190714(2)

Ruby


ECDSA

https://www.rubydoc.info/gems/ecdsa/ECDSA/Group
に載っているものについて出力してみた。 

require 'ecdsa'

def show_key(key)
  p key
  p [key.x, key.y]
end

def Ecdsa(group)
  g = group.generator
  n = group.order
  p "n = #{n}"

  # n*g
  p g.multiply_by_scalar(n)

  (1..10).each{|i|
    p i
    show_key(g.multiply_by_scalar(i))
  }
end

Ecdsa(ECDSA::Group::Nistp192)
Ecdsa(ECDSA::Group::Nistp224)
Ecdsa(ECDSA::Group::Nistp256)
Ecdsa(ECDSA::Group::Nistp384)
Ecdsa(ECDSA::Group::Nistp521)

Ecdsa(ECDSA::Group::Secp112r1)
Ecdsa(ECDSA::Group::Secp112r2)
Ecdsa(ECDSA::Group::Secp128r1)
Ecdsa(ECDSA::Group::Secp128r2)
Ecdsa(ECDSA::Group::Secp160k1)
Ecdsa(ECDSA::Group::Secp160r1)
Ecdsa(ECDSA::Group::Secp160r2)
Ecdsa(ECDSA::Group::Secp192k1)
Ecdsa(ECDSA::Group::Secp192r1)
Ecdsa(ECDSA::Group::Secp224k1)
Ecdsa(ECDSA::Group::Secp224r1)
Ecdsa(ECDSA::Group::Secp256k1)
Ecdsa(ECDSA::Group::Secp256r1)
Ecdsa(ECDSA::Group::Secp384r1)
Ecdsa(ECDSA::Group::Secp521r1)

出力結果
"n = 6277101735386680763835789423176059013767194773182842284081"
#<ECDSA::Point: nistp192, infinity>
1
#<ECDSA::Point: nistp192, 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, 0x7192b95ffc8da78631011ed6b24cdd573f977a11e794811>
[602046282375688656758213480587526111916698976636884684818, 174050332293622031404857552280219410364023488927386650641]
2
#<ECDSA::Point: nistp192, 0xdafebf5828783f2ad35534631588a3f629a70fb16982a888, 0xdd6bda0d993da0fa46b27bbc141b868f59331afa5c7e93ab>
[5369744403678710563432458361254544170966096384586764429448, 5429234379789071039750654906915254128254326554272718558123]
3
#<ECDSA::Point: nistp192, 0x76e32a2557599e6edcd283201fb2b9aadfd0d359cbb263da, 0x782c37e372ba4520aa62e0fed121d49ef3b543660cfd05fd>
[2915109630280678890720206779706963455590627465886103135194, 2946626711558792003980654088990112021985937607003425539581]
4
#<ECDSA::Point: nistp192, 0x35433907297cc378b0015703374729d7a4fe46647084e4ba, 0xa2649984f2135c301ea3acb0776cd4f125389b311db3be32>
[1305994880430903997305943738697779408316929565234787837114, 3981863977451150342116987835776121688410789618551673306674]
5
#<ECDSA::Point: nistp192, 0x10bb8e9840049b183e078d9c300e1605590118ebdd7ff590, 0x31361008476f917badc9f836e62762be312b72543cceaea1>
[410283251116784874018993562136566870110676706936762660240, 1206654674899825246688205669651974202006189255452737318561]
6
#<ECDSA::Point: nistp192, 0xa37abc6c431f9ac398bf5bd1aa6678320ace8ecb93d23f2a, 0x851b3caec99908dbfed7040a1bbda90e081f7c5710bc68f0>
[4008504146453526025173196900303594155799995627910231899946, 3263759301305176906990806636587838100022690095020155627760]
7
#<ECDSA::Point: nistp192, 0x8da75a1f75ddcd7660f923243060edce5de37f007011fcfd, 0x57cb5fcf6860b35418240db8fdb3c01dd4b702f96409ffb5>
[3473339081378406123852871299395262476289672479707038350589, 2152713176906603604200842901176476029776544337891569565621]
8
#<ECDSA::Point: nistp192, 0x2fa1f92d1ecce92014771993cc14899d4b5977883397edde, 0xa338afdef78b7214273b8b5978ef733ff2dd8a8e9738f6c0>
[1167950611014894512313033362696697441497340081390841490910, 4002177906111215127148483369584652296488769677804145538752]
9
#<ECDSA::Point: nistp192, 0x818a4d308b1cabb74e9e8f2ba8d27c9e1d9d375ab980388f, 0x1d1aa5e208d87cd7c292f7cbb457cdf30ea542176c8e739>
[3176317450453705650283775811228493626776489433309636475023, 44601893774669384766793803854980115179612118075017062201]
10
#<ECDSA::Point: nistp192, 0xaa7c4f9ef99e3e96d1aede2bd9238842859bb150d1fe9d85, 0x3212a36547edc62901ee3658b2f4859460eb5eb2491397b0>
[4180294501348368083809563235021370057375591405930992803205, 1227781623738814009517798297176766391967714436501424281520]
"n = 26959946667150639794667015087019625940457807714424391721682722368061"
#<ECDSA::Point: nistp224, infinity>
1
#<ECDSA::Point: nistp224, 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34>
[19277929113566293071110308034699488026831934219452440156649784352033, 19926808758034470970197974370888749184205991990603949537637343198772]
2
#<ECDSA::Point: nistp224, 0x706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6, 0x1c2b76a7bc25e7702a704fa986892849fca629487acf3709d2e4e8bb>
[11838696407187388799350957250141035264678915751356546206913969278886, 2966624012289393637077209076615926844583158638456025172915528198331]
3
#<ECDSA::Point: nistp224, 0xdf1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04, 0xa3f7f03cadd0be444c0aa56830130ddf77d317344e1af3591981a925>
[23495795443371455911734272815198443231796705177085412225858576936196, 17267899494408073472134592504239670969838724875111952463975956982053]
4
#<ECDSA::Point: nistp224, 0xae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301, 0x482580a0ec5bc47e88bc8c378632cd196cb3fa058a7114eb03054c9>
[18387688941486896693314180608234157394110342327606209796024257770241, 474869538468298384918655164606373990117569330548407043967769662665]
5
#<ECDSA::Point: nistp224, 0x31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa, 0x27e8bff1745635ec5ba0c9f1c2ede15414c6507d29ffe37e790a079b>
[5241180935788447299415492279837860720508896463754443826289355788714, 4202927080198900989467433352160374810063042822299340499566031669147]
6
#<ECDSA::Point: nistp224, 0x1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408, 0x89faf0ccb750d99b553c574fad7ecfb0438586eb3952af5b4b153c7e>
[3279702649264362226365706130591890985033768285409743741945602188296, 14531014943579176969516433940263520182884149791831438919418489683070]
7
#<ECDSA::Point: nistp224, 0xdb2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28, 0xf3a30085497f2f611ee2517b163ef8c53b715d18bb4e4808d02b963>
[23082899941265312416076834149127612973281722793605426171718143852072, 1603621376426681438878568404181089291706931574771796688040135670115]
8
#<ECDSA::Point: nistp224, 0x858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550, 0x46dcd3ea5c43898c5c5fc4fdac7db39c2f02ebee4e3541d1e78047a>
[14065129557927240249858914614678013910013270899103922531749823190352, 466418981405194772047450263835226671439563161789125411861941453946]
9
#<ECDSA::Point: nistp224, 0x2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d, 0x371732e4f41bf4f7883035e6a79fcedc0e196eb07b48171697517463>
[5040509874486954907152001659568354790239799257249422621041130600333, 5801719477042191151577191672839035334726563409413076674857195893859]
10
#<ECDSA::Point: nistp224, 0xaea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd, 0x39bb30eab337e0a521b6cba1abe4b2b3a3e524c14a3fe3eb116b655f>
[18394223645928780833749682104922684895691658099010032856578518073597, 6079806569424875768420363755065073818836240443816190687503610242399]
"n = 115792089210356248762697446949407573529996955224135760342422259061068512044369"
#<ECDSA::Point: nistp256, infinity>
1
#<ECDSA::Point: nistp256, 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296, 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5>
[48439561293906451759052585252797914202762949526041747995844080717082404635286, 36134250956749795798585127919587881956611106672985015071877198253568414405109]
2
#<ECDSA::Point: nistp256, 0x7cf27b188d034f7e8a52380304b51ac3c08969e277f21b35a60b48fc47669978, 0x7775510db8ed040293d9ac69f7430dbba7dade63ce982299e04b79d227873d1>
[56515219790691171413109057904011688695424810155802929973526481321309856242040, 3377031843712258259223711451491452598088675519751548567112458094635497583569]
3
#<ECDSA::Point: nistp256, 0x5ecbe4d1a6330a44c8f7ef951d4bf165e6c6b721efada985fb41661bc6e7fd6c, 0x8734640c4998ff7e374b06ce1a64a2ecd82ab036384fb83d9a79b127a27d5032>
[42877656971275811310262564894490210024759287182177196162425349131675946712428, 61154801112014214504178281461992570017247172004704277041681093927569603776562]
4
#<ECDSA::Point: nistp256, 0xe2534a3532d08fbba02dde659ee62bd0031fe2db785596ef509302446b030852, 0xe0f1575a4c633cc719dfee5fda862d764efc96c3f30ee0055c42c23f184ed8c6>
[102369864249653057322725350723741461599905180004905897298779971437827381725266, 101744491111635190512325668403432589740384530506764148840112137220732283181254]
5
#<ECDSA::Point: nistp256, 0x51590b7a515140d2d784c85608668fdfef8c82fd1f5be52421554a0dc3d033ed, 0xe0c17da8904a727d8ae1bf36bf8a79260d012f00d4d80888d1d0bb44fda16da4>
[36794669340896883012101473439538929759152396476648692591795318194054580155373, 101659946828913883886577915207667153874746613498030835602133042203824767462820]
6
#<ECDSA::Point: nistp256, 0xb01a172a76a4602c92d3242cb897dde3024c740debb215b4c6b0aae93c2291a9, 0xe85c10743237dad56fec0e2dfba703791c00f7701c7e16bdfd7c48538fc77fe2>
[79653159259317329199152975905021693207262715618295428672027927511489832980905, 105099244361861367422779349381909628134794498213392835359532911141293690159074]
7
#<ECDSA::Point: nistp256, 0x8e533b6fa0bf7b4625bb30667c01fb607ef9f8b8a80fef5b300628703187b2a3, 0x73eb1dbde03318366d069f83a6f5900053c73633cb041b21c55e1a86c1f400b4>
[64375483017717711348634889601793836329966447963510648681625681211348943876771, 52431391916983504423217627849020916729601969409053901192561322805962577543348]
8
#<ECDSA::Point: nistp256, 0x62d9779dbee9b0534042742d3ab54cadc1d238980fce97dbb4dd9dc1db6fb393, 0xad5accbd91e9d8244ff15d771167cee0a2ed51f6bbe76a78da540a6a0f09957e>
[44710890534849379681007195543719586089737754824560621976448707498688874787731, 78410552107786285403689301656392479612049391334024095564584156230482213311870]
9
#<ECDSA::Point: nistp256, 0xea68d7b6fedf0b71878938d51d71f8729e0acb8c2c6df8b3d79e8a4b90949ee0, 0x2a2744c972c9fce787014a964a8ea0c84d714feaa4de823fe85a224a4dd048fa>
[106026447472237217594103756757091873528548576106367144586170196380839010672352, 19066521425813101412078385704618669688199787690556935461623958781864528857338]
10
#<ECDSA::Point: nistp256, 0xcef66d6b2a3a993e591214d1ea223fb545ca6c471c48306e4c36069404c5723f, 0x878662a229aaae906e123cdd9d3b4c10590ded29fe751eeeca34bbaa44af0773>
[93611846365601674425599200647886473617443872040541410036779615417472400060991, 61299672808462629900136024686264045542397545919962042795596947287593974695795]
"n = 39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643"
#<ECDSA::Point: nistp384, infinity>
1
#<ECDSA::Point: nistp384, 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7, 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f>
[26247035095799689268623156744566981891852923491109213387815615900925518854738050089022388053975719786650872476732087, 8325710961489029985546751289520108179287853048861315594709205902480503199884419224438643760392947333078086511627871]
2
#<ECDSA::Point: nistp384, 0x8d999057ba3d2d969260045c55b97f089025959a6f434d651d207d19fb96e9e4fe0e86ebe0e64f85b96a9c75295df61, 0x8e80f1fa5b1b3cedb7bfe8dffd6dba74b275d875bc6cc43e904e505f256ab4255ffd43e94d39e22d61501e700a940e80>
[1362138308511466522361153706999924933599454966107597910086607881313301390679204654798639248640660900363360053616481, 21933325650940841369538204578070064804451893403314136885642470114978241170633179043576249504748352841115137159204480]
3
#<ECDSA::Point: nistp384, 0x77a41d4606ffa1464793c7e5fdc7d98cb9d3910202dcd06bea4f240d3566da6b408bbae5026580d02d7e5c70500c831, 0xc995f7ca0b0c42837d0bbe9602a9fc998520b41c85115aa5f7684c0edc111eacc24abd6be4b5d298b65f28600a2f1df1>
[1150902892488483458936980703033240421996917307006362560128741616924334451190275252566486993672663650518120360101937, 31026896179475916024120184231935979451435829475766013456640577102369059008378103381483562093497986423351518602141169]
4
#<ECDSA::Point: nistp384, 0x138251cd52ac9298c1c8aad977321deb97e709bd0b4ca0aca55dc8ad51dcfc9d1589a1597e3a5120e1efd631c63e1835, 0xcacae29869a62e1631e8a28181ab56616dc45d918abc09f3ab0e63cf792aa4dced7387be37bba569549f1c02b270ed67>
[3002719260124138234864644293005553694107074621611323149430212532410635475904301642043243286192603916432052661917749, 31212625517239818344942812004487160470862995565736342725949902243255222118943617085729083408956085866876436550315367]
5
#<ECDSA::Point: nistp384, 0x11de24a2c251c777573cac5ea025e467f208e51dbff98fc54f6661cbe56583b037882f4a1ca297e60abcdbc3836d84bc, 0x8fa696c77440f92d0f5837e90a00e7c5284b447754d5dee88c986533b6901aeb3177686d0ae8fb33184414abe6c1713a>
[2750097886727221852871437489830375535902219297598792969027200942344246907638882141082920203987932105239591664846012, 22109872175543161315473274033501382113217372000035529196852092508530348707813916169793617815529384830733840621334842]
6
#<ECDSA::Point: nistp384, 0x627be1acd064d2b2226fe0d26f2d15d3c33ebcbb7f0f5da51cbd41f26257383021317d7202ff30e50937f0854e35c5df, 0x9766a4cb3f8b1c21be6dda6c14f1575b2c95352644f774c99864f613715441604c45b8d84e165311733a408d3f0f934>
[15158061413379800065538248493105902144697876778848367452125464871443609651151271322845514729956502261224296802534879, 1456421203869220836818514483833972558040283856785775367907417308863650512182437695714129960394237275553647337470260]
7
#<ECDSA::Point: nistp384, 0x283c1d7365ce4788f29f8ebf234edffead6fe997fbea5ffa2d58cc9dfa7b1c508b05526f55b9ebb2040f05b48fb6d0e1, 0x9475c99061e41b88ba52efdb8c1690471a61d867ed799729d9c92cd01dbd225630d84ede32a78f9e64664cdac512ef8c>
[6192706248650610585029334828875625541601599068644432283392070678800109693834576236172166289842521288047764778176737, 22850101761352155756627808478921273213930354190738002589669451013939984415721476662192719117631561703668728764493708]
8
#<ECDSA::Point: nistp384, 0x1692778ea596e0be75114297a6fa383445bf227fbe58190a900c3c73256f11fb5a3258d6f403d5ece6e9b269d822c87d, 0xdcd2365700d4106a835388ba3db8fd0e22554adc6d521cd4bd1c30c2ec0eec196bade1e9cdd1708d6f6abfa4022b0ad2>
[3474169820285015935707784759505165025751354558980809204451847681969564642225728669274210426295040866239332835575933, 33987484343743100593269958688158316211807494280296367372570003270207970275375287587045962593543362932932356696902354]
9
#<ECDSA::Point: nistp384, 0x8f0a39a4049bcb3ef1bf29b8b025b78f2216f7291e6fd3bac6cb1ee285fb6e21c388528bfee2b9535c55e4461079118b, 0x62c77e1438b601d6452c4a5322c3a9799a9b3d7ca3c400c6b7678854aed9b3029e743efedfd51b68262da4f9ac664af8>
[22015862039406592161640061395309898573981900544448277583680581570848334956774212068925210279638870991947884190568843, 15203520752271699905529257511401880117129466438770620902510214914921624065453958502658877623620972906864670126000888]
10
#<ECDSA::Point: nistp384, 0xa669c5563bd67eec678d29d6ef4fde864f372d90b79b9e88931d5c29291238cced8e85ab507bf91aa9cb2d13186658fb, 0xa988b72ae7c1279f22d9083db5f0ecddf70119550c183c31c502df78c3b705a8296d8195248288d997784f6ab73a21dd>
[25613330671596181123005601887414536094101619968241601793426634216146173595484114582196490380477558694107707817220347, 26093677688555946946604951835762730654802489834678081288763495518642068008712824154838929891456709573200703804547549]
"n = 6864797660130609714981900799081393217269435300143305409394463459185543183397655394245057746333217197532963996371363321113864768612440380340372808892707005449"
#<ECDSA::Point: nistp521, infinity>
1
#<ECDSA::Point: nistp521, 0xc6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66, 0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650>
[2661740802050217063228768716723360960729859168756973147706671368418802944996427808491545080627771902352094241225065558662157113545570916814161637315895999846, 3757180025770020463545507224491183603594455134769762486694567779615544477440556316691234405012945539562144444537289428522585666729196580810124344277578376784]
2
#<ECDSA::Point: nistp521, 0x433c219024277e7e682fcb288148c282747403279b1ccc06352c6e5505d769be97b3b204da6ef55507aa104a3a35c5af41cf2fa364d60fd967f43e3933ba6d783d, 0xf4bb8cc7f86db26700a7f3eceeeed3f0b5c6b5107c4da97740ab21a29906c42dbbb3e377de9f251f6b93937fa99a3248f4eafcbe95edc0f4f71be356d661f41b02>
[901472452850866198617673658578940391618730359691416279093035377195377079020397774511960179466499271590922803070095487687963115616363390991670183687363590205, 3281327921582527507824747162491172657218985358085640380741461489720525905953211486053138004786012424348623853685340634287932228687534583594738661002099038978]
3
#<ECDSA::Point: nistp521, 0x1a73d352443de29195dd91d6a64b5959479b52a6e5b123d9ab9e5ad7a112d7a8dd1ad3f164a3a4832051da6bd16b59fe21baeb490862c32ea05a5919d2ede37ad7d, 0x13e9b03b97dfa62ddd9979f86c6cab814f2f1557fa82a9d0317d2f8ab1fa355ceec2e2dd4cf8dc575b02d5aced1dec3c70cf105c9bc93a590425f588ca1ee86c0e5>
[5674708455687314755177411224894914551247560982429925442328503936381769479291831722549724502783064471579811889182869230569934709210549404604394803481732951421, 4271801692429350493774172787940824381696861087943454989753620357811953134117882851809933515614164977926164094992857584446095333607804956469237639174332793061]
4
#<ECDSA::Point: nistp521, 0x35b5df64ae2ac204c354b483487c9070cdc61c891c5ff39afc06c5d55541d3ceac8659e24afe3d0750e8b88e9f078af066a1d5025b08e5a5e2fbc87412871902f3, 0x82096f84261279d2b673e0178eb0b4abb65521aef6e6e32e1b5ae63fe2f19907f279f283e54ba385405224f750a95b85eebb7faef04699d1d9e21f47fc346e4d0d>
[720139262829490965228382995842856154672620969623624721491545193380081085740139236944514523432374714314516720643288782059935114497438659217305669829660312307, 1743509213896395704926971995163331058385350704471974861189555515264763786920497129482978082020953735069538018776269773826418065263344470573872048814915734797]
5
#<ECDSA::Point: nistp521, 0x652bf3c52927a432c73dbc3391c04eb0bf7a596efdb53f0d24cf03dab8f177ace4383c0c6d5e3014237112feaf137e79a329d7e1e6d8931738d5ab5096ec8f3078, 0x15be6ef1bdd6601d6ec8a2b73114a8112911cd8fe8e872e0051edd817c9a0347087bb6897c9072cf374311540211cf5ff79d1f007257354f7f8173cc3e8deb090cb>
[1356490565846790255739168589204180496138457916455904646417394236994934604955446470133745046215752716497315667741727281784411650125266382302052918851202396280, 4664604347668020762970169188647728988711329258092833895899217703661992685928809983190581180899656432001123782446415831494072942427109258745206503403498279115]
6
#<ECDSA::Point: nistp521, 0x1ee4569d6cdb59219532eff34f94480d195623d30977fd71cf3981506ade4ab01525fbcca16153f7394e0727a239531be8c2f66e95657f380ae23731bedf79206b9, 0x1de0255ad0cc64f586ae2dd270546e3b1112aabbb73da5a808e7240a926201a8a96cab72d0e56648c9df96c984de274f2203dc7b8b55ca0dade1eaccd7858d44f17>
[6627092593912669792642110945067526420603119632670712106335413291576815883585816148497705827209816819203919053952926123076419905599531213746077243594847159993, 6409054467195497574328769691992291744192825101429818044461519861807844707820590849737648382749606312491164515576381227669620056038791577188683842913641451287]
7
#<ECDSA::Point: nistp521, 0x56d5d1d99d5b7f6346eeb65fda0b073a0c5f22e0e8f5483228f018d2c2f7114c5d8c308d0abfc698d8c9a6df30dce3bbc46f953f50fdc2619a01cead882816ecd4, 0x3d2d1b7d9baaa2a110d1d8317a39d68478b5c582d02824f0dd71dbd98a26cbde556bd0f293cdec9e2b9523a34591ce1a5f9e76712a5ddefc7b5c6b8bc90525251b>
[1164270129742194787021746298790404262615845385569632340556150609652209653392714737798593072499915146233094284387298092872206604386185768403662460504302349524, 820238749192739888211492096736837212740835839662383100764162083366076000951085168184227504476659003461738201421631812073852429309662558977232294321188054299]
8
#<ECDSA::Point: nistp521, 0x822c40fb6301f7262a8348396b010e25bd4e29d8a9b003e0a8b8a3b05f826298f5bfea5b8579f49f08b598c1bc8d79e1ab56289b5a6f4040586f9ea54aa78ce68, 0x16331911d5542fc482048fdab6e78853b9a44f8ede9e2c0715b5083de610677a8f189e9c0aa5911b4bff0ba0df065c578699f3ba940094713538ad642f11f17801c>
[109083299521442500876842833611249336033561763077283587821638741694330082273903024416664243036493783947792437906787000707140664721345204901269860104151813736, 4762367841910623311695901789059609560484960426869206316472308403586084267202597852325933276209196012548531291691842818402620813054843744959471171805306650652]
9
#<ECDSA::Point: nistp521, 0x1585389e359e1e21826a2f5bf157156d488ed34541b988746992c4ab145b8c6b6657429e1396134da35f3c556df725a318f4f50babd85cd28661f45627967cbe207, 0x2a2e618c9a8aedf39f0b55557a27ae938e3088a654ee1cebb6c825ba263ddb446e0d69e5756057ac840ff56ecf4abfd87d736c2ae928880f343aa0ea86b9ad2a4e>
[4616661200726261460425444407382564000458447935977095696549288279032624160572165028883634753543187515864165184548929181253345681100099099865467440109558948359, 565557105841472481223362297865540722006314205571885763530335674978792826921172930992998161356566446473354134360199263577951173812344419108828580268630420046]
10
#<ECDSA::Point: nistp521, 0x190eb8f22bda61f281dfcfe7bb6721ec4cd901d879ac09ac7c34a9246b11ada8910a2c7c178fcc263299daa4da9842093f37c2e411f1a8e819a87ff09a04f2f3320, 0x1eb5d96b8491614ba9dbaeab3b0ca2ba760c2eeb2144251b20ba97fd78a62ef62d2bf5349d44d9864bb536f6163dc57ebeff3689639739faa172954bc98135ec759>
[5375460404355022005936344137910919641482040501042631812229106559568140729369345497476837707660889191626168303541735277230613470977508429228294991448237880096, 6588135334138314282252915335789429562328467280057335182605115845427333280489083939697175013949068040137109843930550149723252770088030396786860186457851479897]
"n = 4451685225093714776491891542548933"
#<ECDSA::Point: secp112r1, infinity>
1
#<ECDSA::Point: secp112r1, 0x9487239995a5ee76b55f9c2f098, 0xa89ce5af8724c0a23e0e0ff77500>
[188281465057972534892223778713752, 3419875491033170827167861896082688]
2
#<ECDSA::Point: secp112r1, 0x57cf52a0f9318000ee0bc032d756, 0x60aee03bbcff537a8d17401f006c>
[1780995437533866901729502362261334, 1960966419089380527792400971530348]
3
#<ECDSA::Point: secp112r1, 0xcfc1e3447fc33e5c2a7d2bf71298, 0x5bd6ac32f0a9e7aab6af722c3cb7>
[4213820159228676125970083014447768, 1862707393714836977900502888758455]
4
#<ECDSA::Point: secp112r1, 0x5b2b9a62eeb59f85ac617e20a27c, 0xc0d34be4dd15ed7c1749ecaeeede>
[1849153865213931762853440645014140, 3910963274246501456563746076815070]
5
#<ECDSA::Point: secp112r1, 0xca188ca33fde3ce02a83f197547c, 0xab5c59cb715e2ddc3e51ad252a5f>
[4098991741095872007391701171131516, 3475608823288928154126370692475487]
6
#<ECDSA::Point: secp112r1, 0x12816a28c5fa3b44daea1fd67e50, 0x2e4a2b63845a4c632bf992cbbed>
[375336660533066168265862748208720, 58679197122383059197917924211693]
7
#<ECDSA::Point: secp112r1, 0xb0e10fc47c14fc35b2cf498cc15f, 0xc9f73c24918f44444d04e77fe46a>
[3587535306618971987602397612261727, 4096352299784313776989792116925546]
8
#<ECDSA::Point: secp112r1, 0x17fc3daaeae82364456158bd6e9b, 0x5931d7b7b7d5b4bb2de33a88746f>
[486480003049887421216682764234395, 1809083396066869444846350460548207]
9
#<ECDSA::Point: secp112r1, 0x3f37cf870b918cd41ee58f58df14, 0xcec3fa5a53ff5a372b583ce40f20>
[1282213580624989398652572019515156, 4193703350494971593276903353749280]
10
#<ECDSA::Point: secp112r1, 0x83fa26cc8f6c01fb3d549676c0b3, 0x89b42c1fff0f9e616526e4f6d83>
[2676814706435466120618005688139955, 174560302560904408930697079647619]
"n = 1112921306273428674967732714786891"
#<ECDSA::Point: secp112r2, infinity>
1
#<ECDSA::Point: secp112r2, 0x4ba30ab5e892b4e1649dd0928643, 0xadcd46f5882e3747def36e956e97>
[1534098225527667214992304222930499, 3525120595527770847583704454622871]
2
#<ECDSA::Point: secp112r2, 0xa0b17a1c4094209b98ec519bba03, 0x849523d32315f1916a9c746a7db6>
[3259246712675377131559956460059139, 2689094151121025183363876896013750]
3
#<ECDSA::Point: secp112r2, 0x2460e4660d50e2991a2eb14b651, 0x7b40184a9e57aa0b667e2edb937c>
[46115208455524075684552521332305, 2499814501498565767543427048379260]
4
#<ECDSA::Point: secp112r2, 0x22368196a1f7377899f9438546d0, 0x62dd9609660892d600a8b469905b>
[693920352969928310994683908409040, 2005231999187161234297367751659611]
5
#<ECDSA::Point: secp112r2, 0x9f4db94fa5b416254a02e0745d8f, 0xd7a77a5bb384d65036ffb97d75fc>
[3231061046508683129165513093307791, 4373987035956193088111410551813628]
6
#<ECDSA::Point: secp112r2, 0x8c57311fa974763903ee15783efe, 0x89d6c06364d8dba2ff7b7cbbc9c6>
[2846445397692384787447137028292350, 2795704483760110227927107442035142]
7
#<ECDSA::Point: secp112r2, 0x288a0d1bd068202a80a52fc3b335, 0x876c5d0711ae1f5e8c6af9d731f1>
[822233927503333110253637448479541, 2746710728696402402162840801063409]
8
#<ECDSA::Point: secp112r2, 0x3c67b5bf0e8de6f29498a0059718, 0x110b1b47e087c36121c027638b3>
[1225161324718409425262106066130712, 21605057252440509691245616314547]
9
#<ECDSA::Point: secp112r2, 0xc757ca0e0b97ac1ac3767d626a41, 0x8e4fc7670105af602971706064a>
[4043154894217112689150966016141889, 180401431287394074262202541803082]
10
#<ECDSA::Point: secp112r2, 0x9a678caf8e077174301979832ee1, 0xc74377027b3de8a20e66c4701ee1>
[3131695119835433235917853910314721, 4041544629731151596034767264423649]
"n = 340282366762482138443322565580356624661"
#<ECDSA::Point: secp128r1, infinity>
1
#<ECDSA::Point: secp128r1, 0x161ff7528b899b2d0c28607ca52c5b86, 0xcf5ac8395bafeb13c02da292dded7a83>
[29408993404948928992877151431649155974, 275621562871047521857442314737465260675]
2
#<ECDSA::Point: secp128r1, 0x8151a0c6b92171db199db84be753a97e, 0x3d853559455caae838395a9275b7e95>
[171894248431803389772200227008324807038, 5110910329096684473053796200617836181]
3
#<ECDSA::Point: secp128r1, 0xad632f542942f23aa423b628a304b3b, 0x7aa67ee421c4e78851e4b4679bcdc41f>
[14404465037560764698468415334262000443, 163030310422358679409407543694089634847]
4
#<ECDSA::Point: secp128r1, 0x47487e914aae409decb6495fbdd2647f, 0x4e67a67404c56ae34783239f70a198d3>
[94751600169349708208269970539136836735, 104217966319590186353349680621703764179]
5
#<ECDSA::Point: secp128r1, 0xe147e5d422bb217e35493632b5d3e53f, 0x85563e321e03170a929451838e740757>
[299449613607480451049965923281059177791, 177235122449319644270601025448142178135]
6
#<ECDSA::Point: secp128r1, 0x624bcc28bf7670b76e6d3b61d2247fef, 0x92c2a43957b12f98bb52f92ba856b06>
[130657906691252335539401630779303034863, 12192370239592071042754015418078554886]
7
#<ECDSA::Point: secp128r1, 0x70416bb15d70a474de75bd2340d215f2, 0xe4361e1eefb356c57cee5c841a4687be>
[149213219093845979543741348864863639026, 303344977992638409527592336554925131710]
8
#<ECDSA::Point: secp128r1, 0xee6682773350c39d5dfae6717fdb254, 0x3209fff0799aa1915d17d982991e966a>
[19805532714603857338416262756482003540, 66513321527815165440339364714903410282]
9
#<ECDSA::Point: secp128r1, 0xc732ae957882f6adeef94ef4fdfdb5a, 0x5f832d3a461b9be0dab9b6efbdaac16a>
[16548720436605548534443556266284407642, 126957767813397988296959920413772267882]
10
#<ECDSA::Point: secp128r1, 0x87d40d444ea04a0c4fdc5981030aefb8, 0x2a8216ca1dced733c943bcff0ac3b392>
[180546815448146533320391376136152215480, 56503036640901222739554410154541953938]
"n = 85070591690620534603955721926813660579"
#<ECDSA::Point: secp128r2, infinity>
1
#<ECDSA::Point: secp128r2, 0x7b6aa5d85e572983e6fb32a7cdebc140, 0x27b6916a894d3aee7106fe805fc34b44>
[164048790688614013222215505581242564928, 52787839253935625605232456597451787076]
2
#<ECDSA::Point: secp128r2, 0xb78b3cccfbc54009b77ed2d74e6d17a7, 0xe6f18d420aa131f92e420094a1b326eb>
[243971685677016516054232268835306411943, 306976647625540108201029099479398295275]
3
#<ECDSA::Point: secp128r2, 0x47b16f39d7b0de241e91f44619c35a83, 0x9f6e63d5e1d65ac5600d3b164c1f83b6>
[95296480174914057202390658607109855875, 211920428888283097873633020448132268982]
4
#<ECDSA::Point: secp128r2, 0x6735114cd890b2156d7cc4ddb359767e, 0x6293a9aca0990cf2c9969b9139ee3f6a>
[137186026188675982351831122621117331070, 131031052629295973160586866272219578218]
5
#<ECDSA::Point: secp128r2, 0x636f3d0296d39dc71955114d34f96b43, 0x50799bb7e405e98ff75dc36dcc4816ac>
[132171153966124764970074032544060894019, 106969665925488019930110524080228144812]
6
#<ECDSA::Point: secp128r2, 0xdce9b6da533faaedd87c58e9c3acddf, 0x11c0633377f5d1a438f0501aa1f4dafb>
[18352729558548226557594696832503172575, 23595808961495199485405225874714057467]
7
#<ECDSA::Point: secp128r2, 0x30fbbeeb950d3cdd3a7c080b23b05aee, 0x6bb377575566a1dd9f61f246532dae1d>
[65110082631740358225612848015699106542, 143159237212687006493626066882899324445]
8
#<ECDSA::Point: secp128r2, 0x94b4f0959d3bdc613451c96be276238b, 0xe9fafa2cdfdc4c41565d72860951f8f9>
[197665236442666423068225844250263561099, 311013271390240649814545997864702703865]
9
#<ECDSA::Point: secp128r2, 0x7241ca2907ea08a206160b733da8edc9, 0xb5a633b1e336a9b07072bf2f6ccd6de2>
[151873591112829098507434158022782938569, 241453237012180286200274347077372046818]
10
#<ECDSA::Point: secp128r2, 0xddc2781fc0e3c4020b2b483d26d4899a, 0x7a1dc548e72fc0ef7cf02a196840c5>
[294769129063944114282601336681436318106, 634064037130178260921834199493132485]
"n = 1461501637330902918203686915170869725397159163571"
#<ECDSA::Point: secp160k1, infinity>
1
#<ECDSA::Point: secp160k1, 0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb, 0x938cf935318fdced6bc28286531733c3f03c4fee>
[338530205676502674729549372677647997389429898939, 842365456698940303598009444920994870805149798382]
2
#<ECDSA::Point: secp160k1, 0x74fc71cb95e965fc54ee5fa0227aff946533a0e3, 0xcec5178957b56930ed3eb7d49f0db1dcf358cdf9>
[667872630170492720756233761457243746176356032739, 1180447395911666948299218979855295458288374173177]
3
#<ECDSA::Point: secp160k1, 0x76bfb34670af0e3305c57012e49d9aea3dae0d5d, 0xf153607068dcb611d14c6d9a1849db711f6bc52f>
[677935970358862357903697512524689170492782677341, 1377726138650483620870431426160482164455605257519]
4
#<ECDSA::Point: secp160k1, 0x61b90cffadce82a730b1ff64dd9f9ee7ba2115d7, 0x193619320ebd43d29f41504fc45b1c2c71e309d2>
[557898874982104051477137708182891929539750991319, 143931204352175193464457417798394483674571803090]
5
#<ECDSA::Point: secp160k1, 0x749367f363868a1072e785957762b463abba2baa, 0xe5cb2945d4a5370bccb026b63ea548c5d989c63f>
[665530194346107659143789090566645353298024606634, 1311889533159821667817434485250462771677386884671]
6
#<ECDSA::Point: secp160k1, 0x438479ebc63d06547b4d697b2492ffb838f679bc, 0xa601478542bc75f7e7f80a40e6d5762a483380b2>
[385456700827861261450253992054049335117086095804, 947720999020519439322450633125855792933335433394]
7
#<ECDSA::Point: secp160k1, 0x803c8476b55389938b7cc78a0547e1a42ba1e89b, 0xe7e0a848ddd5eb9ff5eb1112b1ffc4316d5dd3eb>
[732100402593449603769783621515661711499312883867, 1323786894644014869049543268548629328371877008363]
8
#<ECDSA::Point: secp160k1, 0xfc80d8ac21f671037ab26d350dec424220b72670, 0x7ae3f71f0a112ca5943a40520c8cf2b32c242537>
[1441539044460491971559604582901432987716230260336, 701580670497334847288574073828961207064633550135]
9
#<ECDSA::Point: secp160k1, 0xc1c4f16e4f7ee19b36a86af5eed8085d7be07793, 0x5c8b0a739abdafe3fc07f9c55bba92d3fc74a233>
[1106227196425550762746036135280407456266531665811, 528327864959406529298125987219283421638593651251]
10
#<ECDSA::Point: secp160k1, 0x2939d98ca95b77cc963bb868b8e078258b299bd4, 0xd3c3afd1cce5ff1cb9a5afb20eb4f0ab1a81eee0>
[235358715310786687035094025427315271077993225172, 1208961013998953077056114670756815840447161298656]
"n = 1461501637330902918203687197606826779884643492439"
#<ECDSA::Point: secp160r1, infinity>
1
#<ECDSA::Point: secp160r1, 0x4a96b5688ef573284664698968c38bb913cbfc82, 0x23a628553168947d59dcc912042351377ac5fb32>
[425826231723888350446541592701409065913635568770, 203520114162904107873991457957346892027982641970]
2
#<ECDSA::Point: secp160r1, 0x2f997f33c5ed04c55d3edf8675d3e92e8f46686, 0xf083a323482993e9440e817e21cfb7737df8797b>
[16984103820118642236896513183038186009872590470, 1373093393927139016463695321221277758035357890939]
3
#<ECDSA::Point: secp160r1, 0x7b76ff541ef363f2df13de1650bd48daa958bc59, 0xc915ca790d8c8877b55be0079d12854ffe9f6f5a>
[704859595002530890444080436569091156047721708633, 1147993098458695153857594941635310323215433166682]
4
#<ECDSA::Point: secp160r1, 0xb4041d8683be99f0afe01c307b1ad4c100cf2a88, 0x3f32caed841f08c00660cc74caf4a5bcf9beed08>
[1027710113758332951436243665013750402716577770120, 360799133326126831135284748349110241144321535240]
5
#<ECDSA::Point: secp160r1, 0xe705b180e41192ed772d1e2d424c171303ad6c4e, 0x933fbe35078c8c01465dbf40a12b583364b2a59c>
[1318903834520207702788659510557639291095399361614, 840643159637938677745829567066605908359719855516]
6
#<ECDSA::Point: secp160r1, 0xeb0570b9209f5a76d524362ba006b15dac3a397e, 0x136df96683d22f114ff1cab12049a5fa035338a6>
[1341734154441219884729112587568307290009536969086, 110923331715511427552983461192303384130403645606]
7
#<ECDSA::Point: secp160r1, 0x7a7f99d56472f619577c4e8c9b3a35e961472188, 0x8955c17a4aa7b3ca673c6d55ee00fae62552e356>
[699342469474133237473954832869365533451343045000, 784044153229608343719883568478898218880027779926]
8
#<ECDSA::Point: secp160r1, 0x87311d3d79c5122770d6eb7f8df4fb3888329f1b, 0xf785e0ff393062626b2b507aa27eabba3c87eea6>
[771809037751322577709108225842058956357242101531, 1413106319504962435980586035916327729371200089766]
9
#<ECDSA::Point: secp160r1, 0x25393e48e2b7b5df8142cf731e3f00664d93bbb, 0xe75de5df76185c0d233f23a2e7b973a954694156>
[13281826672513493847192563553427980389717719995, 1320870862117191860165561350239342441476284563798]
10
#<ECDSA::Point: secp160r1, 0xffa7ace32ccc8511279d2fd293bf92c47580d645, 0x4b3a0b0c3311674d7f1e6ab523d9f1de223bcaaf>
[1459531931625059205852835973517814788318971352645, 429468713419717384933394396160429288629076740783]
"n = 1461501637330902918203685083571792140653176136043"
#<ECDSA::Point: secp160r2, infinity>
1
#<ECDSA::Point: secp160r2, 0x52dcb034293a117e1f4ff11b30f7199d3144ce6d, 0xfeaffef2e331f296e071fa0df9982cfea7d43f2e>
[473058756663038503608844550604547710019657059949, 1454008495369951658060798698479395908327453245230]
2
#<ECDSA::Point: secp160r2, 0x26788d2ba41a035954dd638d883e136ab900c8cd, 0xfce35cebd17744978eb33ca3d8daface4b5ffb4a>
[219630036397716191444822623399300352135210780877, 1443736037982763885579793473917740216901716409162]
3
#<ECDSA::Point: secp160r2, 0xe84ff970605dabe350fd9bf375fc37522c5888a5, 0x78de7599c4a72cea3ef4bc3a29982adc894ec182>
[1326269346900729049801889792059404305181301049509, 690039902394987407831956113386023254597038948738]
4
#<ECDSA::Point: secp160r2, 0xcbf011f96ab10ba3a4142bae3d85573bf55ce22c, 0xe18f043772c5b2ee469e3e364256545c447d3f71>
[1164278871105874416379804977979527749874994700844, 1287712297315986182901978210899457564769152483185]
5
#<ECDSA::Point: secp160r2, 0xb5bd4ed6d7ef00a0f3328a2b576575ecaa26a1a1, 0xc33ee33c805f30e6783e8d05e01408623f950c18>
[1037549038227391430834737605384773312214454411681, 1114655641589441574169917076589981482489065311256]
6
#<ECDSA::Point: secp160r2, 0x34ef22e975cda7b580a8db8c8b173aeea0475c17, 0x79fb05e71c656c5ee6cff5c830c16d33c4372247>
[302200439445389144523352729781578535464820235287, 696385884518917190262561260988283833166668964423]
7
#<ECDSA::Point: secp160r2, 0xbf14d96903140f848859aa29b8d34b8f1e5996ab, 0x11e581982137b020573af905400187fa2ab6f657>
[1090882191231111524924407486200209331819902506667, 102171003006427426120348558316921269781397960279]
8
#<ECDSA::Point: secp160r2, 0xecd8e700177e0102b35fa0650fba42e7d16b5266, 0xba50702973381c9efc5de94071f4cbd82939073c>
[1352158905846585472738176844619957903414713340518, 1063666113669870570907754651915408828106060400444]
9
#<ECDSA::Point: secp160r2, 0x20e3f772d5fc9e8bfd8d67dcd8b45399d630d37a, 0x1ff9a1e91849db0dae8c6509bd1c609f51466d17>
[187771529637681527618936243505892021009711682426, 182545703846084608893042401705886036479929904407]
10
#<ECDSA::Point: secp160r2, 0x8d9dafb9b4a0a3c2dd43391f9be0cf62fe7d8b36, 0x47d87e2eaccd0fc9cb9a77826c45e8101966ee73>
[808484223524701747377030101936249350274324204342, 410166297722083457328393810280053497420960951923]
"n = 6277101735386680763835789423061264271957123915200845512077"
#<ECDSA::Point: secp192k1, infinity>
1
#<ECDSA::Point: secp192k1, 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d, 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d>
[5377521262291226325198505011805525673063229037935769709693, 3805108391982600717572440947423858335415441070543209377693]
2
#<ECDSA::Point: secp192k1, 0xf091cf6331b1747684f5d2549cd1d4b3a8bed93b94f93cb6, 0xfd7af42e1e7565a02e6268661c5e42e603da2d98a18f2ed5>
[5898748710631235793867485368048681928976741514058866965686, 6215318586565457819081644608453878670902049430638930374357]
3
#<ECDSA::Point: secp192k1, 0x6e43b7dcae2fd5e0bf2a1ba7615ca3b9065487c9a67b4583, 0xc48dcea47ae08e84d5fedc3d09e4c19606a290f7a19a6a58>
[2703678267954837351785554213274685006315909454394736461187, 4819488447247427566251735083777178500867610886057901058648]
4
#<ECDSA::Point: secp192k1, 0xea525dd5a1353762a14e9e78b9063316d1f2d5e792f87862, 0xa936d583530982690c445427cdf2c5b0bb1c88749247b02e>
[5745552452299990170047708381033538409389829586273531623522, 4149119999643839018748826508502409577574550433904674189358]
5
#<ECDSA::Point: secp192k1, 0x3cd61e370d02ca0687c0b5f7ebf6d0373f4dd0ccccb7cc2d, 0x2c4befd9b02f301eb4014504f0533aa7eb19e9ea56441f78>
[1491704151879778402453634126397704690763245542631007570989, 1086150172285263067604701742344372509326752799303307370360]
6
#<ECDSA::Point: secp192k1, 0xd5cfbcca993f384a5eabc46b81a39a40cdd39ec2a6c44ee9, 0xd2b873da35309b7dac745267c7da4467d42115d5efd0922f>
[5242642099579919307406596072705230873522967147365385129705, 5166852061548564737665954532663259806088915360823645344303]
7
#<ECDSA::Point: secp192k1, 0xdb06629f196458e33eea3a0d6a40f3d34074db3f563d9e83, 0xa5b55dc8c878fcfe37b12b8d1299609e9ea5526d062e718c>
[5370475959698699548314844898721723603195636604449975017091, 4063159672567797276483870227243726761721476925977179091340]
8
#<ECDSA::Point: secp192k1, 0xeabcf674aafe661300fc77ec078b20f73fb6816851d542aa, 0xd70a622b8f604b9e83d45f07d8a5c8b6136eaac8fb4e8d8f>
[5755762337644566273346597553659087301125025659335688405674, 5272779200107879755338583526238658285311566406967341518223]
9
#<ECDSA::Point: secp192k1, 0xefd9da261826e62d1e9d4e9fa35e2575cf03a65d3beba73a, 0xa905d8ef35066fdc102ba8e8033b6b232fdcd0813a66e7f4>
[5881129038202474251604654870077733890964443484002122966842, 4144428012154033294634977955538874035870200447545115076596]
10
#<ECDSA::Point: secp192k1, 0x598955b973468f82ee734058feef3378740882410fa69ec1, 0x376625e46eea0c9171b92a2e52410c37b93f15c18e4d8a9>
[2195427716573228626735708805550391309089593752735430647489, 84898744514630800037018969627919654458794268003351713961]
"n = 6277101735386680763835789423176059013767194773182842284081"
#<ECDSA::Point: secp192r1, infinity>
1
#<ECDSA::Point: secp192r1, 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012, 0x7192b95ffc8da78631011ed6b24cdd573f977a11e794811>
[602046282375688656758213480587526111916698976636884684818, 174050332293622031404857552280219410364023488927386650641]
2
#<ECDSA::Point: secp192r1, 0xdafebf5828783f2ad35534631588a3f629a70fb16982a888, 0xdd6bda0d993da0fa46b27bbc141b868f59331afa5c7e93ab>
[5369744403678710563432458361254544170966096384586764429448, 5429234379789071039750654906915254128254326554272718558123]
3
#<ECDSA::Point: secp192r1, 0x76e32a2557599e6edcd283201fb2b9aadfd0d359cbb263da, 0x782c37e372ba4520aa62e0fed121d49ef3b543660cfd05fd>
[2915109630280678890720206779706963455590627465886103135194, 2946626711558792003980654088990112021985937607003425539581]
4
#<ECDSA::Point: secp192r1, 0x35433907297cc378b0015703374729d7a4fe46647084e4ba, 0xa2649984f2135c301ea3acb0776cd4f125389b311db3be32>
[1305994880430903997305943738697779408316929565234787837114, 3981863977451150342116987835776121688410789618551673306674]
5
#<ECDSA::Point: secp192r1, 0x10bb8e9840049b183e078d9c300e1605590118ebdd7ff590, 0x31361008476f917badc9f836e62762be312b72543cceaea1>
[410283251116784874018993562136566870110676706936762660240, 1206654674899825246688205669651974202006189255452737318561]
6
#<ECDSA::Point: secp192r1, 0xa37abc6c431f9ac398bf5bd1aa6678320ace8ecb93d23f2a, 0x851b3caec99908dbfed7040a1bbda90e081f7c5710bc68f0>
[4008504146453526025173196900303594155799995627910231899946, 3263759301305176906990806636587838100022690095020155627760]
7
#<ECDSA::Point: secp192r1, 0x8da75a1f75ddcd7660f923243060edce5de37f007011fcfd, 0x57cb5fcf6860b35418240db8fdb3c01dd4b702f96409ffb5>
[3473339081378406123852871299395262476289672479707038350589, 2152713176906603604200842901176476029776544337891569565621]
8
#<ECDSA::Point: secp192r1, 0x2fa1f92d1ecce92014771993cc14899d4b5977883397edde, 0xa338afdef78b7214273b8b5978ef733ff2dd8a8e9738f6c0>
[1167950611014894512313033362696697441497340081390841490910, 4002177906111215127148483369584652296488769677804145538752]
9
#<ECDSA::Point: secp192r1, 0x818a4d308b1cabb74e9e8f2ba8d27c9e1d9d375ab980388f, 0x1d1aa5e208d87cd7c292f7cbb457cdf30ea542176c8e739>
[3176317450453705650283775811228493626776489433309636475023, 44601893774669384766793803854980115179612118075017062201]
10
#<ECDSA::Point: secp192r1, 0xaa7c4f9ef99e3e96d1aede2bd9238842859bb150d1fe9d85, 0x3212a36547edc62901ee3658b2f4859460eb5eb2491397b0>
[4180294501348368083809563235021370057375591405930992803205, 1227781623738814009517798297176766391967714436501424281520]
"n = 26959946667150639794667015087019640346510327083120074548994958668279"
#<ECDSA::Point: secp224k1, infinity>
1
#<ECDSA::Point: secp224k1, 0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c, 0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5>
[16983810465656793445178183341822322175883642221536626637512293983324, 13272896753306862154536785447615077600479862871316829862783613755813]
2
#<ECDSA::Point: secp224k1, 0x86c0deb56aeb9712390999a0232b9bf596b9639fa1ce8cf426749e60, 0x8f598c954e1085555b474a79906b855c539ed633dbf4a9fa9f06b69a>
[14191189181360997996379806745274750789977788778343874198743228391008, 15096496093532566179992225909830564705001954583177558844225647720090]
3
#<ECDSA::Point: secp224k1, 0xfa182dc268cc40ad9fc1976af6f1b667d9701679b3d03ec4f7a0dd28, 0xdde2c5f5ae938e863c6f383d2340638959a80a613ba39dd0c121661f>
[26338019477022588327452439506199889327710570287702626938118679354664, 23367305575205031305688808102144495894527252402636734842205645137439]
4
#<ECDSA::Point: secp224k1, 0x916462f9bfe7491e9fa620e6944e9b7d9dd774980d3327140599242a, 0xc65b5df0d3aa1c57f504d2c61208ec7caea5fbb4912df4a4c6935c6f>
[15311578953505950849138991054788417020452164109036646876727924565034, 20889419935985911298223933746785044754401242136012707615277665442927]
5
#<ECDSA::Point: secp224k1, 0x4db89aa8d4b0368e3e0df667bcaaab4867ebc4093d5dfabe24400371, 0x42117761e36a41a6fa0578d50c41e9178870b1b1e857b3acd647188e>
[8184988196342689020396374051399578597950529088148208617500687991665, 6957796484575725750899603584509965167453307114760847059524931491982]
6
#<ECDSA::Point: secp224k1, 0xeca9c439bb9c982765b09d6503bf04d30e41a811af85b73158a20029, 0x283f2763796a4e3e0c59fdda80d4ce28cece7ce065aaa048da6b374a>
[24923538723578016112449516011106640254810696814979541884062461460521, 4238471658513987791005711479024383435196192195712451386956399195978]
7
#<ECDSA::Point: secp224k1, 0x721f62c5214c0b3f74ff434e6a6388923dd18d3f91154b38b4c0dd96, 0xdc041bfc3b40d3437a5572d2dca0beb1e8fb57ad49a6eaf1e9b62fee>
[12018512627868579090339921402646513160154156378653420007430306192790, 23170394642249619405597430024067260105321439613647022508985279721454]
8
#<ECDSA::Point: secp224k1, 0xca2ce099a0ec086f9f03966ae3facee5d536c98f1953bbedcfe5832e, 0xa78feab3b76332f2f1f68fd6061a890a27b97dbf57ebde7eca1069fa>
[21291544385643360557561316392984022524600750730957114438629649122094, 17646356648173498854599833940378305412830908526669294038660963920378]
9
#<ECDSA::Point: secp224k1, 0x25074dc8b37f5f277a132610a7da957e4cf904b470425610061d67ac, 0xfe0a2921c1f2f28b076f4811269f4857abec0113a52adcf4f9d7e5dd>
[3899559418762950051794944049353765868599210553102243583510401869740, 26753501941566616294128398354355388748954195183603072765208588445149]
10
#<ECDSA::Point: secp224k1, 0x1264edcba9470e80fcaa5564b02d011dfdbfc1e326d893aacf1c9f37, 0xa2c9e53d1a2f438774b57529f81d602eaf97b0e64768731aa2261fd3>
[1937140986685874993808395098410783670514236661131690802473716195127, 17143646226669041132338230813112996392907217363289440464798528970707]
"n = 26959946667150639794667015087019625940457807714424391721682722368061"
#<ECDSA::Point: secp224r1, infinity>
1
#<ECDSA::Point: secp224r1, 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34>
[19277929113566293071110308034699488026831934219452440156649784352033, 19926808758034470970197974370888749184205991990603949537637343198772]
2
#<ECDSA::Point: secp224r1, 0x706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6, 0x1c2b76a7bc25e7702a704fa986892849fca629487acf3709d2e4e8bb>
[11838696407187388799350957250141035264678915751356546206913969278886, 2966624012289393637077209076615926844583158638456025172915528198331]
3
#<ECDSA::Point: secp224r1, 0xdf1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04, 0xa3f7f03cadd0be444c0aa56830130ddf77d317344e1af3591981a925>
[23495795443371455911734272815198443231796705177085412225858576936196, 17267899494408073472134592504239670969838724875111952463975956982053]
4
#<ECDSA::Point: secp224r1, 0xae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301, 0x482580a0ec5bc47e88bc8c378632cd196cb3fa058a7114eb03054c9>
[18387688941486896693314180608234157394110342327606209796024257770241, 474869538468298384918655164606373990117569330548407043967769662665]
5
#<ECDSA::Point: secp224r1, 0x31c49ae75bce7807cdff22055d94ee9021fedbb5ab51c57526f011aa, 0x27e8bff1745635ec5ba0c9f1c2ede15414c6507d29ffe37e790a079b>
[5241180935788447299415492279837860720508896463754443826289355788714, 4202927080198900989467433352160374810063042822299340499566031669147]
6
#<ECDSA::Point: secp224r1, 0x1f2483f82572251fca975fea40db821df8ad82a3c002ee6c57112408, 0x89faf0ccb750d99b553c574fad7ecfb0438586eb3952af5b4b153c7e>
[3279702649264362226365706130591890985033768285409743741945602188296, 14531014943579176969516433940263520182884149791831438919418489683070]
7
#<ECDSA::Point: secp224r1, 0xdb2f6be630e246a5cf7d99b85194b123d487e2d466b94b24a03c3e28, 0xf3a30085497f2f611ee2517b163ef8c53b715d18bb4e4808d02b963>
[23082899941265312416076834149127612973281722793605426171718143852072, 1603621376426681438878568404181089291706931574771796688040135670115]
8
#<ECDSA::Point: secp224r1, 0x858e6f9cc6c12c31f5df124aa77767b05c8bc021bd683d2b55571550, 0x46dcd3ea5c43898c5c5fc4fdac7db39c2f02ebee4e3541d1e78047a>
[14065129557927240249858914614678013910013270899103922531749823190352, 466418981405194772047450263835226671439563161789125411861941453946]
9
#<ECDSA::Point: secp224r1, 0x2fdcccfee720a77ef6cb3bfbb447f9383117e3daa4a07e36ed15f78d, 0x371732e4f41bf4f7883035e6a79fcedc0e196eb07b48171697517463>
[5040509874486954907152001659568354790239799257249422621041130600333, 5801719477042191151577191672839035334726563409413076674857195893859]
10
#<ECDSA::Point: secp224r1, 0xaea9e17a306517eb89152aa7096d2c381ec813c51aa880e7bee2c0fd, 0x39bb30eab337e0a521b6cba1abe4b2b3a3e524c14a3fe3eb116b655f>
[18394223645928780833749682104922684895691658099010032856578518073597, 6079806569424875768420363755065073818836240443816190687503610242399]
"n = 115792089237316195423570985008687907852837564279074904382605163141518161494337"
#<ECDSA::Point: secp256k1, infinity>
1
#<ECDSA::Point: secp256k1, 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798, 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8>
[55066263022277343669578718895168534326250603453777594175500187360389116729240, 32670510020758816978083085130507043184471273380659243275938904335757337482424]
2
#<ECDSA::Point: secp256k1, 0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5, 0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a>
[89565891926547004231252920425935692360644145829622209833684329913297188986597, 12158399299693830322967808612713398636155367887041628176798871954788371653930]
3
#<ECDSA::Point: secp256k1, 0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9, 0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672>
[112711660439710606056748659173929673102114977341539408544630613555209775888121, 25583027980570883691656905877401976406448868254816295069919888960541586679410]
4
#<ECDSA::Point: secp256k1, 0xe493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13, 0x51ed993ea0d455b75642e2098ea51448d967ae33bfbdfe40cfe97bdc47739922>
[103388573995635080359749164254216598308788835304023601477803095234286494993683, 37057141145242123013015316630864329550140216928701153669873286428255828810018]
5
#<ECDSA::Point: secp256k1, 0x2f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4, 0xd8ac222636e5e3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6>
[21505829891763648114329055987619236494102133314575206970830385799158076338148, 98003708678762621233683240503080860129026887322874138805529884920309963580118]
6
#<ECDSA::Point: secp256k1, 0xfff97bd5755eeea420453a14355235d382f6472f8568a18b2f057a1460297556, 0xae12777aacfbb620f3be96017f45c560de80f0f6518fe4a03c870c36b075f297>
[115780575977492633039504758427830329241728645270042306223540962614150928364886, 78735063515800386211891312544505775871260717697865196436804966483607426560663]
7
#<ECDSA::Point: secp256k1, 0x5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc, 0x6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da>
[41948375291644419605210209193538855353224492619856392092318293986323063962044, 48361766907851246668144012348516735800090617714386977531302791340517493990618]
8
#<ECDSA::Point: secp256k1, 0x2f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a01, 0x5c4da8a741539949293d082a132d13b4c2e213d6ba5b7617b5da2cb76cbde904>
[21262057306151627953595685090280431278183829487175876377991189246716355947009, 41749993296225487051377864631615517161996906063147759678534462689479575333124]
9
#<ECDSA::Point: secp256k1, 0xacd484e2f0c7f65309ad178a9f559abde09796974c57e714c35f110dfc27ccbe, 0xcc338921b0a7d9fd64380971763b61e9add888a4375f8e0f05cc262ac64f9c37>
[78173298682877769088723994436027545680738210601369041078747105985693655485630, 92362876758821804597230797234617159328445543067760556585160674174871431781431]
10
#<ECDSA::Point: secp256k1, 0xa0434d9e47f3c86235477c7b1ae6ae5d3442d49b1943c2b752a68e2a47e247c7, 0x893aba425419bc27a3b6c7e693a24c696f794c2ed877a1593cbee53b037368d7>
[72488970228380509287422715226575535698893157273063074627791787432852706183111, 62070622898698443831883535403436258712770888294397026493185421712108624767191]
"n = 115792089210356248762697446949407573529996955224135760342422259061068512044369"
#<ECDSA::Point: secp256r1, infinity>
1
#<ECDSA::Point: secp256r1, 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296, 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5>
[48439561293906451759052585252797914202762949526041747995844080717082404635286, 36134250956749795798585127919587881956611106672985015071877198253568414405109]
2
#<ECDSA::Point: secp256r1, 0x7cf27b188d034f7e8a52380304b51ac3c08969e277f21b35a60b48fc47669978, 0x7775510db8ed040293d9ac69f7430dbba7dade63ce982299e04b79d227873d1>
[56515219790691171413109057904011688695424810155802929973526481321309856242040, 3377031843712258259223711451491452598088675519751548567112458094635497583569]
3
#<ECDSA::Point: secp256r1, 0x5ecbe4d1a6330a44c8f7ef951d4bf165e6c6b721efada985fb41661bc6e7fd6c, 0x8734640c4998ff7e374b06ce1a64a2ecd82ab036384fb83d9a79b127a27d5032>
[42877656971275811310262564894490210024759287182177196162425349131675946712428, 61154801112014214504178281461992570017247172004704277041681093927569603776562]
4
#<ECDSA::Point: secp256r1, 0xe2534a3532d08fbba02dde659ee62bd0031fe2db785596ef509302446b030852, 0xe0f1575a4c633cc719dfee5fda862d764efc96c3f30ee0055c42c23f184ed8c6>
[102369864249653057322725350723741461599905180004905897298779971437827381725266, 101744491111635190512325668403432589740384530506764148840112137220732283181254]
5
#<ECDSA::Point: secp256r1, 0x51590b7a515140d2d784c85608668fdfef8c82fd1f5be52421554a0dc3d033ed, 0xe0c17da8904a727d8ae1bf36bf8a79260d012f00d4d80888d1d0bb44fda16da4>
[36794669340896883012101473439538929759152396476648692591795318194054580155373, 101659946828913883886577915207667153874746613498030835602133042203824767462820]
6
#<ECDSA::Point: secp256r1, 0xb01a172a76a4602c92d3242cb897dde3024c740debb215b4c6b0aae93c2291a9, 0xe85c10743237dad56fec0e2dfba703791c00f7701c7e16bdfd7c48538fc77fe2>
[79653159259317329199152975905021693207262715618295428672027927511489832980905, 105099244361861367422779349381909628134794498213392835359532911141293690159074]
7
#<ECDSA::Point: secp256r1, 0x8e533b6fa0bf7b4625bb30667c01fb607ef9f8b8a80fef5b300628703187b2a3, 0x73eb1dbde03318366d069f83a6f5900053c73633cb041b21c55e1a86c1f400b4>
[64375483017717711348634889601793836329966447963510648681625681211348943876771, 52431391916983504423217627849020916729601969409053901192561322805962577543348]
8
#<ECDSA::Point: secp256r1, 0x62d9779dbee9b0534042742d3ab54cadc1d238980fce97dbb4dd9dc1db6fb393, 0xad5accbd91e9d8244ff15d771167cee0a2ed51f6bbe76a78da540a6a0f09957e>
[44710890534849379681007195543719586089737754824560621976448707498688874787731, 78410552107786285403689301656392479612049391334024095564584156230482213311870]
9
#<ECDSA::Point: secp256r1, 0xea68d7b6fedf0b71878938d51d71f8729e0acb8c2c6df8b3d79e8a4b90949ee0, 0x2a2744c972c9fce787014a964a8ea0c84d714feaa4de823fe85a224a4dd048fa>
[106026447472237217594103756757091873528548576106367144586170196380839010672352, 19066521425813101412078385704618669688199787690556935461623958781864528857338]
10
#<ECDSA::Point: secp256r1, 0xcef66d6b2a3a993e591214d1ea223fb545ca6c471c48306e4c36069404c5723f, 0x878662a229aaae906e123cdd9d3b4c10590ded29fe751eeeca34bbaa44af0773>
[93611846365601674425599200647886473617443872040541410036779615417472400060991, 61299672808462629900136024686264045542397545919962042795596947287593974695795]
"n = 39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942643"
#<ECDSA::Point: secp384r1, infinity>
1
#<ECDSA::Point: secp384r1, 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7, 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f>
[26247035095799689268623156744566981891852923491109213387815615900925518854738050089022388053975719786650872476732087, 8325710961489029985546751289520108179287853048861315594709205902480503199884419224438643760392947333078086511627871]
2
#<ECDSA::Point: secp384r1, 0x8d999057ba3d2d969260045c55b97f089025959a6f434d651d207d19fb96e9e4fe0e86ebe0e64f85b96a9c75295df61, 0x8e80f1fa5b1b3cedb7bfe8dffd6dba74b275d875bc6cc43e904e505f256ab4255ffd43e94d39e22d61501e700a940e80>
[1362138308511466522361153706999924933599454966107597910086607881313301390679204654798639248640660900363360053616481, 21933325650940841369538204578070064804451893403314136885642470114978241170633179043576249504748352841115137159204480]
3
#<ECDSA::Point: secp384r1, 0x77a41d4606ffa1464793c7e5fdc7d98cb9d3910202dcd06bea4f240d3566da6b408bbae5026580d02d7e5c70500c831, 0xc995f7ca0b0c42837d0bbe9602a9fc998520b41c85115aa5f7684c0edc111eacc24abd6be4b5d298b65f28600a2f1df1>
[1150902892488483458936980703033240421996917307006362560128741616924334451190275252566486993672663650518120360101937, 31026896179475916024120184231935979451435829475766013456640577102369059008378103381483562093497986423351518602141169]
4
#<ECDSA::Point: secp384r1, 0x138251cd52ac9298c1c8aad977321deb97e709bd0b4ca0aca55dc8ad51dcfc9d1589a1597e3a5120e1efd631c63e1835, 0xcacae29869a62e1631e8a28181ab56616dc45d918abc09f3ab0e63cf792aa4dced7387be37bba569549f1c02b270ed67>
[3002719260124138234864644293005553694107074621611323149430212532410635475904301642043243286192603916432052661917749, 31212625517239818344942812004487160470862995565736342725949902243255222118943617085729083408956085866876436550315367]
5
#<ECDSA::Point: secp384r1, 0x11de24a2c251c777573cac5ea025e467f208e51dbff98fc54f6661cbe56583b037882f4a1ca297e60abcdbc3836d84bc, 0x8fa696c77440f92d0f5837e90a00e7c5284b447754d5dee88c986533b6901aeb3177686d0ae8fb33184414abe6c1713a>
[2750097886727221852871437489830375535902219297598792969027200942344246907638882141082920203987932105239591664846012, 22109872175543161315473274033501382113217372000035529196852092508530348707813916169793617815529384830733840621334842]
6
#<ECDSA::Point: secp384r1, 0x627be1acd064d2b2226fe0d26f2d15d3c33ebcbb7f0f5da51cbd41f26257383021317d7202ff30e50937f0854e35c5df, 0x9766a4cb3f8b1c21be6dda6c14f1575b2c95352644f774c99864f613715441604c45b8d84e165311733a408d3f0f934>
[15158061413379800065538248493105902144697876778848367452125464871443609651151271322845514729956502261224296802534879, 1456421203869220836818514483833972558040283856785775367907417308863650512182437695714129960394237275553647337470260]
7
#<ECDSA::Point: secp384r1, 0x283c1d7365ce4788f29f8ebf234edffead6fe997fbea5ffa2d58cc9dfa7b1c508b05526f55b9ebb2040f05b48fb6d0e1, 0x9475c99061e41b88ba52efdb8c1690471a61d867ed799729d9c92cd01dbd225630d84ede32a78f9e64664cdac512ef8c>
[6192706248650610585029334828875625541601599068644432283392070678800109693834576236172166289842521288047764778176737, 22850101761352155756627808478921273213930354190738002589669451013939984415721476662192719117631561703668728764493708]
8
#<ECDSA::Point: secp384r1, 0x1692778ea596e0be75114297a6fa383445bf227fbe58190a900c3c73256f11fb5a3258d6f403d5ece6e9b269d822c87d, 0xdcd2365700d4106a835388ba3db8fd0e22554adc6d521cd4bd1c30c2ec0eec196bade1e9cdd1708d6f6abfa4022b0ad2>
[3474169820285015935707784759505165025751354558980809204451847681969564642225728669274210426295040866239332835575933, 33987484343743100593269958688158316211807494280296367372570003270207970275375287587045962593543362932932356696902354]
9
#<ECDSA::Point: secp384r1, 0x8f0a39a4049bcb3ef1bf29b8b025b78f2216f7291e6fd3bac6cb1ee285fb6e21c388528bfee2b9535c55e4461079118b, 0x62c77e1438b601d6452c4a5322c3a9799a9b3d7ca3c400c6b7678854aed9b3029e743efedfd51b68262da4f9ac664af8>
[22015862039406592161640061395309898573981900544448277583680581570848334956774212068925210279638870991947884190568843, 15203520752271699905529257511401880117129466438770620902510214914921624065453958502658877623620972906864670126000888]
10
#<ECDSA::Point: secp384r1, 0xa669c5563bd67eec678d29d6ef4fde864f372d90b79b9e88931d5c29291238cced8e85ab507bf91aa9cb2d13186658fb, 0xa988b72ae7c1279f22d9083db5f0ecddf70119550c183c31c502df78c3b705a8296d8195248288d997784f6ab73a21dd>
[25613330671596181123005601887414536094101619968241601793426634216146173595484114582196490380477558694107707817220347, 26093677688555946946604951835762730654802489834678081288763495518642068008712824154838929891456709573200703804547549]
"n = 6864797660130609714981900799081393217269435300143305409394463459185543183397655394245057746333217197532963996371363321113864768612440380340372808892707005449"
#<ECDSA::Point: secp521r1, infinity>
1
#<ECDSA::Point: secp521r1, 0xc6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66, 0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650>
[2661740802050217063228768716723360960729859168756973147706671368418802944996427808491545080627771902352094241225065558662157113545570916814161637315895999846, 3757180025770020463545507224491183603594455134769762486694567779615544477440556316691234405012945539562144444537289428522585666729196580810124344277578376784]
2
#<ECDSA::Point: secp521r1, 0x433c219024277e7e682fcb288148c282747403279b1ccc06352c6e5505d769be97b3b204da6ef55507aa104a3a35c5af41cf2fa364d60fd967f43e3933ba6d783d, 0xf4bb8cc7f86db26700a7f3eceeeed3f0b5c6b5107c4da97740ab21a29906c42dbbb3e377de9f251f6b93937fa99a3248f4eafcbe95edc0f4f71be356d661f41b02>
[901472452850866198617673658578940391618730359691416279093035377195377079020397774511960179466499271590922803070095487687963115616363390991670183687363590205, 3281327921582527507824747162491172657218985358085640380741461489720525905953211486053138004786012424348623853685340634287932228687534583594738661002099038978]
3
#<ECDSA::Point: secp521r1, 0x1a73d352443de29195dd91d6a64b5959479b52a6e5b123d9ab9e5ad7a112d7a8dd1ad3f164a3a4832051da6bd16b59fe21baeb490862c32ea05a5919d2ede37ad7d, 0x13e9b03b97dfa62ddd9979f86c6cab814f2f1557fa82a9d0317d2f8ab1fa355ceec2e2dd4cf8dc575b02d5aced1dec3c70cf105c9bc93a590425f588ca1ee86c0e5>
[5674708455687314755177411224894914551247560982429925442328503936381769479291831722549724502783064471579811889182869230569934709210549404604394803481732951421, 4271801692429350493774172787940824381696861087943454989753620357811953134117882851809933515614164977926164094992857584446095333607804956469237639174332793061]
4
#<ECDSA::Point: secp521r1, 0x35b5df64ae2ac204c354b483487c9070cdc61c891c5ff39afc06c5d55541d3ceac8659e24afe3d0750e8b88e9f078af066a1d5025b08e5a5e2fbc87412871902f3, 0x82096f84261279d2b673e0178eb0b4abb65521aef6e6e32e1b5ae63fe2f19907f279f283e54ba385405224f750a95b85eebb7faef04699d1d9e21f47fc346e4d0d>
[720139262829490965228382995842856154672620969623624721491545193380081085740139236944514523432374714314516720643288782059935114497438659217305669829660312307, 1743509213896395704926971995163331058385350704471974861189555515264763786920497129482978082020953735069538018776269773826418065263344470573872048814915734797]
5
#<ECDSA::Point: secp521r1, 0x652bf3c52927a432c73dbc3391c04eb0bf7a596efdb53f0d24cf03dab8f177ace4383c0c6d5e3014237112feaf137e79a329d7e1e6d8931738d5ab5096ec8f3078, 0x15be6ef1bdd6601d6ec8a2b73114a8112911cd8fe8e872e0051edd817c9a0347087bb6897c9072cf374311540211cf5ff79d1f007257354f7f8173cc3e8deb090cb>
[1356490565846790255739168589204180496138457916455904646417394236994934604955446470133745046215752716497315667741727281784411650125266382302052918851202396280, 4664604347668020762970169188647728988711329258092833895899217703661992685928809983190581180899656432001123782446415831494072942427109258745206503403498279115]
6
#<ECDSA::Point: secp521r1, 0x1ee4569d6cdb59219532eff34f94480d195623d30977fd71cf3981506ade4ab01525fbcca16153f7394e0727a239531be8c2f66e95657f380ae23731bedf79206b9, 0x1de0255ad0cc64f586ae2dd270546e3b1112aabbb73da5a808e7240a926201a8a96cab72d0e56648c9df96c984de274f2203dc7b8b55ca0dade1eaccd7858d44f17>
[6627092593912669792642110945067526420603119632670712106335413291576815883585816148497705827209816819203919053952926123076419905599531213746077243594847159993, 6409054467195497574328769691992291744192825101429818044461519861807844707820590849737648382749606312491164515576381227669620056038791577188683842913641451287]
7
#<ECDSA::Point: secp521r1, 0x56d5d1d99d5b7f6346eeb65fda0b073a0c5f22e0e8f5483228f018d2c2f7114c5d8c308d0abfc698d8c9a6df30dce3bbc46f953f50fdc2619a01cead882816ecd4, 0x3d2d1b7d9baaa2a110d1d8317a39d68478b5c582d02824f0dd71dbd98a26cbde556bd0f293cdec9e2b9523a34591ce1a5f9e76712a5ddefc7b5c6b8bc90525251b>
[1164270129742194787021746298790404262615845385569632340556150609652209653392714737798593072499915146233094284387298092872206604386185768403662460504302349524, 820238749192739888211492096736837212740835839662383100764162083366076000951085168184227504476659003461738201421631812073852429309662558977232294321188054299]
8
#<ECDSA::Point: secp521r1, 0x822c40fb6301f7262a8348396b010e25bd4e29d8a9b003e0a8b8a3b05f826298f5bfea5b8579f49f08b598c1bc8d79e1ab56289b5a6f4040586f9ea54aa78ce68, 0x16331911d5542fc482048fdab6e78853b9a44f8ede9e2c0715b5083de610677a8f189e9c0aa5911b4bff0ba0df065c578699f3ba940094713538ad642f11f17801c>
[109083299521442500876842833611249336033561763077283587821638741694330082273903024416664243036493783947792437906787000707140664721345204901269860104151813736, 4762367841910623311695901789059609560484960426869206316472308403586084267202597852325933276209196012548531291691842818402620813054843744959471171805306650652]
9
#<ECDSA::Point: secp521r1, 0x1585389e359e1e21826a2f5bf157156d488ed34541b988746992c4ab145b8c6b6657429e1396134da35f3c556df725a318f4f50babd85cd28661f45627967cbe207, 0x2a2e618c9a8aedf39f0b55557a27ae938e3088a654ee1cebb6c825ba263ddb446e0d69e5756057ac840ff56ecf4abfd87d736c2ae928880f343aa0ea86b9ad2a4e>
[4616661200726261460425444407382564000458447935977095696549288279032624160572165028883634753543187515864165184548929181253345681100099099865467440109558948359, 565557105841472481223362297865540722006314205571885763530335674978792826921172930992998161356566446473354134360199263577951173812344419108828580268630420046]
10
#<ECDSA::Point: secp521r1, 0x190eb8f22bda61f281dfcfe7bb6721ec4cd901d879ac09ac7c34a9246b11ada8910a2c7c178fcc263299daa4da9842093f37c2e411f1a8e819a87ff09a04f2f3320, 0x1eb5d96b8491614ba9dbaeab3b0ca2ba760c2eeb2144251b20ba97fd78a62ef62d2bf5349d44d9864bb536f6163dc57ebeff3689639739faa172954bc98135ec759>
[5375460404355022005936344137910919641482040501042631812229106559568140729369345497476837707660889191626168303541735277230613470977508429228294991448237880096, 6588135334138314282252915335789429562328467280057335182605115845427333280489083939697175013949068040137109843930550149723252770088030396786860186457851479897]

190714

Ruby


公開鍵作成（ビットコイン）(2)

Ruby でも求めてみた。 

require 'ecdsa'

def show_key(key)
  p key
  p [key.x, key.y]
end

group = ECDSA::Group::Secp256k1
G = group.generator
N = group.order
p "N = #{N}"

# N*G
p G.multiply_by_scalar(N)

show_key(G.multiply_by_scalar(2017101920171019))

(1..50).each{|i|
  p i
  show_key(G.multiply_by_scalar(i))
}

出力結果
"N = 115792089237316195423570985008687907852837564279074904382605163141518161494337"
#<ECDSA::Point: secp256k1, infinity>
#<ECDSA::Point: secp256k1, 0x50db8e79db5f57e6f71d73c7a3cc93f590ba1e8dc9b43911e27379fefbac6a22, 0x607c05d00f857f2640b18898ebcb79c6c9ddf683ecf0bcc12e48fd8c082bdf83>
[36572950727085182085382801403406684418997739286809164939833038507156062366242, 43641162618061335383666517243600726585787626462467298998793806674351551668099]
1
#<ECDSA::Point: secp256k1, 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798, 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8>
[55066263022277343669578718895168534326250603453777594175500187360389116729240, 32670510020758816978083085130507043184471273380659243275938904335757337482424]
2
#<ECDSA::Point: secp256k1, 0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5, 0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a>
[89565891926547004231252920425935692360644145829622209833684329913297188986597, 12158399299693830322967808612713398636155367887041628176798871954788371653930]
3
#<ECDSA::Point: secp256k1, 0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9, 0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672>
[112711660439710606056748659173929673102114977341539408544630613555209775888121, 25583027980570883691656905877401976406448868254816295069919888960541586679410]
4
#<ECDSA::Point: secp256k1, 0xe493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13, 0x51ed993ea0d455b75642e2098ea51448d967ae33bfbdfe40cfe97bdc47739922>
[103388573995635080359749164254216598308788835304023601477803095234286494993683, 37057141145242123013015316630864329550140216928701153669873286428255828810018]
5
#<ECDSA::Point: secp256k1, 0x2f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4, 0xd8ac222636e5e3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6>
[21505829891763648114329055987619236494102133314575206970830385799158076338148, 98003708678762621233683240503080860129026887322874138805529884920309963580118]
6
#<ECDSA::Point: secp256k1, 0xfff97bd5755eeea420453a14355235d382f6472f8568a18b2f057a1460297556, 0xae12777aacfbb620f3be96017f45c560de80f0f6518fe4a03c870c36b075f297>
[115780575977492633039504758427830329241728645270042306223540962614150928364886, 78735063515800386211891312544505775871260717697865196436804966483607426560663]
7
#<ECDSA::Point: secp256k1, 0x5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc, 0x6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da>
[41948375291644419605210209193538855353224492619856392092318293986323063962044, 48361766907851246668144012348516735800090617714386977531302791340517493990618]
8
#<ECDSA::Point: secp256k1, 0x2f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a01, 0x5c4da8a741539949293d082a132d13b4c2e213d6ba5b7617b5da2cb76cbde904>
[21262057306151627953595685090280431278183829487175876377991189246716355947009, 41749993296225487051377864631615517161996906063147759678534462689479575333124]
9
#<ECDSA::Point: secp256k1, 0xacd484e2f0c7f65309ad178a9f559abde09796974c57e714c35f110dfc27ccbe, 0xcc338921b0a7d9fd64380971763b61e9add888a4375f8e0f05cc262ac64f9c37>
[78173298682877769088723994436027545680738210601369041078747105985693655485630, 92362876758821804597230797234617159328445543067760556585160674174871431781431]
10
#<ECDSA::Point: secp256k1, 0xa0434d9e47f3c86235477c7b1ae6ae5d3442d49b1943c2b752a68e2a47e247c7, 0x893aba425419bc27a3b6c7e693a24c696f794c2ed877a1593cbee53b037368d7>
[72488970228380509287422715226575535698893157273063074627791787432852706183111, 62070622898698443831883535403436258712770888294397026493185421712108624767191]
11
#<ECDSA::Point: secp256k1, 0x774ae7f858a9411e5ef4246b70c65aac5649980be5c17891bbec17895da008cb, 0xd984a032eb6b5e190243dd56d7b7b365372db1e2dff9d6a8301d74c9c953c61b>
[53957576663012291606402345341061437133522758407718089353314528343643821967563, 98386217607324929854432842186271083758341411730506808463586570492533445740059]
12
#<ECDSA::Point: secp256k1, 0xd01115d548e7561b15c38f004d734633687cf4419620095bc5b0f47070afe85a, 0xa9f34ffdc815e0d7a8b64537e17bd81579238c5dd9a86d526b051b13f4062327>
[94111259592240215275188773285036844871058226277992966241101117022315524122714, 76870767327212528811304566602812752860184934880685532702451763239157141742375]
13
#<ECDSA::Point: secp256k1, 0xf28773c2d975288bc7d1d205c3748651b075fbc6610e58cddeeddf8f19405aa8, 0xab0902e8d880a89758212eb65cdaf473a1a06da521fa91f29b5cb52db03ed81>
[109699032664856045668214896063362497021339186688470416858630178803463338613416, 4835088675770141268294878046681321747490758260515711581034896622314066275713]
14
#<ECDSA::Point: secp256k1, 0x499fdf9e895e719cfd64e67f07d38e3226aa7b63678949e6e49b241a60e823e4, 0xcac2f6c4b54e855190f044e4a7b3d464464279c27a3f95bcc65f40d403a13f5b>
[33301309993451753050311554695703528430361259803437469669590207169100761277412, 91711666877231500617203373035680263572492971120307578300405368749466283229019]
15
#<ECDSA::Point: secp256k1, 0xd7924d4f7d43ea965a465ae3095ff41131e5946f3c85f79e44adbcf8e27e080e, 0x581e2872a86c72a683842ec228cc6defea40af2bd896d3a5c504dc9ff6a26b58>
[97505755694356382817881959832717013755620551362654128955029190924747025549326, 39856815248295663243990443767776362321337592747889787217974905533720651000664]
16
#<ECDSA::Point: secp256k1, 0xe60fce93b59e9ec53011aabc21c23e97b2a31369b87a5ae9c44ee89e2a6dec0a, 0xf7e3507399e595929db99f34f57937101296891e44d23f0be1f32cce69616821>
[104059883622109321374094289636044428849728529177856482232626205340719788190730, 112122903140080327253741791678230372394936108416576609264408917599318947489825]
17
#<ECDSA::Point: secp256k1, 0xdefdea4cdb677750a420fee807eacf21eb9898ae79b9768766e4faa04a2d4a34, 0x4211ab0694635168e997b0ead2a93daeced1f4a04a95c0f6cfb199f69e56eb77>
[100862081773581120499222301212791081193994281440454033593790618293887747050036, 29883864782608871580821802176208615141762369223249393426421538275393411672951]
18
#<ECDSA::Point: secp256k1, 0x5601570cb47f238d2b0286db4a990fa0f3ba28d1a319f5e7cf55c2a2444da7cc, 0xc136c1dc0cbeb930e9e298043589351d81d8e0bc736ae2a1f5192e5e8b061d58>
[38901272619685732968285380035171577070479117282397203902622597987558769928140, 87393127487643849618870152207476122589010570440825041333620493866032028851544]
19
#<ECDSA::Point: secp256k1, 0x2b4ea0a797a443d293ef5cff444f4979f06acfebd7e86d277475656138385b6c, 0x85e89bc037945d93b343083b5a1c86131a01f60c50269763b570c854e5c09b7a>
[19588375357829479297593261744848590434972900972071148260168833594658324503404, 60568592333449737531184420002591396163903580402725242236305558432410218044282]
20
#<ECDSA::Point: secp256k1, 0x4ce119c96e2fa357200b559b2f7dd5a5f02d5290aff74b03f3e471b273211c97, 0x12ba26dcb10ec1625da61fa10a844c676162948271d96967450288ee9233dc3a>
[34773495056115281091786765947597603724784643419904767525769502836017890139287, 8470533044743364938367028725608288731153024648869546164814808839694950063162]
21
#<ECDSA::Point: secp256k1, 0x352bbf4a4cdd12564f93fa332ce333301d9ad40271f8107181340aef25be59d5, 0x321eb4075348f534d59c18259dda3e1f4a1b3b2e71b1039c67bd3d8bcf81998c>
[24049875635381557237058143631624836741422505207761609709712554171343558302165, 22669890352939653242079781319904043788036611953081321775127194249638113810828]
22
#<ECDSA::Point: secp256k1, 0x421f5fc9a21065445c96fdb91c0c1e2f2431741c72713b4b99ddcb316f31e9fc, 0x2b90f16d11dabdb616f6db7e225d1e14743034b37b223115db20717ad1cd6781>
[29908081367423272746086114569421970207888665320998202915346633185016778189308, 19705544727792599099830884487151299095417296550955739824847212341657057716097]
23
#<ECDSA::Point: secp256k1, 0x2fa2104d6b38d11b0230010559879124e42ab8dfeff5ff29dc9cdadd4ecacc3f, 0x2de1068295dd865b64569335bd5dd80181d70ecfc882648423ba76b532b7d67>
[21545045623056848826483343441081830815719530893582365358444562918095175994431, 1296978981679745807043951140304019026881137717020402959957988455650813508967]
24
#<ECDSA::Point: secp256k1, 0xfe72c435413d33d48ac09c9161ba8b09683215439d62b7940502bda8b202e6ce, 0x6851de067ff24a68d3ab47e09d72998101dc88e36b4a9d22978ed2fbcf58c5bf>
[115090238283566018960826468250608273126387416636633736439689841211757211870926, 47185183227829754668635270747409548752084785367264057948864458978444304762303]
25
#<ECDSA::Point: secp256k1, 0x9248279b09b4d68dab21a9b066edda83263c3d84e09572e269ca0cd7f5453714, 0x73016f7bf234aade5d1aa71bdea2b1ff3fc0de2a887912ffe54a32ce97cb3402>
[66165162229742397718677620062386824252848999675912518712054484685772795754260, 52018513869565587577673992057861898728543589604141463438466108080111932355586]
26
#<ECDSA::Point: secp256k1, 0x6687cdb5b650d558f40cbdefc8e40997c03fe1b2abb840885e5cad81710c4c8a, 0x3fd502b3111178b11a1fa873825c72000ef8e529f033f272b32e83b25c83ad64>
[46375854666189782329411331467438732923135312366454677774518044107217916677258, 28872066516664221627799718496556756366588329842312456769228220433104069963108]
27
#<ECDSA::Point: secp256k1, 0xdaed4f2be3a8bf278e70132fb0beb7522f570e144bf615c07e996d443dee8729, 0xa69dce4a7d6c98e8d4a1aca87ef8d7003f83c230f3afa726ab40e52290be1c55>
[99023490166718961467148584643029653267652245207820783364668071358307234645801, 75362751621984629832705305750958516370071248757681753180287377123479199292501]
28
#<ECDSA::Point: secp256k1, 0x55eb67d7b7238a70a7fa6f64d5dc3c826b31536da6eb344dc39a66f904f97968, 0x7d916a47b2b581400b1e718bf404258540973bce1c95052dd0689f2f493be3c8>
[38862517885349586199469132990077977525522399615397327331631717567532241615208, 56796032415390392137148811074183321813766115156763923072036584114852967736264]
29
#<ECDSA::Point: secp256k1, 0xc44d12c7065d812e8acf28d7cbb19f9011ecd9e9fdf281b0e6a3b5e87d22e7db, 0x2119a460ce326cdc76c45926c982fdac0e106e861edf61c5a039063f0e0e6482>
[88789495143442116025801984763830218317601484092281216301053684219001740388315, 14971629676138079947354454610178388572791590863859394042797260533911845233794]
30
#<ECDSA::Point: secp256k1, 0x6d2b085e9e382ed10b69fc311a03f8641ccfff21574de0927513a49d9a688a00, 0xacb82eb93309ad1cc739ddfa33604a83776238aa0bd5ff248dbac47a17f388fb>
[49378132684229722274313556995573891527709373183446262831552359577455015004672, 78123232289538034746933569305416412888858560602643272431489024958214987548923]
31
#<ECDSA::Point: secp256k1, 0x6a245bf6dc698504c89a20cfded60853152b695336c28063b61c65cbd269e6b4, 0xe022cf42c2bd4a708b3f5126f16a24ad8b33ba48d0423b6efd5e6348100d8a82>
[48009403158434809478298710137233764200988036438868259456275038304221065242292, 101379581344212856035375194820281365028426536613141130008386086305632315345538]
32
#<ECDSA::Point: secp256k1, 0xd30199d74fb5a22d47b6e054e2f378cedacffcb89904a61d75d0dbd407143e65, 0x95038d9d0ae3d5c3b3d6dec9e98380651f760cc364ed819605b3ff1f24106ab9>
[95440839670107969455973995843666399663662641812074432045896568980475242364517, 67400892360194400039319989411395972789004161889863182881857158544061243615929]
33
#<ECDSA::Point: secp256k1, 0x1697ffa6fd9de627c077e3d2fe541084ce13300b0bec1146f95ae57f0d0bd6a5, 0xb9c398f186806f5d27561506e4557433a2cf15009e498ae7adee9d63d01b2396>
[10219441022991940610048493520113102240595005085840974180672104038719657072293, 84023467742492607926612431243360899514584580916128500081114886405247779677078]
34
#<ECDSA::Point: secp256k1, 0x1be68a5a028f2601d0e80d468c344ba331d611b96c358b6032e8b4da0547fc11, 0xbebc47511ade7308b3ca6265f9400779c076329c75146bc6ff1822f5d1f30e79>
[12619776604307790469550660645393525758448419897555601226868753617320214526993, 86272100689574882152938150858861318820088413186167100601966648021512258522745]
35
#<ECDSA::Point: secp256k1, 0x605bdb019981718b986d0f07e834cb0d9deb8360ffb7f61df982345ef27a7479, 0x2972d2de4f8d20681a78d93ec96fe23c26bfae84fb14db43b01e1e9056b8c49>
[43584328072464330665967763306297595761508151294385275883849271528835646125177, 1171731419844835688478928898148416329180259014376715189840427072871218252873]
36
#<ECDSA::Point: secp256k1, 0xe0392cfa338aaf2f0b56c563e3e5e67a5d5fefe3388f85d90c899da20f0198f9, 0x76d458642a2c93adee7a347a5e4681f9bb5b10f4bd8aa51edfd6e3f50e7da3ac>
[101419098787597942766661010883841213675986572091206578880178916574081925093625, 53748097764673089702489673031527129553025318704228137363806494938199580582828]
37
#<ECDSA::Point: secp256k1, 0x62d14dab4150bf497402fdc45a215e10dcb01c354959b10cfe31c7e9d87ff33d, 0x80fc06bd8cc5b01098088a1950eed0db01aa132967ab472235f5642483b25eaf>
[44696466249196887777481833878429299174322536392992392205634510941844339159869, 58341336599715296255997469230977942456412351469447624645098110293822755987119]
38
#<ECDSA::Point: secp256k1, 0xb699a30e6e184cdfa88ac16c7d80bffd38e2e1fc705821ea69cd5fdf1691fff7, 0xd505700c51d860ce5a096ee637ebed3bd9d7268126c76a16b745bc318a51ab04>
[82592391416753704330480457266605199466589998476548643675167586509583694299127, 96352244311289141626709213538144106127822954871227876742730890119647945927428]
39
#<ECDSA::Point: secp256k1, 0x80c60ad0040f27dade5b4b06c408e56b2c50e9f56b9b8b425e555c2f86308b6f, 0x1c38303f1cc5c30f26e66bad7fe72f70a65eed4cbe7024eb1aa01f56430bd57a>
[58245954963044076335222193032419637688317373475605757277584156718458924469103, 12764036181290433088658499435961200322530176588733628912045896254235383420282]
40
#<ECDSA::Point: secp256k1, 0x91de2f6bb67b11139f0e21203041bf080eacf59a33d99cd9f1929141bb0b4d0b, 0xeb9ef6c031eed31de34e7a1009f8725155b03158202a9d3e9a9a2e83124a7899>
[65977930378964483966842705159007630837451149704819265634327747226133817150731, 106574384264472205627876631445935175739834375489227447805380155393950263965849]
41
#<ECDSA::Point: secp256k1, 0x7a9375ad6167ad54aa74c6348cc54d344cc5dc9487d847049d5eabb0fa03c8fb, 0xd0e3fa9eca8726909559e0d79269046bdc59ea10c70ce2b02d499ec224dc7f7>
[55442706224332212356956949983947160877073898960448236395042968736464621521147, 5905242281663190858892708265754696019921609450612128937011632221309721495543]
42
#<ECDSA::Point: secp256k1, 0xfe8d1eb1bcb3432b1db5833ff5f2226d9cb5e65cee430558c18ed3a3c86ce1af, 0x7b158f244cd0de2134ac7c1d371cffbfae4db40801a2572e531c573cda9b5b4>
[115136800820456833737994126771386015026287095034625623644186278108926690779567, 3479535755779840016334846590594739014278212596066547564422106861430200972724]
43
#<ECDSA::Point: secp256k1, 0xd528ecd9b696b54c907a9ed045447a79bb408ec39b68df504bb51f459bc3ffc9, 0xeecf41253136e5f99966f21881fd656ebc4345405c520dbc063465b521409933>
[96414945312501980282409358461754977502747357521062737878469375231739675541449, 108016644921439980219149763541432916357155273945921323318636524851968650287411]
44
#<ECDSA::Point: secp256k1, 0x5d045857332d5b9e541514731622af8d60c180165d971a61e06b70a9b3834765, 0xdb2ba972802d45fd2decbab8d098a8c2a1d1f34761c6cf261879a7cabf06fb68>
[42072772011086351294328511389423850314698152445154323541536957340534349973349, 99133657745585934968186133288050721248258413615930917407282740640761199917928]
45
#<ECDSA::Point: secp256k1, 0x49370a4b5f43412ea25f514e8ecdad05266115e4a7ecb1387231808f8b45963, 0x758f3f41afd6ed428b3081b0512fd62a54c3f3afbb5b6764b653052a12949c9a>
[2069755349039566255304036353648839232649715781170511813011535420394543798627, 53173698995439924366951845531266805314230463309822098990695656330917108292762]
46
#<ECDSA::Point: secp256k1, 0xf8b0b03d44112259f903b3d100e3950d980fdde9c7e85701c16baedc90235717, 0xbd8e9dc301d9adc96be1883b362f123bd0a986928ac79972517ab5c246242203>
[112485767891133126222498548010271946438760990210983300801299715976951536768791, 85739109496996784368776054024999276184984966609644199395125789597014054674947]
47
#<ECDSA::Point: secp256k1, 0x77f230936ee88cbbd73df930d64702ef881d811e0e1498e2f1c13eb1fc345d74, 0x958ef42a7886b6400a08266e9ba1b37896c95330d97077cbbe8eb3c7671c60d6>
[54253141229701892740678441538472478126466317116121420289154985997987923385716, 67647191893224491627918802490479062705030965032432110320079555712709270724822]
48
#<ECDSA::Point: secp256k1, 0x6eca335d9645307db441656ef4e65b4bfc579b27452bebc19bd870aa1118e5c3, 0xd50123b57a7a0710592f579074b875a03a496a3a3bf8ec34498a2f7805a08668>
[50111670963408569345385204828013406423962206186815367070190059614189255189955, 96344650049071302355595011727277439354119658646232861677212062449792674989672]
49
#<ECDSA::Point: secp256k1, 0xf2dac991cc4ce4b9ea44887e5c7c0bce58c80074ab9d4dbaeb28531b7739f530, 0xe0dedc9b3b2f8dad4da1f32dec2531df9eb5fbeb0598e4fd1a117dba703a3c37>
[109846273198995465046214558810696509369395695668678477567979041624391316796720, 101711840700253487202274292900077312932162220876743713596510869779955653950519]
50
#<ECDSA::Point: secp256k1, 0x29757774cc6f3be1d5f1774aefa8f02e50bc64404230e7a67e8fde79bd559a9a, 0xc39d07337ddc9268a0eba45a7a41876d151b423eac4033b550bd28c17c470134>
[18752372355191540835222161239240920883340654532661984440989362140194381601434, 88478450163343634110113046083156231725329016889379853417393465962619872936244]

190713(2)

Sage

公開鍵作成（ビットコイン）(1)

https://qiita.com/rintaromasuda/items/2e54f35683facb519446
の記事を見ながら、公開鍵を計算してみた。

sage: p=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
sage: p
115792089237316195423570985008687907853269984665640564039457584007908834671663
sage: E=EllipticCurve(GF(p), [0, 7])
sage: Gx=0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
sage: Gy=0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
sage: G=E([Gx, Gy])
sage: N=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
sage: N
115792089237316195423570985008687907852837564279074904382605163141518161494337
sage: N*G
(0 : 1 : 0)
sage: 2017101920171019*G
(36572950727085182085382801403406684418997739286809164939833038507156062366242 : 43641162618061335383666517243600726585787626462467298998793806674351551668099 : 1)
sage: for i in [1..50]:
....:     print [i, i*G]
....:
[1, (55066263022277343669578718895168534326250603453777594175500187360389116729240 : 32670510020758816978083085130507043184471273380659243275938904335757337482424 : 1)]
[2, (89565891926547004231252920425935692360644145829622209833684329913297188986597 : 12158399299693830322967808612713398636155367887041628176798871954788371653930 : 1)]
[3, (112711660439710606056748659173929673102114977341539408544630613555209775888121 : 25583027980570883691656905877401976406448868254816295069919888960541586679410 : 1)]
[4, (103388573995635080359749164254216598308788835304023601477803095234286494993683 : 37057141145242123013015316630864329550140216928701153669873286428255828810018 : 1)]
[5, (21505829891763648114329055987619236494102133314575206970830385799158076338148 : 98003708678762621233683240503080860129026887322874138805529884920309963580118 : 1)]
[6, (115780575977492633039504758427830329241728645270042306223540962614150928364886 : 78735063515800386211891312544505775871260717697865196436804966483607426560663 : 1)]
[7, (41948375291644419605210209193538855353224492619856392092318293986323063962044 : 48361766907851246668144012348516735800090617714386977531302791340517493990618 : 1)]
[8, (21262057306151627953595685090280431278183829487175876377991189246716355947009 : 41749993296225487051377864631615517161996906063147759678534462689479575333124 : 1)]
[9, (78173298682877769088723994436027545680738210601369041078747105985693655485630 : 92362876758821804597230797234617159328445543067760556585160674174871431781431 : 1)]
[10, (72488970228380509287422715226575535698893157273063074627791787432852706183111 : 62070622898698443831883535403436258712770888294397026493185421712108624767191 : 1)]
[11, (53957576663012291606402345341061437133522758407718089353314528343643821967563 : 98386217607324929854432842186271083758341411730506808463586570492533445740059 : 1)]
[12, (94111259592240215275188773285036844871058226277992966241101117022315524122714 : 76870767327212528811304566602812752860184934880685532702451763239157141742375 : 1)]
[13, (109699032664856045668214896063362497021339186688470416858630178803463338613416 : 4835088675770141268294878046681321747490758260515711581034896622314066275713 : 1)]
[14, (33301309993451753050311554695703528430361259803437469669590207169100761277412 : 91711666877231500617203373035680263572492971120307578300405368749466283229019 : 1)]
[15, (97505755694356382817881959832717013755620551362654128955029190924747025549326 : 39856815248295663243990443767776362321337592747889787217974905533720651000664 : 1)]
[16, (104059883622109321374094289636044428849728529177856482232626205340719788190730 : 112122903140080327253741791678230372394936108416576609264408917599318947489825 : 1)]
[17, (100862081773581120499222301212791081193994281440454033593790618293887747050036 : 29883864782608871580821802176208615141762369223249393426421538275393411672951 : 1)]
[18, (38901272619685732968285380035171577070479117282397203902622597987558769928140 : 87393127487643849618870152207476122589010570440825041333620493866032028851544 : 1)]
[19, (19588375357829479297593261744848590434972900972071148260168833594658324503404 : 60568592333449737531184420002591396163903580402725242236305558432410218044282 : 1)]
[20, (34773495056115281091786765947597603724784643419904767525769502836017890139287 : 8470533044743364938367028725608288731153024648869546164814808839694950063162 : 1)]
[21, (24049875635381557237058143631624836741422505207761609709712554171343558302165 : 22669890352939653242079781319904043788036611953081321775127194249638113810828 : 1)]
[22, (29908081367423272746086114569421970207888665320998202915346633185016778189308 : 19705544727792599099830884487151299095417296550955739824847212341657057716097 : 1)]
[23, (21545045623056848826483343441081830815719530893582365358444562918095175994431 : 1296978981679745807043951140304019026881137717020402959957988455650813508967 : 1)]
[24, (115090238283566018960826468250608273126387416636633736439689841211757211870926 : 47185183227829754668635270747409548752084785367264057948864458978444304762303 : 1)]
[25, (66165162229742397718677620062386824252848999675912518712054484685772795754260 : 52018513869565587577673992057861898728543589604141463438466108080111932355586 : 1)]
[26, (46375854666189782329411331467438732923135312366454677774518044107217916677258 : 28872066516664221627799718496556756366588329842312456769228220433104069963108 : 1)]
[27, (99023490166718961467148584643029653267652245207820783364668071358307234645801 : 75362751621984629832705305750958516370071248757681753180287377123479199292501 : 1)]
[28, (38862517885349586199469132990077977525522399615397327331631717567532241615208 : 56796032415390392137148811074183321813766115156763923072036584114852967736264 : 1)]
[29, (88789495143442116025801984763830218317601484092281216301053684219001740388315 : 14971629676138079947354454610178388572791590863859394042797260533911845233794 : 1)]
[30, (49378132684229722274313556995573891527709373183446262831552359577455015004672 : 78123232289538034746933569305416412888858560602643272431489024958214987548923 : 1)]
[31, (48009403158434809478298710137233764200988036438868259456275038304221065242292 : 101379581344212856035375194820281365028426536613141130008386086305632315345538 : 1)]
[32, (95440839670107969455973995843666399663662641812074432045896568980475242364517 : 67400892360194400039319989411395972789004161889863182881857158544061243615929 : 1)]
[33, (10219441022991940610048493520113102240595005085840974180672104038719657072293 : 84023467742492607926612431243360899514584580916128500081114886405247779677078 : 1)]
[34, (12619776604307790469550660645393525758448419897555601226868753617320214526993 : 86272100689574882152938150858861318820088413186167100601966648021512258522745 : 1)]
[35, (43584328072464330665967763306297595761508151294385275883849271528835646125177 : 1171731419844835688478928898148416329180259014376715189840427072871218252873 : 1)]
[36, (101419098787597942766661010883841213675986572091206578880178916574081925093625 : 53748097764673089702489673031527129553025318704228137363806494938199580582828 : 1)]
[37, (44696466249196887777481833878429299174322536392992392205634510941844339159869 : 58341336599715296255997469230977942456412351469447624645098110293822755987119 : 1)]
[38, (82592391416753704330480457266605199466589998476548643675167586509583694299127 : 96352244311289141626709213538144106127822954871227876742730890119647945927428 : 1)]
[39, (58245954963044076335222193032419637688317373475605757277584156718458924469103 : 12764036181290433088658499435961200322530176588733628912045896254235383420282 : 1)]
[40, (65977930378964483966842705159007630837451149704819265634327747226133817150731 : 106574384264472205627876631445935175739834375489227447805380155393950263965849 : 1)]
[41, (55442706224332212356956949983947160877073898960448236395042968736464621521147 : 5905242281663190858892708265754696019921609450612128937011632221309721495543 : 1)]
[42, (115136800820456833737994126771386015026287095034625623644186278108926690779567 : 3479535755779840016334846590594739014278212596066547564422106861430200972724 : 1)]
[43, (96414945312501980282409358461754977502747357521062737878469375231739675541449 : 108016644921439980219149763541432916357155273945921323318636524851968650287411 : 1)]
[44, (42072772011086351294328511389423850314698152445154323541536957340534349973349 : 99133657745585934968186133288050721248258413615930917407282740640761199917928 : 1)]
[45, (2069755349039566255304036353648839232649715781170511813011535420394543798627 : 53173698995439924366951845531266805314230463309822098990695656330917108292762 : 1)]
[46, (112485767891133126222498548010271946438760990210983300801299715976951536768791 : 85739109496996784368776054024999276184984966609644199395125789597014054674947 : 1)]
[47, (54253141229701892740678441538472478126466317116121420289154985997987923385716 : 67647191893224491627918802490479062705030965032432110320079555712709270724822 : 1)]
[48, (50111670963408569345385204828013406423962206186815367070190059614189255189955 : 96344650049071302355595011727277439354119658646232861677212062449792674989672 : 1)]
[49, (109846273198995465046214558810696509369395695668678477567979041624391316796720 : 101711840700253487202274292900077312932162220876743713596510869779955653950519 : 1)]
[50, (18752372355191540835222161239240920883340654532661984440989362140194381601434 : 88478450163343634110113046083156231725329016889379853417393465962619872936244 : 1)]

190713

Sage

楕円曲線上の演算

E : y^2 = x^3 + x + 1 (mod 23)
E上に点P (0, 1)がある。
P, 2*P, 3*P, ... を求めてみた。 

sage: E=EllipticCurve(GF(23), [1, 1])
sage: P=E([0, 1])
sage: for i in [1..56]:
....:     print [i, i*P]
....:
[1, (0 : 1 : 1)]
[2, (6 : 19 : 1)]
[3, (3 : 13 : 1)]
[4, (13 : 16 : 1)]
[5, (18 : 3 : 1)]
[6, (7 : 11 : 1)]
[7, (11 : 3 : 1)]
[8, (5 : 19 : 1)]
[9, (19 : 18 : 1)]
[10, (12 : 4 : 1)]
[11, (1 : 16 : 1)]
[12, (17 : 20 : 1)]
[13, (9 : 16 : 1)]
[14, (4 : 0 : 1)]
[15, (9 : 7 : 1)]
[16, (17 : 3 : 1)]
[17, (1 : 7 : 1)]
[18, (12 : 19 : 1)]
[19, (19 : 5 : 1)]
[20, (5 : 4 : 1)]
[21, (11 : 20 : 1)]
[22, (7 : 12 : 1)]
[23, (18 : 20 : 1)]
[24, (13 : 7 : 1)]
[25, (3 : 10 : 1)]
[26, (6 : 4 : 1)]
[27, (0 : 22 : 1)]
[28, (0 : 1 : 0)]
[29, (0 : 1 : 1)]
[30, (6 : 19 : 1)]
[31, (3 : 13 : 1)]
[32, (13 : 16 : 1)]
[33, (18 : 3 : 1)]
[34, (7 : 11 : 1)]
[35, (11 : 3 : 1)]
[36, (5 : 19 : 1)]
[37, (19 : 18 : 1)]
[38, (12 : 4 : 1)]
[39, (1 : 16 : 1)]
[40, (17 : 20 : 1)]
[41, (9 : 16 : 1)]
[42, (4 : 0 : 1)]
[43, (9 : 7 : 1)]
[44, (17 : 3 : 1)]
[45, (1 : 7 : 1)]
[46, (12 : 19 : 1)]
[47, (19 : 5 : 1)]
[48, (5 : 4 : 1)]
[49, (11 : 20 : 1)]
[50, (7 : 12 : 1)]
[51, (18 : 20 : 1)]
[52, (13 : 7 : 1)]
[53, (3 : 10 : 1)]
[54, (6 : 4 : 1)]
[55, (0 : 22 : 1)]
[56, (0 : 1 : 0)]