module ECDSA

Defined in:

ecdsa.cr
ecdsa/curves.cr
ecdsa/exceptions/not_invertible.cr
ecdsa/exceptions/point_not_in_group.cr
ecdsa/exceptions/points_group_mismatch.cr
ecdsa/exceptions/public_key_is_infinity.cr
ecdsa/exceptions/signature_not_in_range.cr
ecdsa/group.cr
ecdsa/math.cr
ecdsa/point.cr
ecdsa/precomputed.cr
ecdsa/signature.cr
ecdsa/version.cr

Constant Summary

CURVES = {:secp192k1 => {d: 192, p: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFEE37", base: 16), a: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000", base: 16), b: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000003", base: 16), gx: BigInt.new("DB4FF10E C057E9AE 26B07D02 80B7F434 1DA5D1B1 EAE06C7D", base: 16), gy: BigInt.new("9B2F2F6D 9C5628A7 844163D0 15BE8634 4082AA88 D95E2F9D", base: 16), n: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFE 26F2FC17 0F69466A 74DEFD8D", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp192r1 => {d: 192, p: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF FFFFFFFF", base: 16), a: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF FFFFFFFC", base: 16), b: BigInt.new("64210519 E59C80E7 0FA7E9AB 72243049 FEB8DEEC C146B9B1", base: 16), gx: BigInt.new("188DA80E B03090F6 7CBF20EB 43A18800 F4FF0AFD 82FF1012", base: 16), gy: BigInt.new("07192B95 FFC8DA78 631011ED 6B24CDD5 73F977A1 1E794811", base: 16), n: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF 99DEF836 146BC9B1 B4D22831", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp224k1 => {d: 224, p: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFE56D", base: 16), a: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000", base: 16), b: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000005", base: 16), gx: BigInt.new("A1455B33 4DF099DF 30FC28A1 69A467E9 E47075A9 0F7E650E B6B7A45C", base: 16), gy: BigInt.new("7E089FED 7FBA3442 82CAFBD6 F7E319F7 C0B0BD59 E2CA4BDB 556D61A5", base: 16), n: BigInt.new("01 00000000 00000000 00000000 0001DCE8 D2EC6184 CAF0A971 769FB1F7", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp224r1 => {p: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF 00000000 00000000 00000001", base: 16), a: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFE", base: 16), b: BigInt.new("B4050A85 0C04B3AB F5413256 5044B0B7 D7BFD8BA 270B3943 2355FFB4", base: 16), gx: BigInt.new("B70E0CBD 6BB4BF7F 321390B9 4A03C1D3 56C21122 343280D6 115C1D21", base: 16), gy: BigInt.new("BD376388 B5F723FB 4C22DFE6 CD4375A0 5A074764 44D58199 85007E34", base: 16), n: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFF16A2 E0B8F03E 13DD2945 5C5C2A3D", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp256k1 => {p: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F", base: 16), a: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000", base: 16), b: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000007", base: 16), gx: BigInt.new("79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798", base: 16), gy: BigInt.new("483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8", base: 16), n: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp256k1_PRE => {p: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F", base: 16), a: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000", base: 16), b: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000007", base: 16), gx: BigInt.new("79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798", base: 16), gy: BigInt.new("483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8", base: 16), n: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp256r1 => {p: BigInt.new("FFFFFFFF 00000001 00000000 00000000 00000000 FFFFFFFF FFFFFFFF FFFFFFFF", base: 16), a: BigInt.new("FFFFFFFF 00000001 00000000 00000000 00000000 FFFFFFFF FFFFFFFF FFFFFFFC", base: 16), b: BigInt.new("5AC635D8 AA3A93E7 B3EBBD55 769886BC 651D06B0 CC53B0F6 3BCE3C3E 27D2604B", base: 16), gx: BigInt.new("6B17D1F2 E12C4247 F8BCE6E5 63A440F2 77037D81 2DEB33A0 F4A13945 D898C296", base: 16), gy: BigInt.new("4FE342E2 FE1A7F9B 8EE7EB4A 7C0F9E16 2BCE3357 6B315ECE CBB64068 37BF51F5", base: 16), n: BigInt.new("FFFFFFFF 00000000 FFFFFFFF FFFFFFFF BCE6FAAD A7179E84 F3B9CAC2 FC632551", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp256r1_PRE => {p: BigInt.new("FFFFFFFF 00000001 00000000 00000000 00000000 FFFFFFFF FFFFFFFF FFFFFFFF", base: 16), a: BigInt.new("FFFFFFFF 00000001 00000000 00000000 00000000 FFFFFFFF FFFFFFFF FFFFFFFC", base: 16), b: BigInt.new("5AC635D8 AA3A93E7 B3EBBD55 769886BC 651D06B0 CC53B0F6 3BCE3C3E 27D2604B", base: 16), gx: BigInt.new("6B17D1F2 E12C4247 F8BCE6E5 63A440F2 77037D81 2DEB33A0 F4A13945 D898C296", base: 16), gy: BigInt.new("4FE342E2 FE1A7F9B 8EE7EB4A 7C0F9E16 2BCE3357 6B315ECE CBB64068 37BF51F5", base: 16), n: BigInt.new("FFFFFFFF 00000000 FFFFFFFF FFFFFFFF BCE6FAAD A7179E84 F3B9CAC2 FC632551", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp384r1 => {p: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF 00000000 00000000 FFFFFFFF", base: 16), a: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF 00000000 00000000 FFFFFFFC", base: 16), b: BigInt.new("B3312FA7 E23EE7E4 988E056B E3F82D19 181D9C6E FE814112 0314088F 5013875A C656398D 8A2ED19D 2A85C8ED D3EC2AEF", base: 16), gx: BigInt.new("AA87CA22 BE8B0537 8EB1C71E F320AD74 6E1D3B62 8BA79B98 59F741E0 82542A38 5502F25D BF55296C 3A545E38 72760AB7", base: 16), gy: BigInt.new("3617DE4A 96262C6F 5D9E98BF 9292DC29 F8F41DBD 289A147C E9DA3113 B5F0B8C0 0A60B1CE 1D7E819D 7A431D7C 90EA0E5F", base: 16), n: BigInt.new("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF C7634D81 F4372DDF 581A0DB2 48B0A77A ECEC196A CCC52973", base: 16), h: BigInt.new("00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}, :secp521r1 => {p: BigInt.new("1FF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF", base: 16), a: BigInt.new("1FF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFC", base: 16), b: BigInt.new("051 953EB961 8E1C9A1F 929A21A0 B68540EE A2DA725B 99B315F3 B8B48991 8EF109E1 56193951 EC7E937B 1652C0BD 3BB1BF07 3573DF88 3D2C34F1 EF451FD4 6B503F00", base: 16), gx: BigInt.new("0C6 858E06B7 0404E9CD 9E3ECB66 2395B442 9C648139 053FB521 F828AF60 6B4D3DBA A14B5E77 EFE75928 FE1DC127 A2FFA8DE 3348B3C1 856A429B F97E7E31 C2E5BD66", base: 16), gy: BigInt.new("118 39296A78 9A3BC004 5C8A5FB4 2C7D1BD9 98F54449 579B4468 17AFBD17 273E662C 97EE7299 5EF42640 C550B901 3FAD0761 353C7086 A272C240 88BE9476 9FD16650", base: 16), n: BigInt.new("1FF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFA 51868783 BF2F966B 7FCC0148 F709A5D0 3BB5C9B8 899C47AE BB6FB71E 91386409", base: 16), h: BigInt.new("000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000001", base: 16)}}

PRECOMPUTED = {:secp256k1_PRE => {[BigInt.new("55066263022277343669578718895168534326250603453777594175500187360389116729240", base: 10), BigInt.new("32670510020758816978083085130507043184471273380659243275938904335757337482424", base: 10)], [BigInt.new("89565891926547004231252920425935692360644145829622209833684329913297188986597", base: 10), BigInt.new("12158399299693830322967808612713398636155367887041628176798871954788371653930", base: 10)], [BigInt.new("103388573995635080359749164254216598308788835304023601477803095234286494993683", base: 10), BigInt.new("37057141145242123013015316630864329550140216928701153669873286428255828810018", base: 10)], [BigInt.new("21262057306151627953595685090280431278183829487175876377991189246716355947009", base: 10), BigInt.new("41749993296225487051377864631615517161996906063147759678534462689479575333124", base: 10)], [BigInt.new("104059883622109321374094289636044428849728529177856482232626205340719788190730", base: 10), BigInt.new("112122903140080327253741791678230372394936108416576609264408917599318947489825", base: 10)], [BigInt.new("95440839670107969455973995843666399663662641812074432045896568980475242364517", base: 10), BigInt.new("67400892360194400039319989411395972789004161889863182881857158544061243615929", base: 10)], [BigInt.new("86454928033100054822938644242727206101601557724291916072342392316125160730507", base: 10), BigInt.new("41929975541376036990359335647717381527212342035893043668288666074313354583455", base: 10)], [BigInt.new("23971227478092690611538379282579297124953800109492367109857348294863777014350", base: 10), BigInt.new("42342609885299334444880650568116455571250837701978463648617679521175848103706", base: 10)], [BigInt.new("59030624050581421406270513075794029219285200067000787157698366092408912155912", base: 10), BigInt.new("8128656248049033031875480515138402531865803579197128279783442554673902546095", base: 10)], [BigInt.new("31809325515952716603993860438135646801954922215901515683284707473623428145741", base: 10), BigInt.new("24377531977987817432088011602449325046972761657480460991275213238540072159220", base: 10)], [BigInt.new("16339661702852967382840638396154683021742565846854739320600712521008743256863", base: 10), BigInt.new("36728284022334234592863792440353097018527397507662959793213172092233334129261", base: 10)], [BigInt.new("42114313391321156005599920754056349597018482182309287550535575450912996590705", base: 10), BigInt.new("18211792713336063942313736004207749605328499756363387606667481967702897602819", base: 10)], [BigInt.new("10569428376872096169397247199835207726595431926877749141789405073030710146873", base: 10), BigInt.new("95580118375493152898771330185112988759633284070886792649665201458589961475733", base: 10)], [BigInt.new("29955133736896634235893587837609964910900820068836768599575322235881802975190", base: 10), BigInt.new("83725361430957575604497772232028370201521594201253320640285202099397696195124", base: 10)], [BigInt.new("7741290454269945723504810030002187313337519274815056282137434463684850516554", base: 10), BigInt.new("2979905666851018206144735065445742806952013006906430309532921989383330523600", base: 10)], [BigInt.new("33602655200186679430886431101373729519010186911116350037909320311808627496821", base: 10), BigInt.new("37360103261735091089003680850413001554296156453961728314327616229790563817069", base: 10)], [BigInt.new("24533671068980092868630552346995129420983823672304585196401986911541584152128", base: 10), BigInt.new("2209357222459695347071765155987393997305194371900031813817445740077485301225", base: 10)], [BigInt.new("34424533203459102608471296411716955901929203809676354171491737723302766101825", base: 10), BigInt.new("87733804348534428731161926933835660863551297059124747814746905172819546464288", base: 10)], [BigInt.new("74193831669845249654938577341216601539929459848933807922451592200153851425745", base: 10), BigInt.new("29361396017150706741613988342393505196301946421006103373231627829781191611577", base: 10)], [BigInt.new("75996994270594548260051104099040009002173474732108538694613575188101535421242", base: 10), BigInt.new("67731220512052072417843278921450425890601471538300788051881284779249943090810", base: 10)], [BigInt.new("63004655751848499058589887215149057167805706207141784701705408548476267919372", base: 10), BigInt.new("33776887358425213876727286236887696644549240079971817446727643228044518554934", base: 10)], [BigInt.new("107219988410259287649822325760828753777881271537028923079899200557009639695550", base: 10), BigInt.new("15425677638027042728233515882140468124385010133809940201784713737762399581231", base: 10)], [BigInt.new("113496403293373161892995045761087341014991661230000874253822611507549586770091", base: 10), BigInt.new("92288978233865387499357228995099386605786555025834285738713074898639193985136", base: 10)], [BigInt.new("4402168996420289224849535114023409990325018394340995944430318114273800335863", base: 10), BigInt.new("67104318001466418430256649108646734852945972191921730406768272163045294283904", base: 10)], [BigInt.new("51670963786757573841189746283202124387362261809800652891978209018731111316698", base: 10), BigInt.new("68257551575553566084241009552849606333781498777275567535225153774080710909791", base: 10)], [BigInt.new("39774650486605686761949696375291962760476627649023643684500799050103063064789", base: 10), BigInt.new("97280577493662175430906331419179376788053309764979933526226118285088405860254", base: 10)], [BigInt.new("17321708023578332183628700857357458473789564616208564602894355867116410260949", base: 10), BigInt.new("97919434988400284406895062116320315016365801759636091852848099981382771845905", base: 10)], [BigInt.new("76575849854364972542951978758356689466650880857178783481542510110017069529320", base: 10), BigInt.new("81925384519567487405199682290695043524776979911807891169446287270330277192180", base: 10)], [BigInt.new("107989063369659015153804811955459434214410196483964476598208978660096898619386", base: 10), BigInt.new("42338160021087805224648939485129818613830046750563614152037885753448952924569", base: 10)], [BigInt.new("25379507781751782970997391382797328968603613636745039424586338729874508912637", base: 10), BigInt.new("66678967052843214385960608145916057604491714224625771583834324020892145369029", base: 10)], [BigInt.new("102193949730178242338502490474683128513913323030888946433219655522103301391692", base: 10), BigInt.new("6691527371710806382780054211605006078697403702312160758173793149761505802135", base: 10)], [BigInt.new("37586094085820668222219663528035831988292035114036566702275484810122124564900", base: 10), BigInt.new("110500050436317590116317882856153568952218728972968181243435825114259637008685", base: 10)], [BigInt.new("7263983490427117408129518121638485560698559702481803384958991237905117384112", base: 10), BigInt.new("93109094002033366773627505914545361927166820241279828474630961892312310241801", base: 10)], [BigInt.new("63340652510566015247975818591385417300086272434074184937732392505693958960902", base: 10), BigInt.new("113667876764634414158091221422353531108236715357465572941896170017035409095320", base: 10)], [BigInt.new("113783330688848408326400254714688308943084902760190583586245237148771972268029", base: 10), BigInt.new("49136863138091630742201940998618633678196612987804544425991276550671171170453", base: 10)], [BigInt.new("104610067874554658939189781067288826551534040873032177114963645859116975547034", base: 10), BigInt.new("109770660671288161864329498510482442986586271328087679077837897757717839673046", base: 10)], [BigInt.new("101775883922931432108027453607406809406988783938200607927691949357708936019245", base: 10), BigInt.new("71211677518830069576439009135279320536125727843027256193157225588947573710861", base: 10)], [BigInt.new("110691637496015646289262932234825854023102359733628734435283445248364686115670", base: 10), BigInt.new("75300502224888127283828373326871043861231715295745491495384349459792808386515", base: 10)], [BigInt.new("4441278141344175957087852960979663063777598386288590018731867755649013517962", base: 10), BigInt.new("7836136238007924788592053766414363238944904687598451784829364216715569810500", base: 10)], [BigInt.new("89749383265034677666862365486905244671167444330802547291623325584186528137154", base: 10), BigInt.new("98309468026548637860626714749357698670012533693024507288465476348752328350038", base: 10)], [BigInt.new("115301655840403608332148854465368444683257224081574702572138639602380667382125", base: 10), BigInt.new("103799472776126890762485670055583971987299536955028941653349419016168013365384", base: 10)], [BigInt.new("34828167905024529293425261847016829712897759939934247610415071312015953046280", base: 10), BigInt.new("47968762878478268758489427369126262603811724231741657789486393243885145959658", base: 10)], [BigInt.new("51545007865675218331521052163329117547916750428334376359731030798802230204655", base: 10), BigInt.new("106410582405992915570439467813541861485454771813746638713688333696184247730702", base: 10)], [BigInt.new("73599252554810039763407176139974374780648488828183406696254895715553023853401", base: 10), BigInt.new("47578048250598054907858110438316220654276129654309504967125355240893257809602", base: 10)], [BigInt.new("98787353431067487068174780415369765662128367506208336868623541747762523303089", base: 10), BigInt.new("70413563958895942572205979769129125709431089683617469237670049369710274330141", base: 10)], 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BigInt.new("1304413387522005593658644986431870580741763784891793039747684854470403546711", base: 10)], [BigInt.new("43571678054870652892977980703416468486567639676451044763536517937451273544315", base: 10), BigInt.new("49954115042924243391312436036996713150425283228309118668010174666521820679010", base: 10)], [BigInt.new("873704202273142968625579162198467507032750183849493641986922225446071932933", base: 10), BigInt.new("67998537520975131039647709652900653944752336764739237101720732749663019388079", base: 10)], [BigInt.new("54139800690483426297301952631437925110587960422887277029841182266555965057876", base: 10), BigInt.new("74115984295944166045948184427653282211014700048525035879938298669454420895743", base: 10)]}}

VERSION = "1.0.0"

Class Method Summary

• .get_group(c : Symbol)

Class Method Detail