, t0);
+ for (; i >= 0; --i) {
+ ge_p3_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]);
+ }
+
+ ge_p1p1_to_p3 (r, &t);
}
- /* 2^40 - 2^0 */ curve25519_ref_mult (t0, t1, z2_20_0);
+}
- /* 2^41 - 2^1 */ curve25519_ref_square (t1, t0);
- /* 2^42 - 2^2 */ curve25519_ref_square (t0, t1);
- /* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) {
- curve25519_ref_square (t1, t0);
- curve25519_ref_square (t0, t1);
+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;
}
- /* 2^50 - 2^0 */ curve25519_ref_mult (z2_50_0, t0, z2_10_0);
+ /* each e[i] is between 0 and 15 */
+ /* e[63] is between 0 and 7 */
- /* 2^51 - 2^1 */ curve25519_ref_square (t0, z2_50_0);
- /* 2^52 - 2^2 */ curve25519_ref_square (t1, t0);
- /* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) {
- curve25519_ref_square (t0, t1);
- curve25519_ref_square (t1, t0);
+ carry = 0;
+ for (i = 0; i < 63; ++i) {
+ e[i] += carry;
+ carry = e[i] + 8;
+ carry >>= 4;
+ e[i] -= carry * ((signed char) 1 << 4);
}
- /* 2^100 - 2^0 */ curve25519_ref_mult (z2_100_0, t1, z2_50_0);
+ e[63] += carry;
+ /* each e[i] is between -8 and 8 */
- /* 2^101 - 2^1 */ curve25519_ref_square (t1, z2_100_0);
- /* 2^102 - 2^2 */ curve25519_ref_square (t0, t1);
- /* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) {
- curve25519_ref_square (t1, t0);
- curve25519_ref_square (t0, t1);
+ ge_p3_0 (h);
+ for (i = 1; i < 64; i += 2) {
+ ge_select (&t, i / 2, e[i]);
+ ge_madd (&r, h, &t);
+ ge_p1p1_to_p3 (h, &r);
}
- /* 2^200 - 2^0 */ curve25519_ref_mult (t1, t0, z2_100_0);
- /* 2^201 - 2^1 */ curve25519_ref_square (t0, t1);
- /* 2^202 - 2^2 */ curve25519_ref_square (t1, t0);
- /* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) {
- curve25519_ref_square (t0, t1);
- curve25519_ref_square (t1, t0);
+ 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) {
+ ge_select (&t, i / 2, e[i]);
+ ge_madd (&r, h, &t);
+ ge_p1p1_to_p3 (h, &r);
}
- /* 2^250 - 2^0 */ curve25519_ref_mult (t0, t1, z2_50_0);
+}
- /* 2^251 - 2^1 */ curve25519_ref_square (t1, t0);
- /* 2^252 - 2^2 */ curve25519_ref_square (t0, t1);
- /* 2^253 - 2^3 */ curve25519_ref_square (t1, t0);
- /* 2^254 - 2^4 */ curve25519_ref_square (t0, t1);
- /* 2^255 - 2^5 */ curve25519_ref_square (t1, t0);
- /* 2^255 - 21 */ curve25519_ref_mult (out, t1, z11);
+/*
+ Input:
+ a[0]+256*a[1]+...+256^31*a[31] = a
+ b[0]+256*b[1]+...+256^31*b[31] = b
+ c[0]+256*c[1]+...+256^31*c[31] = c
+
+ Output:
+ s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+ where l = 2^252 + 27742317777372353535851937790883648493.
+ */
+
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b,
+ const unsigned char *c)
+{
+ 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 + (int64_t) (1L << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 * ((uint64_t) 1L << 21);
+ carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 * ((uint64_t) 1L << 21);
+ carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 * ((uint64_t) 1L << 21);
+ carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+ carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 * ((uint64_t) 1L << 21);
+ carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 * ((uint64_t) 1L << 21);
+ carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 * ((uint64_t) 1L << 21);
+ carry18 = (s18 + (int64_t) (1L << 20)) >> 21;
+ s19 += carry18;
+ s18 -= carry18 * ((uint64_t) 1L << 21);
+ carry20 = (s20 + (int64_t) (1L << 20)) >> 21;
+ s21 += carry20;
+ s20 -= carry20 * ((uint64_t) 1L << 21);
+ carry22 = (s22 + (int64_t) (1L << 20)) >> 21;
+ s23 += carry22;
+ s22 -= carry22 * ((uint64_t) 1L << 21);
+
+ carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 * ((uint64_t) 1L << 21);
+ carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 * ((uint64_t) 1L << 21);
+ carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 * ((uint64_t) 1L << 21);
+ carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * ((uint64_t) 1L << 21);
+ carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 * ((uint64_t) 1L << 21);
+ carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 * ((uint64_t) 1L << 21);
+ carry17 = (s17 + (int64_t) (1L << 20)) >> 21;
+ s18 += carry17;
+ s17 -= carry17 * ((uint64_t) 1L << 21);
+ carry19 = (s19 + (int64_t) (1L << 20)) >> 21;
+ s20 += carry19;
+ s19 -= carry19 * ((uint64_t) 1L << 21);
+ carry21 = (s21 + (int64_t) (1L << 20)) >> 21;
+ s22 += carry21;
+ s21 -= carry21 * ((uint64_t) 1L << 21);
+
+ s11 += s23 * 666643;
+ s12 += s23 * 470296;
+ s13 += s23 * 654183;
+ s14 -= s23 * 997805;
+ s15 += s23 * 136657;
+ s16 -= s23 * 683901;
+
+ s10 += s22 * 666643;
+ s11 += s22 * 470296;
+ s12 += s22 * 654183;
+ s13 -= s22 * 997805;
+ s14 += s22 * 136657;
+ s15 -= s22 * 683901;
+
+ s9 += s21 * 666643;
+ s10 += s21 * 470296;
+ s11 += s21 * 654183;
+ s12 -= s21 * 997805;
+ s13 += s21 * 136657;
+ s14 -= s21 * 683901;
+
+ s8 += s20 * 666643;
+ s9 += s20 * 470296;
+ s10 += s20 * 654183;
+ s11 -= s20 * 997805;
+ s12 += s20 * 136657;
+ s13 -= s20 * 683901;
+
+ s7 += s19 * 666643;
+ s8 += s19 * 470296;
+ s9 += s19 * 654183;
+ s10 -= s19 * 997805;
+ s11 += s19 * 136657;
+ s12 -= s19 * 683901;
+
+ s6 += s18 * 666643;
+ s7 += s18 * 470296;
+ s8 += s18 * 654183;
+ s9 -= s18 * 997805;
+ s10 += s18 * 136657;
+ s11 -= s18 * 683901;
+
+ carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+ carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 * ((uint64_t) 1L << 21);
+ carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 * ((uint64_t) 1L << 21);
+ carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 * ((uint64_t) 1L << 21);
+
+ carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * ((uint64_t) 1L << 21);
+ carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 * ((uint64_t) 1L << 21);
+ carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 * ((uint64_t) 1L << 21);
+
+ s5 += s17 * 666643;
+ s6 += s17 * 470296;
+ s7 += s17 * 654183;
+ s8 -= s17 * 997805;
+ s9 += s17 * 136657;
+ s10 -= s17 * 683901;
+
+ s4 += s16 * 666643;
+ s5 += s16 * 470296;
+ s6 += s16 * 654183;
+ s7 -= s16 * 997805;
+ s8 += s16 * 136657;
+ s9 -= s16 * 683901;
+
+ s3 += s15 * 666643;
+ s4 += s15 * 470296;
+ s5 += s15 * 654183;
+ s6 -= s15 * 997805;
+ s7 += s15 * 136657;
+ s8 -= s15 * 683901;
+
+ s2 += s14 * 666643;
+ s3 += s14 * 470296;
+ s4 += s14 * 654183;
+ s5 -= s14 * 997805;
+ s6 += s14 * 136657;
+ s7 -= s14 * 683901;
+
+ s1 += s13 * 666643;
+ s2 += s13 * 470296;
+ s3 += s13 * 654183;
+ s4 -= s13 * 997805;
+ s5 += s13 * 136657;
+ s6 -= s13 * 683901;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 * ((uint64_t) 1L << 21);
+ carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 * ((uint64_t) 1L << 21);
+ carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 * ((uint64_t) 1L << 21);
+ carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+
+ carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 * ((uint64_t) 1L << 21);
+ carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 * ((uint64_t) 1L << 21);
+ carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 * ((uint64_t) 1L << 21);
+ carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * ((uint64_t) 1L << 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 * ((uint64_t) 1L << 21);
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 * ((uint64_t) 1L << 21);
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 * ((uint64_t) 1L << 21);
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 * ((uint64_t) 1L << 21);
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 * ((uint64_t) 1L << 21);
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 * ((uint64_t) 1L << 21);
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+ carry11 = s11 >> 21;
+ s12 += carry11;
+ s11 -= carry11 * ((uint64_t) 1L << 21);
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 * ((uint64_t) 1L << 21);
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 * ((uint64_t) 1L << 21);
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 * ((uint64_t) 1L << 21);
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 * ((uint64_t) 1L << 21);
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 * ((uint64_t) 1L << 21);
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 * ((uint64_t) 1L << 21);
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+
+ s[0] = s0 >> 0;
+ s[1] = s0 >> 8;
+ s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
+ s[3] = s1 >> 3;
+ s[4] = s1 >> 11;
+ s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
+ s[6] = s2 >> 6;
+ s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
+ s[8] = s3 >> 1;
+ s[9] = s3 >> 9;
+ s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
+ s[11] = s4 >> 4;
+ s[12] = s4 >> 12;
+ s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
+ s[14] = s5 >> 7;
+ s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
+ s[16] = s6 >> 2;
+ s[17] = s6 >> 10;
+ s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
+ s[19] = s7 >> 5;
+ s[20] = s7 >> 13;
+ s[21] = s8 >> 0;
+ s[22] = s8 >> 8;
+ s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
+ s[24] = s9 >> 3;
+ s[25] = s9 >> 11;
+ s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
+ s[27] = s10 >> 6;
+ s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
+ s[29] = s11 >> 1;
+ s[30] = s11 >> 9;
+ s[31] = s11 >> 17;
}
-int scalarmult_ref (unsigned char *q,
- const unsigned char *n,
- const unsigned char *p)
+/*
+ Input:
+ s[0]+256*s[1]+...+256^63*s[63] = s
+
+ Output:
+ s[0]+256*s[1]+...+256^31*s[31] = s mod l
+ where l = 2^252 + 27742317777372353535851937790883648493.
+ Overwrites s in place.
+ */
+
+void sc_reduce(unsigned char *s)
+{
+ int64_t s0 = 2097151 & load_3 (s);
+ int64_t s1 = 2097151 & (load_4 (s + 2) >> 5);
+ int64_t s2 = 2097151 & (load_3 (s + 5) >> 2);
+ int64_t s3 = 2097151 & (load_4 (s + 7) >> 7);
+ int64_t s4 = 2097151 & (load_4 (s + 10) >> 4);
+ int64_t s5 = 2097151 & (load_3 (s + 13) >> 1);
+ int64_t s6 = 2097151 & (load_4 (s + 15) >> 6);
+ int64_t s7 = 2097151 & (load_3 (s + 18) >> 3);
+ int64_t s8 = 2097151 & load_3 (s + 21);
+ int64_t s9 = 2097151 & (load_4 (s + 23) >> 5);
+ int64_t s10 = 2097151 & (load_3 (s + 26) >> 2);
+ int64_t s11 = 2097151 & (load_4 (s + 28) >> 7);
+ int64_t s12 = 2097151 & (load_4 (s + 31) >> 4);
+ int64_t s13 = 2097151 & (load_3 (s + 34) >> 1);
+ int64_t s14 = 2097151 & (load_4 (s + 36) >> 6);
+ int64_t s15 = 2097151 & (load_3 (s + 39) >> 3);
+ int64_t s16 = 2097151 & load_3 (s + 42);
+ int64_t s17 = 2097151 & (load_4 (s + 44) >> 5);
+ int64_t s18 = 2097151 & (load_3 (s + 47) >> 2);
+ int64_t s19 = 2097151 & (load_4 (s + 49) >> 7);
+ int64_t s20 = 2097151 & (load_4 (s + 52) >> 4);
+ int64_t s21 = 2097151 & (load_3 (s + 55) >> 1);
+ int64_t s22 = 2097151 & (load_4 (s + 57) >> 6);
+ int64_t s23 = (load_4 (s + 60) >> 3);
+ int64_t carry0;
+ int64_t carry1;
+ int64_t carry2;
+ int64_t carry3;
+ int64_t carry4;
+ int64_t carry5;
+ int64_t carry6;
+ int64_t carry7;
+ int64_t carry8;
+ int64_t carry9;
+ int64_t carry10;
+ int64_t carry11;
+ int64_t carry12;
+ int64_t carry13;
+ int64_t carry14;
+ int64_t carry15;
+ int64_t carry16;
+
+ s11 += s23 * 666643;
+ s12 += s23 * 470296;
+ s13 += s23 * 654183;
+ s14 -= s23 * 997805;
+ s15 += s23 * 136657;
+ s16 -= s23 * 683901;
+
+ s10 += s22 * 666643;
+ s11 += s22 * 470296;
+ s12 += s22 * 654183;
+ s13 -= s22 * 997805;
+ s14 += s22 * 136657;
+ s15 -= s22 * 683901;
+
+ s9 += s21 * 666643;
+ s10 += s21 * 470296;
+ s11 += s21 * 654183;
+ s12 -= s21 * 997805;
+ s13 += s21 * 136657;
+ s14 -= s21 * 683901;
+
+ s8 += s20 * 666643;
+ s9 += s20 * 470296;
+ s10 += s20 * 654183;
+ s11 -= s20 * 997805;
+ s12 += s20 * 136657;
+ s13 -= s20 * 683901;
+
+ s7 += s19 * 666643;
+ s8 += s19 * 470296;
+ s9 += s19 * 654183;
+ s10 -= s19 * 997805;
+ s11 += s19 * 136657;
+ s12 -= s19 * 683901;
+
+ s6 += s18 * 666643;
+ s7 += s18 * 470296;
+ s8 += s18 * 654183;
+ s9 -= s18 * 997805;
+ s10 += s18 * 136657;
+ s11 -= s18 * 683901;
+
+ carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+ carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
+ s13 += carry12;
+ s12 -= carry12 * ((uint64_t) 1L << 21);
+ carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
+ s15 += carry14;
+ s14 -= carry14 * ((uint64_t) 1L << 21);
+ carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
+ s17 += carry16;
+ s16 -= carry16 * ((uint64_t) 1L << 21);
+
+ carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * ((uint64_t) 1L << 21);
+ carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
+ s14 += carry13;
+ s13 -= carry13 * ((uint64_t) 1L << 21);
+ carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
+ s16 += carry15;
+ s15 -= carry15 * ((uint64_t) 1L << 21);
+
+ s5 += s17 * 666643;
+ s6 += s17 * 470296;
+ s7 += s17 * 654183;
+ s8 -= s17 * 997805;
+ s9 += s17 * 136657;
+ s10 -= s17 * 683901;
+
+ s4 += s16 * 666643;
+ s5 += s16 * 470296;
+ s6 += s16 * 654183;
+ s7 -= s16 * 997805;
+ s8 += s16 * 136657;
+ s9 -= s16 * 683901;
+
+ s3 += s15 * 666643;
+ s4 += s15 * 470296;
+ s5 += s15 * 654183;
+ s6 -= s15 * 997805;
+ s7 += s15 * 136657;
+ s8 -= s15 * 683901;
+
+ s2 += s14 * 666643;
+ s3 += s14 * 470296;
+ s4 += s14 * 654183;
+ s5 -= s14 * 997805;
+ s6 += s14 * 136657;
+ s7 -= s14 * 683901;
+
+ s1 += s13 * 666643;
+ s2 += s13 * 470296;
+ s3 += s13 * 654183;
+ s4 -= s13 * 997805;
+ s5 += s13 * 136657;
+ s6 -= s13 * 683901;
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+ s12 = 0;
+
+ carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
+ s1 += carry0;
+ s0 -= carry0 * ((uint64_t) 1L << 21);
+ carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
+ s3 += carry2;
+ s2 -= carry2 * ((uint64_t) 1L << 21);
+ carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
+ s5 += carry4;
+ s4 -= carry4 * ((uint64_t) 1L << 21);
+ carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+
+ carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
+ s2 += carry1;
+ s1 -= carry1 * ((uint64_t) 1L << 21);
+ carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
+ s4 += carry3;
+ s3 -= carry3 * ((uint64_t) 1L << 21);
+ carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
+ s6 += carry5;
+ s5 -= carry5 * ((uint64_t) 1L << 21);
+ carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
+ s12 += carry11;
+ s11 -= carry11 * ((uint64_t) 1L << 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 * ((uint64_t) 1L << 21);
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 * ((uint64_t) 1L << 21);
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 * ((uint64_t) 1L << 21);
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 * ((uint64_t) 1L << 21);
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 * ((uint64_t) 1L << 21);
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 * ((uint64_t) 1L << 21);
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+ carry11 = s11 >> 21;
+ s12 += carry11;
+ s11 -= carry11 * ((uint64_t) 1L << 21);
+
+ s0 += s12 * 666643;
+ s1 += s12 * 470296;
+ s2 += s12 * 654183;
+ s3 -= s12 * 997805;
+ s4 += s12 * 136657;
+ s5 -= s12 * 683901;
+
+ carry0 = s0 >> 21;
+ s1 += carry0;
+ s0 -= carry0 * ((uint64_t) 1L << 21);
+ carry1 = s1 >> 21;
+ s2 += carry1;
+ s1 -= carry1 * ((uint64_t) 1L << 21);
+ carry2 = s2 >> 21;
+ s3 += carry2;
+ s2 -= carry2 * ((uint64_t) 1L << 21);
+ carry3 = s3 >> 21;
+ s4 += carry3;
+ s3 -= carry3 * ((uint64_t) 1L << 21);
+ carry4 = s4 >> 21;
+ s5 += carry4;
+ s4 -= carry4 * ((uint64_t) 1L << 21);
+ carry5 = s5 >> 21;
+ s6 += carry5;
+ s5 -= carry5 * ((uint64_t) 1L << 21);
+ carry6 = s6 >> 21;
+ s7 += carry6;
+ s6 -= carry6 * ((uint64_t) 1L << 21);
+ carry7 = s7 >> 21;
+ s8 += carry7;
+ s7 -= carry7 * ((uint64_t) 1L << 21);
+ carry8 = s8 >> 21;
+ s9 += carry8;
+ s8 -= carry8 * ((uint64_t) 1L << 21);
+ carry9 = s9 >> 21;
+ s10 += carry9;
+ s9 -= carry9 * ((uint64_t) 1L << 21);
+ carry10 = s10 >> 21;
+ s11 += carry10;
+ s10 -= carry10 * ((uint64_t) 1L << 21);
+
+ s[0] = s0 >> 0;
+ s[1] = s0 >> 8;
+ s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
+ s[3] = s1 >> 3;
+ s[4] = s1 >> 11;
+ s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
+ s[6] = s2 >> 6;
+ s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
+ s[8] = s3 >> 1;
+ s[9] = s3 >> 9;
+ s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
+ s[11] = s4 >> 4;
+ s[12] = s4 >> 12;
+ s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
+ s[14] = s5 >> 7;
+ s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
+ s[16] = s6 >> 2;
+ s[17] = s6 >> 10;
+ s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
+ s[19] = s7 >> 5;
+ s[20] = s7 >> 13;
+ s[21] = s8 >> 0;
+ s[22] = s8 >> 8;
+ s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
+ s[24] = s9 >> 3;
+ s[25] = s9 >> 11;
+ s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
+ s[27] = s10 >> 6;
+ s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
+ s[29] = s11 >> 1;
+ s[30] = s11 >> 9;
+ s[31] = s11 >> 17;
+}
+
+/*
+Replace (f,g) with (g,f) if b == 1;
+replace (f,g) with (f,g) if b == 0.
+
+Preconditions: b in {0,1}.
+*/
+
+static void fe_cswap(fe f, 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;
+ b = (unsigned int) (-(int) 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;
+ g[0] = g0 ^ x0;
+ g[1] = g1 ^ x1;
+ g[2] = g2 ^ x2;
+ g[3] = g3 ^ x3;
+ g[4] = g4 ^ x4;
+ g[5] = g5 ^ x5;
+ g[6] = g6 ^ x6;
+ g[7] = g7 ^ x7;
+ g[8] = g8 ^ x8;
+ g[9] = g9 ^ x9;
+}
+
+/*
+ h = f * 121666
+ 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.
+ */
+
+static void fe_mul121666(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];
+ int64_t h0 = f0 * (int64_t) 121666;
+ int64_t h1 = f1 * (int64_t) 121666;
+ int64_t h2 = f2 * (int64_t) 121666;
+ int64_t h3 = f3 * (int64_t) 121666;
+ int64_t h4 = f4 * (int64_t) 121666;
+ int64_t h5 = f5 * (int64_t) 121666;
+ int64_t h6 = f6 * (int64_t) 121666;
+ int64_t h7 = f7 * (int64_t) 121666;
+ int64_t h8 = f8 * (int64_t) 121666;
+ int64_t h9 = f9 * (int64_t) 121666;
+ 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;
+
+ 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;
+}
+
+int
+scalarmult_ref(unsigned char *q,
+ const unsigned char *n, const unsigned char *p)
{
- unsigned int work[96];
unsigned char e[32];
unsigned int i;
+ fe x1;
+ fe x2;
+ fe z2;
+ fe x3;
+ fe z3;
+ fe tmp0;
+ fe tmp1;
+ int pos;
+ unsigned int swap;
+ unsigned int b;
+
for (i = 0; i < 32; ++i)
e[i] = n[i];
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
- for (i = 0; i < 32; ++i)
- work[i] = p[i];
- work[31] &= 127;
- mainloop (work, e);
- recip (work + 32, work + 32);
- curve25519_ref_mult (work + 64, work, work + 32);
- curve25519_ref_freeze (work + 64);
- for (i = 0; i < 32; ++i)
- q[i] = work[64 + i];
+ fe_frombytes (x1, p);
+ fe_1 (x2);
+ fe_0 (z2);
+ fe_copy (x3, x1);
+ fe_1 (z3);
+
+ swap = 0;
+ for (pos = 254; pos >= 0; --pos) {
+ b = e[pos / 8] >> (pos & 7);
+ b &= 1;
+ swap ^= b;
+ fe_cswap (x2, x3, swap);
+ fe_cswap (z2, z3, swap);
+ swap = b;
+ fe_sub (tmp0, x3, z3);
+ fe_sub (tmp1, x2, z2);
+ fe_add (x2, x2, z2);
+ fe_add (z2, x3, z3);
+ fe_mul (z3, tmp0, x2);
+ fe_mul (z2, z2, tmp1);
+ fe_sq (tmp0, tmp1);
+ fe_sq (tmp1, x2);
+ fe_add (x3, z3, z2);
+ fe_sub (z2, z3, z2);
+ fe_mul (x2, tmp1, tmp0);
+ fe_sub (tmp1, tmp1, tmp0);
+ fe_sq (z2, z2);
+ fe_mul121666 (z3, tmp1);
+ fe_sq (x3, x3);
+ fe_add (tmp0, tmp0, z3);
+ fe_mul (z3, x1, z2);
+ fe_mul (z2, tmp1, tmp0);
+ }
+ fe_cswap (x2, x3, swap);
+ fe_cswap (z2, z3, swap);
+
+ fe_invert (z2, z2);
+ fe_mul (x2, x2, z2);
+ fe_tobytes (q, x2);
return 0;
}
+static void edwards_to_montgomery(fe montgomeryX, const fe edwardsY,
+ const fe edwardsZ)
+{
+ fe tempX;
+ fe tempZ;
+
+ fe_add (tempX, edwardsZ, edwardsY);
+ fe_sub (tempZ, edwardsZ, edwardsY);
+ fe_invert (tempZ, tempZ);
+ fe_mul (montgomeryX, tempX, tempZ);
+}
+
int
-scalarmult_base_ref (unsigned char *q,
+scalarmult_base_ref(unsigned char *q,
const unsigned char *n)
{
- return scalarmult_ref (q, n, curve25519_basepoint);
+ unsigned char e[32];
+ ge_p3 A;
+ fe pk;
+ unsigned int i;
+
+ for (i = 0; i < 32; ++i)
+ e[i] = n[i];
+ e[0] &= 248;
+ e[31] &= 127;
+ e[31] |= 64;
+ ge_scalarmult_base (&A, e);
+ edwards_to_montgomery (pk, A.Y, A.Z);
+ fe_tobytes (q, pk);
+ return 0;
}
projects / rspamd.git / commitdiff