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1132 lines (1092 loc) · 140 KB
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/*
* A runnable main program that tests the functionality of class CurvePoint.
*
* Bitcoin cryptography library
* Copyright (c) Project Nayuki
*
* https://www.nayuki.io/page/bitcoin-cryptography-library
* https://github.com/nayuki/Bitcoin-Cryptography-Library
*/
#include "TestHelper.hpp"
#include <cstdio>
#include <cstdlib>
#include "CurvePoint.hpp"
#include "FieldInt.hpp"
#include "Uint256.hpp"
/*---- Structures ----*/
struct TwoStrings {
const char *a;
const char *b;
};
struct ThreeStrings {
const char *a;
const char *b;
const char *c;
};
struct FourStrings {
const char *a;
const char *b;
const char *c;
const char *d;
};
struct SixStrings {
const char *a;
const char *b;
const char *c;
const char *d;
const char *e;
const char *f;
};
// Global variables
static int numTestCases = 0;
/*---- Test cases ----*/
static void testReplace() {
CurvePoint p(CurvePoint::G);
CurvePoint q(CurvePoint::G);
q.twice();
assert(p != q);
p.replace(q, 0);
assert(p != q);
p.replace(q, 1);
assert(p == q);
numTestCases++;
}
static void testTwice() {
// Double zero
{
CurvePoint p(CurvePoint::ZERO);
p.twice();
assert(p == CurvePoint::ZERO);
numTestCases++;
}
// Repeatedly double the base point
{
const vector<TwoStrings> cases{
{"C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5", "1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A"},
{"E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13", "51ED993EA0D455B75642E2098EA51448D967AE33BFBDFE40CFE97BDC47739922"},
{"2F01E5E15CCA351DAFF3843FB70F3C2F0A1BDD05E5AF888A67784EF3E10A2A01", "5C4DA8A741539949293D082A132D13B4C2E213D6BA5B7617B5DA2CB76CBDE904"},
{"E60FCE93B59E9EC53011AABC21C23E97B2A31369B87A5AE9C44EE89E2A6DEC0A", "F7E3507399E595929DB99F34F57937101296891E44D23F0BE1F32CCE69616821"},
{"D30199D74FB5A22D47B6E054E2F378CEDACFFCB89904A61D75D0DBD407143E65", "95038D9D0AE3D5C3B3D6DEC9E98380651F760CC364ED819605B3FF1F24106AB9"},
{"BF23C1542D16EAB70B1051EAF832823CFC4C6F1DCDBAFD81E37918E6F874EF8B", "5CB3866FC33003737AD928A0BA5392E4C522FC54811E2F784DC37EFE66831D9F"},
{"34FF3BE4033F7A06696C3D09F7D1671CBCF55CD700535655647077456769A24E", "5D9D11623A236C553F6619D89832098C55DF16C3E8F8B6818491067A73CC2F1A"},
{"8282263212C609D9EA2A6E3E172DE238D8C39CABD5AC1CA10646E23FD5F51508", "11F8A8098557DFE45E8256E830B60ACE62D613AC2F7B17BED31B6EAFF6E26CAF"},
{"465370B287A79FF3905A857A9CF918D50ADBC968D9E159D0926E2C00EF34A24D", "35E531B38368C082A4AF8BDAFDEEC2C1588E09B215D37A10A2F8FB20B33887F4"},
{"241FEBB8E23CBD77D664A18F66AD6240AAEC6ECDC813B088D5B901B2E285131F", "513378D9FF94F8D3D6C420BD13981DF8CD50FD0FBD0CB5AFABB3E66F2750026D"},
};
CurvePoint p(CurvePoint::G);
for (const TwoStrings &tc : cases) {
p.twice();
p.normalize();
assert(p == CurvePoint(tc.a, tc.b));
numTestCases++;
}
}
// Repeatedly double without normalizing
{
CurvePoint p(CurvePoint::G);
for (int i = 0; i < 10; i++)
p.twice();
p.normalize();
assert(p == CurvePoint("241FEBB8E23CBD77D664A18F66AD6240AAEC6ECDC813B088D5B901B2E285131F","513378D9FF94F8D3D6C420BD13981DF8CD50FD0FBD0CB5AFABB3E66F2750026D"));
numTestCases++;
}
// Use random points on the curve
{
const vector<FourStrings> cases{
{"519C7E9CED6032BCA4BD9D3AC556AEE94C78394C6D531E614BA892BE111D3228", "1D67BE39439273C04E45089733ECD781A109EBBEF5EE1F09E4F495C8F7C529A0", "A0084A358B4FEC688E3360B1420ABEF644683C9FF4133191828BAA7E8185CE63", "6DF39473D82E971C128FD67C0DF9F75BC49EA71B3F163DF357C0DDF8067507B8"},
{"AA4371E2C7093E0BEAF8DD7A898C126716DB5574D818D9BA1905F989FED9C571", "DB7EE81642570539973EC10AE45C191D0C3090AF9161842AD57659AB4A38393D", "04569C88ECB1555F4E92C8820894A00FC2F56EAA2D340B6BFE4648DFB8ADA25B", "CC913C5F473BFF97CF30AC21E5FA7AF227F9738A3CBCFD2AFAE25EAD3B0E20B0"},
{"ED2C92C9848F3E04A17F9CA6916B343DD512BBABFAB178466DC7B8E6F2F7CA6D", "6AA652DAF0C26FBAF980CE316D8A318569D688CD6746B485FC9B0EDE004CE394", "C08E2B39E5282085B202F7CD11E36A66D601F5B98DD6F797C003B80B5665207C", "AD970B0ABAD8230B079FE862ADBB1F778D88118C844B4769F347AB801640B8D9"},
{"CEDB1DA17B8831849418535618435343CE78811CFBA7337BAE9FB3C369DA7639", "BAC85CA6F0C510F050EC7DC0C3C8A3D90E3007BD3CE96B3F78621AEE3C80F93A", "995E3E760FDF98009D4C63ACAA192D59840F5A2F4C156B1956E937BF1D659071", "E1569B822166D8DD04AD80E7BDCEFC01D969A61B13A88B2852796A37849D15C9"},
{"AA68B41E78BF070865CD9CE5A3A05F8B4A192C468B7DD31087FB64EFE3A7B3FF", "A844698C828074FDA3F2B9D416951C348AB517CB7C097B5F6126E622E06F31F6", "EA9080CC7B7FB4354647E5ADF1F47EA1960BE93315984DC94B7B846642686A1A", "0953033E7BDD130603C366D21F6E2A75DC440A1DF8A4B22ED7A13D4E326C1B8C"},
{"D526E0EEFCE73DBA5237BC60057B1763937BC03233FCFAA73387B1AA4961F72B", "8DB3A0D205898FBF5119CD5B6596295BB59134A0695DD9755C1FE315106EE4C8", "1409BC7A8C63C9C8B33F9B2FA98408625CE0A16B2FD9D6CA0B62655AADB4C27C", "26D238D64B43018860ED17088F9FA2300D31A5FB4FE978E381932E5B395CAB46"},
{"92AF8FFE082444BDD0EF3C39425C76D2FD811BE457AB78B5EF56AA35D6AA7459", "F135DF2307846D4CA38B783A74FE54FE5BE2B0DD513C4FB1587CA8C594206CD7", "B2A4A75D51755608E2DC211F3D15E5D476A7C378C3B3C6A1C0D3197EEA0D6538", "6394ABCEB681011A1BB3BD5ACE5F6D6E3F5F2BAF4304D5A45369993BCE8F8823"},
{"A70AEEBAC92D7AB9686921F7FB2EC09135A2E688907CE49650EDC628FA7B4236", "049AA0BC2249000605FBFDB47D25F9B6D5F407B09DE5C5DE76EDDA994331945E", "DCC173F45D003E2F3FDAC662CB49CCBC6BD87EFA6713D51F84493E5F1D871E5E", "4F179D378E610AADF1457785EF0B72AAF0E9DDB2486DFF8C2DA83D1ACE38EAFF"},
{"0E2F2E1DA252EC1424B1CC3ED61B89A29B54E7386C822F1D59108FF1A234CAD3", "8DC6F464456EED6908A6D4B96D06BF97E3C249386811B0B4205E501C4DE080AB", "F9B4C16D1CA570BAF5D8CEE33A5D312F0F35A42DB2347FC39316AD81343E1E3C", "2C5B66BDFA482F762748C33E41DF5DFBAE544F5B69F318367277AD8157F7BBB7"},
{"94CD8D4775B5FA6EB0B042A5041976EFB4B09B8AA8C6E58F87B2F8A9D3F79008", "B0AAC0E44E27E5326DC2150E89411343AEA33109CF9E5272B2A3D15DCE16A738", "16BC08CCA1C03DA886D708B1B5B38AB552E2C83C9DFEE67443B273BC57D7120A", "9A5B39A9DBB35F27ECA6CAB384FFE508D26679742D7BDB13887ED13A04572D20"},
};
for (const FourStrings &tc : cases) {
CurvePoint p(tc.a, tc.b);
p.twice();
p.normalize();
assert(p == CurvePoint(tc.c, tc.d));
numTestCases++;
}
}
}
static void testAdd() {
// Add zero to zero
{
CurvePoint p(CurvePoint::ZERO);
p.add(CurvePoint::ZERO);
p.normalize();
assert(p == CurvePoint::ZERO);
numTestCases++;
}
// Add zero to point
{
const vector<TwoStrings> cases{
{"293827D4BF13A446EF11307B4A59BF5F4DC029CF8EDDD65BC54E577C6A625970", "7C387AD917234368CF93F16033B8A76ABD68CDAE2DF1994934EFDACF6585CD85"},
{"306024DDE1D3137C37890D50CE2732A382DFA0ECC4C3A11F25853C488C806EB8", "0E7958E2A35EB9FAA24C87C280E145CD760760B5636B708A3FBCC4C22A9C2F87"},
{"0C02CC2FC9B01F59863B4069C575C85C19A188C3B484667530863F4CAED1AB07", "9986DAA568C51553D0B24251337DABC1FE90162A51A34A40242DBA6CB25A343E"},
{"9684E3A232DBC19E2DA72F4FAD2D421EB6159334ABF3D4B0C25FC10910D300B4", "73FEB4332777B19887E097D2A4248EB7C1527E8D96BEB84DF57A643A541D7DD7"},
};
for (const TwoStrings &tc : cases) {
CurvePoint p(tc.a, tc.b);
CurvePoint q(p);
p.add(CurvePoint::ZERO);
p.normalize();
assert(p == q);
numTestCases++;
}
}
// Add point to zero
{
const vector<TwoStrings> cases{
{"8EFFBA535D10029DF26EC3665E19DB891317F29981FA73489C60194AC35AA356", "D74944644796AA05281F231EAD92783A23AEBA166E362D0B435A872C575CF6BF"},
{"A838E02CE52424511AFAF7D32AC14D003EFC4CE16CFA7D451DC2D78976384DCD", "630C1613B8C8964C54B3711EF7E71095EF181D0104DEF6F827776C894168E15B"},
{"60EE39B1A743E3E4B6EABF2170EB52DEFB851782C1C6DB67D66E764B202825BF", "B75D2F1286DABF517013FFCE45B7E7C3906BF19AF6FB35E9A53A3642FB44514D"},
{"250C66A625C171A512D500217F3F46092B1F620E4E1EEDF1F2F36794C2F6C40D", "6D8B37BE53BE61836CFA6ECE75B5A6FDD1A4D57FFBD93CD51889AEE899971D5C"},
};
for (const TwoStrings &tc : cases) {
CurvePoint p(CurvePoint::ZERO);
CurvePoint q(tc.a, tc.b);
p.add(q);
p.normalize();
assert(p == q);
numTestCases++;
}
}
// Add point to vertical reflection
{
const vector<ThreeStrings> cases{
{"B8993C93A35F7FE3AEB60239FFA96BE23BB789A6F4DE7FFD914C2394CC4C3BB3", "F43985DA101E21D73481AC98284B7533D8C5E2F37BC5D414D8081E7FAF368073", "0BC67A25EFE1DE28CB7E5367D7B48ACC273A1D0C843A2BEB27F7E17F50C97BBC"},
{"700BF4F2A3AFA4921F70B2CF207F766D9682A54DAF2EFA75D8097DAC2A494D07", "38FA9B454D542094D7EBD9C3452C70F7A478A93BB9B4CA9A63994437896FD502", "C70564BAB2ABDF6B2814263CBAD38F085B8756C4464B35659C66BBC77690272D"},
{"7EFEB5F0FB582FEAF601B334E546CD13CAC6B4CC6FA2D0EFC0F4C2C56036DB54", "0450C1C4025C33FE2F96236498C2F6BC85603871A1128A8A8DF6285AB41BC303", "FBAF3E3BFDA3CC01D069DC9B673D09437A9FC78E5EED75757209D7A44BE4392C"},
{"96CD45BA6181E7C383E1FA133C8C6F22F8925AE9B2F58D51F103DC1FC2983AE7", "52E36EB7A20B1BA11F30FED7DB840B225FE51CFDC404C1018553A2C40AC6332F", "AD1C91485DF4E45EE0CF0128247BF4DDA01AE3023BFB3EFE7AAC5D3AF539C900"},
};
for (const ThreeStrings &tc : cases) {
CurvePoint p(tc.a, tc.b);
p.add(CurvePoint(tc.a, tc.c));
p.normalize();
assert(p == CurvePoint::ZERO);
numTestCases++;
}
}
// Repeatedly add base point to itself (doubling)
{
const vector<TwoStrings> cases{
{"C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5", "1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A"},
{"E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13", "51ED993EA0D455B75642E2098EA51448D967AE33BFBDFE40CFE97BDC47739922"},
{"2F01E5E15CCA351DAFF3843FB70F3C2F0A1BDD05E5AF888A67784EF3E10A2A01", "5C4DA8A741539949293D082A132D13B4C2E213D6BA5B7617B5DA2CB76CBDE904"},
{"E60FCE93B59E9EC53011AABC21C23E97B2A31369B87A5AE9C44EE89E2A6DEC0A", "F7E3507399E595929DB99F34F57937101296891E44D23F0BE1F32CCE69616821"},
{"D30199D74FB5A22D47B6E054E2F378CEDACFFCB89904A61D75D0DBD407143E65", "95038D9D0AE3D5C3B3D6DEC9E98380651F760CC364ED819605B3FF1F24106AB9"},
};
CurvePoint p(CurvePoint::G);
for (const TwoStrings &tc : cases) {
p.add(p);
p.normalize();
assert(p == CurvePoint(tc.a, tc.b));
numTestCases++;
}
}
// Repeatedly add base point
{
const vector<TwoStrings> cases{
{"C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5", "1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A"},
{"F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9", "388F7B0F632DE8140FE337E62A37F3566500A99934C2231B6CB9FD7584B8E672"},
{"E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13", "51ED993EA0D455B75642E2098EA51448D967AE33BFBDFE40CFE97BDC47739922"},
{"2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4", "D8AC222636E5E3D6D4DBA9DDA6C9C426F788271BAB0D6840DCA87D3AA6AC62D6"},
{"FFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A1460297556", "AE12777AACFBB620F3BE96017F45C560DE80F0F6518FE4A03C870C36B075F297"},
{"5CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC", "6AEBCA40BA255960A3178D6D861A54DBA813D0B813FDE7B5A5082628087264DA"},
{"2F01E5E15CCA351DAFF3843FB70F3C2F0A1BDD05E5AF888A67784EF3E10A2A01", "5C4DA8A741539949293D082A132D13B4C2E213D6BA5B7617B5DA2CB76CBDE904"},
{"ACD484E2F0C7F65309AD178A9F559ABDE09796974C57E714C35F110DFC27CCBE", "CC338921B0A7D9FD64380971763B61E9ADD888A4375F8E0F05CC262AC64F9C37"},
{"A0434D9E47F3C86235477C7B1AE6AE5D3442D49B1943C2B752A68E2A47E247C7", "893ABA425419BC27A3B6C7E693A24C696F794C2ED877A1593CBEE53B037368D7"},
{"774AE7F858A9411E5EF4246B70C65AAC5649980BE5C17891BBEC17895DA008CB", "D984A032EB6B5E190243DD56D7B7B365372DB1E2DFF9D6A8301D74C9C953C61B"},
};
CurvePoint p(CurvePoint::G);
for (const TwoStrings &tc : cases) {
p.add(CurvePoint::G);
p.normalize();
assert(p == CurvePoint(tc.a, tc.b));
numTestCases++;
}
}
// Add two random points on curve
{
const vector<SixStrings> cases{
{"D8E2F51F86CCB79F9774D7F56EEB6D65E012076726EEDEA4C9BEDFC25C780AF1", "8546CF18D7F20800376CB6D6C6A3042F39E4DA8738EE9A81949DEEF77FE8CDFE", "F01DC6BB112FB5FFE8E77D173453DB479A368794B12B4AC616154B454B7A99CC", "C6A200D4B689220345C67D2F8FD3C9A4789A7A0139EFA829E783285E7B7099C7", "0DA4159113DA119C4D351FE5FA148433251B7868C80C68114FBD1ADDC660831F", "EA70B1A7FB90118F7491F47AE86596A5763D1BE2E58A122E75F137F677B97C8B"},
{"4F49D384BDBAB681DA3612E6F31A460445EC2CFFEEDDFF2E1D6ABE0BDB483702", "A6154DAD136B01339E899F014D93E009E07ACFBF258024B3B8C6135627984143", "7A47CF13069A4E516A73E8FC0362B77088E842542B4F5CBDAAC77DB39508561C", "47E98EADBF4BE548F9DB09B2E4A36DE92049FFD5735651D5CDB794FB22A1A2A5", "0A10B520547BE0572A326FE3D375069BCC47B84F80BC5F6155B41C42DD059E93", "6E448864523A61FDF536576C799C2DB0F1782F7C1ACD9D89E854E778D370A3A7"},
{"3D2602F0F70649CD7E03254326F24DECC79A7040A948AD5A21D97F3AE82A2AF9", "15528860FDA6A013614A58B7A80791AA6903CAC1C0BFFF13C0BFE6D80040B7DC", "FC6192342B488F5C1CC356F5B16E68C8C843375DFEB6F1D5E60586A223958AB6", "5A9C457E4AA9B0622401B7B6D1AA8A78D100557E37F01839BE4B008292FD19B8", "43FA9A65C8DE9F4B5E0CCC959C8CF1CBF59D58287AB34F84D79FCACFBF5AE138", "EA5DF38D09BE2155D88CD7A10FEC168D3281BEBBF1B6FAC1FB6A6E0FF7C61ECE"},
{"8CD590E2FA6E47BA831510A742E31C5967282CC5AF705BB7EE05DDB1AE0A70CC", "3CC503DE45487E796B4E87B7E7805450A2411D2162390F8BB2F37F7A8BC0A43F", "2650633F2C463AE2C423A8370D37C89F9415DE52ED6E701C8208F0032D74BE9D", "41D7E50961A0C46258EF2EBC62165686F68773AB8F0C430504A50C65535F6B0A", "E683B66A22E2FA01B4B9BD2FCC1136A2634A65A9F29803C8F86FB9E953169F0B", "F7AC842DF72FE9E7872DB5671797A1856F9DC161EE6C26F016B1D1ED3DDFE877"},
{"D4F1595AF9FCD0200007504053D531EBFAAFA9AD8B824CD41FD3CBF3A6F89CCF", "7543303D5AD16221371DECA33F883DBA7E70382A5EBF2B22F5BFC64548F67E09", "19DEF82A4CAC5A0D1C6A1328A3BF31ABC4C4739C700033B89A6964CB57ED72DC", "1E98A224F7A980BFB0EB601ED34BD549D8F6E9B5C9893CC0142621F48FD12301", "7994C996E639207E9B2BAC683AEED5F6554DA0D4573DF0C018201DA32F43658D", "E5BD7828F71A1471F16139D1955DFC2877C829CE2C2B4DA88F88CEBCAD32489D"},
{"B4171048A82B057ECBB2410CB5CCA894FEFD753CB3DBF08F5AE7D1DA53B32460", "A612C60587A7471941A690D294EF44E5009CDB2C88609DA8E7A3F20851E061A4", "4E84C012316583837A181EED9F4B6B2C93180D59B8401AB9F000C1E794B63B56", "0A2248DD75A023B25710EB8D6F2202D2A8AFDDCB5A1D3167F24F32F989DEF523", "658CC032552673790961D1AA665BC5E6904E9C34B2BD188081F29EF01FA088B2", "2DA31FE2272C8C35E1A7A8C89630D4690B0D2BC852B4B99FEDBAB0144575DC7B"},
{"6BF99F31F70956A43FF30A3DFE7015A1BDEA1C72D360BB0C2CBE9009E8EB8DF8", "F40A505797BD58F6474B5AA95C1660F9D471196CEEBB29944920325A71EE9EF7", "C2674E87CF2F148FA4CD5A5D7301C2F928D9324987B63150A6A23010C51179CD", "A35B2AB12251D0306F28E5A6BD68BBCA88681CF318746579A64A8532830F4283", "56A652E288A1243E0F110A5D5B1E27AD47B4A2A2CC0E00BA9F07385B9AE2D26B", "45DB788A74CB0A8F4EC82458B8008C0A3395D36851BACD07A2E346FED23D1455"},
{"EC0CEBC10E8A40A62A79D6D71C188EFAEFE627DB850D8FC39CA98311EE9681E1", "B8A6D325F045E42750506BC316860DF05270A0034A6A3DF329AAC51ABD267E6B", "F05137FE20F64E3C0B134928A2697F1E7E530A4529CD6DDB4FA897BDB20CFFC4", "070E580DE65D8F984DB6E7CC08CFBA4B0A2684B0F1C30CB89B22AEE8DB81D4F4", "42B4614B78E06A98AF4F459C74E75DEBB462123FFD3C623060A10A245765597B", "E6C6C5BCF997A5717A01031AEDE414987625475CEC47E9E171F0C959E0A5D123"},
{"A14224FC7C828F17F47CF41E993904837F146F4CEB3A580FC2D1C904C11C230B", "39088E64F90572C0A95EC6FE2169C95189E177A4E51E6A97156832177033DD28", "7DE79E3064BAC0E0C51D9CB0BE4E29D7D92E901506292CAABE373D7CA1602E1B", "2AC948DD8724036D0D7B3D3A61BCFDE20AFE50277F3F14BD03475617770B8EA9", "835937C7310E89CE70937D7E2DF2567FA15B12525CCCD13F266D2A5031B09111", "BA7FBA3C8751C14F9A0E650CFACA9176BC1A592671AA1CE9547D3007632A1455"},
{"C152768B4ED3F7E3F0D680838C172402185556AB704FF0B0AA862ADDAD05824E", "CD5F61613C622615F1679D4AE82DE6CD886E51989FCBCBC769913F24C3D5252A", "D896C04205CAC67544C5176E8F257464EE19364A641442F0921A9E3C883237A5", "1BC74789D084C7C100C74466D9FF0DD5B195C57FB0A172ECDF9CAE26168A7D1E", "AD6C4498E4E18A48A905910601472E975EC00CBC89DD8714F27BD730533653CE", "1009AD5ABD73BCD7CC5C814CA9D2AEE18E90FD4127C8EC30C7217F6E794A7932"},
};
for (const SixStrings &tc : cases) {
CurvePoint p(tc.a, tc.b);
p.add(CurvePoint(tc.c, tc.d));
p.normalize();
assert(p == CurvePoint(tc.e, tc.f));
numTestCases++;
}
}
}
static void testMultiply() {
const vector<ThreeStrings> cases{
// Small multiples
{"0000000000000000000000000000000000000000000000000000000000000000", nullptr, nullptr},
{"0000000000000000000000000000000000000000000000000000000000000001", "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8"},
{"0000000000000000000000000000000000000000000000000000000000000002", "C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5", "1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A"},
{"0000000000000000000000000000000000000000000000000000000000000003", "F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9", "388F7B0F632DE8140FE337E62A37F3566500A99934C2231B6CB9FD7584B8E672"},
{"0000000000000000000000000000000000000000000000000000000000000004", "E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13", "51ED993EA0D455B75642E2098EA51448D967AE33BFBDFE40CFE97BDC47739922"},
{"0000000000000000000000000000000000000000000000000000000000000005", "2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4", "D8AC222636E5E3D6D4DBA9DDA6C9C426F788271BAB0D6840DCA87D3AA6AC62D6"},
{"0000000000000000000000000000000000000000000000000000000000000006", "FFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A1460297556", "AE12777AACFBB620F3BE96017F45C560DE80F0F6518FE4A03C870C36B075F297"},
{"0000000000000000000000000000000000000000000000000000000000000007", "5CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC", "6AEBCA40BA255960A3178D6D861A54DBA813D0B813FDE7B5A5082628087264DA"},
{"0000000000000000000000000000000000000000000000000000000000000008", "2F01E5E15CCA351DAFF3843FB70F3C2F0A1BDD05E5AF888A67784EF3E10A2A01", "5C4DA8A741539949293D082A132D13B4C2E213D6BA5B7617B5DA2CB76CBDE904"},
{"0000000000000000000000000000000000000000000000000000000000000009", "ACD484E2F0C7F65309AD178A9F559ABDE09796974C57E714C35F110DFC27CCBE", "CC338921B0A7D9FD64380971763B61E9ADD888A4375F8E0F05CC262AC64F9C37"},
{"000000000000000000000000000000000000000000000000000000000000000A", "A0434D9E47F3C86235477C7B1AE6AE5D3442D49B1943C2B752A68E2A47E247C7", "893ABA425419BC27A3B6C7E693A24C696F794C2ED877A1593CBEE53B037368D7"},
{"000000000000000000000000000000000000000000000000000000000000000B", "774AE7F858A9411E5EF4246B70C65AAC5649980BE5C17891BBEC17895DA008CB", "D984A032EB6B5E190243DD56D7B7B365372DB1E2DFF9D6A8301D74C9C953C61B"},
{"000000000000000000000000000000000000000000000000000000000000000C", "D01115D548E7561B15C38F004D734633687CF4419620095BC5B0F47070AFE85A", "A9F34FFDC815E0D7A8B64537E17BD81579238C5DD9A86D526B051B13F4062327"},
{"000000000000000000000000000000000000000000000000000000000000000D", "F28773C2D975288BC7D1D205C3748651B075FBC6610E58CDDEEDDF8F19405AA8", "0AB0902E8D880A89758212EB65CDAF473A1A06DA521FA91F29B5CB52DB03ED81"},
{"000000000000000000000000000000000000000000000000000000000000000E", "499FDF9E895E719CFD64E67F07D38E3226AA7B63678949E6E49B241A60E823E4", "CAC2F6C4B54E855190F044E4A7B3D464464279C27A3F95BCC65F40D403A13F5B"},
{"000000000000000000000000000000000000000000000000000000000000000F", "D7924D4F7D43EA965A465AE3095FF41131E5946F3C85F79E44ADBCF8E27E080E", "581E2872A86C72A683842EC228CC6DEFEA40AF2BD896D3A5C504DC9FF6A26B58"},
{"0000000000000000000000000000000000000000000000000000000000000010", "E60FCE93B59E9EC53011AABC21C23E97B2A31369B87A5AE9C44EE89E2A6DEC0A", "F7E3507399E595929DB99F34F57937101296891E44D23F0BE1F32CCE69616821"},
// Large multiples
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364139", "2F01E5E15CCA351DAFF3843FB70F3C2F0A1BDD05E5AF888A67784EF3E10A2A01", "A3B25758BEAC66B6D6C2F7D5ECD2EC4B3D1DEC2945A489E84A25D3479342132B"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036413A", "5CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC", "951435BF45DAA69F5CE8729279E5AB2457EC2F47EC02184A5AF7D9D6F78D9755"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036413B", "FFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A1460297556", "51ED8885530449DF0C4169FE80BA3A9F217F0F09AE701B5FC378F3C84F8A0998"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036413C", "2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4", "2753DDD9C91A1C292B24562259363BD90877D8E454F297BF235782C459539959"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036413D", "E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13", "AE1266C15F2BAA48A9BD1DF6715AEBB7269851CC404201BF30168422B88C630D"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036413E", "F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9", "C77084F09CD217EBF01CC819D5C80CA99AFF5666CB3DDCE4934602897B4715BD"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036413F", "C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5", "E51E970159C23CC65C3A7BE6B99315110809CD9ACD992F1EDC9BCE55AF301705"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140", "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", "B7C52588D95C3B9AA25B0403F1EEF75702E84BB7597AABE663B82F6F04EF2777"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", nullptr, nullptr},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364142", "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364143", "C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5", "1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364144", "F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9", "388F7B0F632DE8140FE337E62A37F3566500A99934C2231B6CB9FD7584B8E672"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364145", "E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13", "51ED993EA0D455B75642E2098EA51448D967AE33BFBDFE40CFE97BDC47739922"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364146", "2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4", "D8AC222636E5E3D6D4DBA9DDA6C9C426F788271BAB0D6840DCA87D3AA6AC62D6"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364147", "FFF97BD5755EEEA420453A14355235D382F6472F8568A18B2F057A1460297556", "AE12777AACFBB620F3BE96017F45C560DE80F0F6518FE4A03C870C36B075F297"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364148", "5CBDF0646E5DB4EAA398F365F2EA7A0E3D419B7E0330E39CE92BDDEDCAC4F9BC", "6AEBCA40BA255960A3178D6D861A54DBA813D0B813FDE7B5A5082628087264DA"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364149", "2F01E5E15CCA351DAFF3843FB70F3C2F0A1BDD05E5AF888A67784EF3E10A2A01", "5C4DA8A741539949293D082A132D13B4C2E213D6BA5B7617B5DA2CB76CBDE904"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF8", "D8975566D098BC58D56AC778EB2445A8BBBBFEA11A70E0AED7258D899E1C0613", "94E691957255FF0C5F2D79BBCDEAEA3C25DF63C268A10AF2E43E7B90E57E9252"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF9", "0527CF8A882B7A8335CC794152791AAC0A2E3580F2375C4EABFA99861C8A90C1", "AE4C367F859C2FE818492912A3237E0C33A5ABA4E30874287281C44C5C9F032A"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA", "1FF4DDB68AF6AEB749B8107B38D76108C0C4562F8EFE6087E04575305516CAA5", "991A7CCA5073B7F44BCC834D6DFE90EB155EE54D774122E3B9387CD26B7A7156"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFB", "64F6309019333DAF98303B4630EFCC46DEF0C895D16F830D140C833947F00E1B", "50E58E52650ED0DC8BB1D178A4B14187B4FD9EDC98A29327B5F2A7B4E6108115"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC", "2CB62EA7395B82DF182570F2ADC7326C7CC7FE8D1DB31A2071C5E831E3B0DF74", "A0FADE1641324FC1E4DE38568CE5124D9E161A82FDBC40F2DF4AADE4D58DCF56"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFD", "3FBEAC6EF73D496E597DAB76C75848E2633CFE3A8492B360D7A21B223AFCE95D", "1A9128BFF344CA910E8334027DE4308B3ACABCFE6B9799C7A0BFDE45A6FACF67"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE", "E0A65740C1C5148111A8305938C56322FBF345A18CB90CF48A788961C6B3FF91", "8AAF0580FD9E8BE571E97BEF4A067FA7911DA0FF0E1A5F307FEA63E3ECD903AF"},
{"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", "9166C289B9F905E55F9E3DF9F69D7F356B4A22095F894F4715714AA4B56606AF", "F181EB966BE4ACB5CFF9E16B66D809BE94E214F06C93FD091099AF98499255E7"},
// Random multiples
{"45528A55356F7C32CA753F1E58627BC33863670A1072D9C8DD0663EB5691D87F", "86F12A5BDA1DB7F296B4F1545E417D2DABB28C1E7C96475B97D5AEB9FCAD71A5", "2FE6419626EB949DB7A6439C6D54A78D42AA596ED74F117E51A6E1CD7AF78C1A"},
{"11D6DD13D560E703C7F0189140DF2F692B603EF57A5E10E29C3E163ACD1E8FF8", "E222674C42D1B962E51F11C4138A6A75E5ED73D16921C7D381DCA0692B2C172E", "90747484C1616B024139138492C716092E41F4A631015196022330B3C5BFF7CB"},
{"E1E1DD6FBA9D293B4F5F46BE5A3F05A7BCE9CDBD8993BC0282DCF6B975D285F1", "75608FB5896949F01C5AB5C655C55B91E56AA40DEB0B66DEA9BFFAC718A8BE42", "5C75D5CA6ABC9F8171E6BBB4EF9B1BE632A2FB25BAB0E345548505ECC1F3A45E"},
{"3CBD5DE8E80196F3F5DB4D925A29638E4BFE4A9A848A9424BAD5C46136837C1F", "A964798AE92F981676341BED95E95646FD357DE2929666FA967F605F3FB1C739", "06BCBB55BF3C38660C778029A64CECA44BD7AF9AE346164FA7BA5A99A292A899"},
{"EFA4125849134857FBC1A97675A43B5DE6C1D268E2CA7AB1E179DB25F13DE00C", "4E3E7A7387C7D8AB2F90DF43191F2CF56FB4F09BF1B1ED66501E4E231E4D65A6", "855323DD2B0BDED7E96E641A97B5E4D1BCC97EA2A4453BEC003208C18896E9C1"},
{"B177E15F7CF844C240A7749F332DF50A692A372D6AFFD786629686540C8E73F2", "79B63C33938948A2BEBF8670ED0A21AF7395584D644B0C7F2667A9672030B199", "089FFB15F84A98BE1BB2FABD4CFC9FC2B748EC158974D1B5A9AA5191ECB7E7D4"},
{"9806E0E601FDE9777CFBA9BE56FE90453023E6B08F5BE6CB18555156DE3AB5C3", "2F413CA9CB2A6E15120B1FCB4F57E907AD3D54E5034A7D7D7EFADF59EF5BF50F", "F83C779A884E36D307E6B588B53F62A6407D6F8815708D831AE8102EE26940F3"},
{"B26C14ECABF65120BC8786A981EDAD985E8C1D42B146D7F66A8759919B02AE11", "D5E97EFBB234E24B4CD39D59062E925A355901EE4D89899C638B4CD9B16CF829", "AF21FC31E958C61DC1C6DDA55E99444BF04E55940FA71B891540AA4AC94DA3BF"},
{"F56A9E89525FF39CFE2D18BADA4E050D0875BF2A2C97237BAC9B0F31D191E250", "95CECE9600B90D3352E868A5B497F9D134C05A882CB1308FE583061DD6C59F24", "FC8B7A4555770FF9E05A96A3828141AE69B9B89A8E06DEA1D5B6DA42C95513B8"},
{"6C2CE63745F8D521BF120F360FBCDC56C8411E177AB6637389E18D289257D435", "222D89AD4CB409AD7ADA41AB280D8D2BCC723DE7B8521CAFA03AD8C839D6CBD1", "C26957D3094F04B394A45E3DBCD11B631BD4F473D293D85E7E92457AB2F23737"},
{"9CE2B3D4ECBB3CE8CBFEBC365D5B0EE3D1DCDE114F0A7944CF357A770D27A5E5", "0F92952B176BB2B66B7251016B6EF3A10979A7DD20E3DE017498F339B7D47740", "CE2E23AFDDB77590D6F2B6DA13AD70FA212B89A885FF44545CF7EADE9DBD1627"},
{"8E237B486DE3BB3156BB7F1493F31E5709449113779B2E70C061BA6EC748DE5B", "62D8F6D03A41EB698D845B27E1CFD862A6D4E178B55DB4979AC0B01A84599E5C", "8B1926377D460E2A77F0687741DCF5E7B720A24E8189FE2D1706055FA0727B49"},
{"BA83B8BB8081B74DE6B7A2F24D9AA80BEB36A8F3670F62715846C4B66B6BF55D", "8A841F13C93473387B2D6DB8F43C82EC80A561DFF790D0C02F54AC6E8BABE596", "981B5EA656254E84EFDB72552164DEAE0E6C452ED2A462763DDA1DFB7431775C"},
{"1BEBE58F680EF4F9B05904AD0A06B28DA2796F5FCAD0EF7A6156DC5B981C89EA", "04F307974E735568BF7ED84D6D9E47C8CBF78362347216103D599233606E02EA", "EF06A534B729AB791C13F93567DAD39BC6A85EBAC3E607AD1045C4A2EC45ABAE"},
{"FA4BB94494E7DD1FD59EA728946E17434EAA6D5E0B9BAE191581C55E6A04ADDF", "A705FDBBD5F8C8F64BED6F13D667357ED200EF4738FAAA9D253A3687C0F3E194", "14A40DDD8053BEF96529E8A6E4D96579AF294FEC43986AD483302250A91CB52E"},
{"F30C65DFE796F9F5E72FFBF00A5693F69BFA56D4A9ABA2F12A7F19000E7D2884", "1B24B78E17D1CCC8BE2B901DBF3C9F36C3D0BE35A30E29B9425C17D06579C3AE", "5EE17B92E7C33F4B4376316AD409CFA729872F06AA70CACB3214B054FC17005C"},
{"DF3A3DC1913CEB70718FA0A07118454B8D5CE9894E0AEF5E40DF7EB55E32D9DF", "DA4316FB9D85BF0485E0CE6380B99210F8BEA0CAF641684F98EF586BDD1295E5", "07860148AABDB47C310DEDAE95116E40858C1A0E2DD296D821618B3D822ED9EE"},
{"771057BBA5B9C168F34204651C9BD9948CA7F819B717F213C020176BC47C01FE", "8BC8442E4B445DF8AE1A723104047B5B599A495A006521041D49819D9BBC4DC3", "CD655AAC8D8E1C69FFE8142D12B6445DA7CE239F115C63DB3CAA688C68143C99"},
{"815A1EF6BB5458AD1567571AACF0B7DA2FB5D4307CB52059B1211F3A40469E0E", "C7EB10C596CD9AD02970170B8CA424C310A123589468E615AB1CCB08C0889F67", "26C39AD0442D3B294345EAEDA3316DC8BBE5FCB91677068CA6BF4E78D07CF2E6"},
{"866924A28917A33FE144DB60B4D7A27F1DC8B0D26D63372F76E629642245A76B", "6058612C8520CB807E753132E14D497BFD9EC74B172356E5DDC78DA1D2AA97A8", "4EBF15D5285A619C6987D47079AF89E544C7987795C427939BC5728663295FC4"},
{"FAE4AFECD392E1F88EEB28B8FF0C25569530B8DC7141B8061397AED9A49CF9F2", "F46E371AB5FD98A0ED4B15C92CFADECB0787319326A7E561DDD8A6C6080F8642", "1D2B15146F7A7171A1A2D66FB55F50AD970122E7F87F3754A6016D0A52818DE0"},
{"3BFD4640F65AE89E5E46B027D969ABCF046AF5BDE20F8E923787DE6473811965", "4BF1E32C1B69D7E0B95726EB8DCF293FB9AFB5F4CBA7C00F95E2CCD4EE0FD14D", "725352959BE783B2E64055F76FF1EACE840FA43FA8F72DF4DB0889FF3E997DDC"},
{"3DD6E832384E4C1283DEBF1CD9AF94484A6A4458D7FA88FCB853317E923BFEE1", "488CECBFED358EDE1CE51FCB9F2B34C23F7FEB67A800063AB8212871E1941D13", "FBE324AB8FA3C3A3B6D71281FE4555AC80689EA29453F43445D8B74257039F13"},
{"CA0CCB9483483BD0601220B8A1E5A2F93ACAD18C794C9EB14C8AB7D8A4001E2E", "8013D6BC2F12A279617C93DE87FE85AEE7A9F82BD01274301DA32126A3D5E8AC", "BED9ED257D0CC0B956F192BCC1F00190A7D0293C222648EB600D28FB3F22CF66"},
{"9C6236188056AC2CB99CC60FD38CED951590E004282480883BC88B74A1EAB3A7", "8333198B3B42E44586A25F0CF5371133220703B44C9B7612FD83ABBBBA4F78D8", "4C633A0CA354671CF632ED36F749C66BF9D979414ED52DCF04270A0A60224C7A"},
{"F563BBA48829799D3D60E66AC9C0537D1DBDD32A1C2D893153A8384FEB0062D8", "2EE54FBB45B4B7A0BF8C5BA332B898D7AEDCCCE1B3E4CDA56872FF77FB1F7A2C", "7D5B84B9C5164DF9979C5DBFD6FC31D112939F196A9A437329A36742D5E51611"},
{"406DC83D14DE5D2D272C480C42F5988AD6154ADCDBA66F1D03E7AA36693FF7D3", "D706B8D7ED2E83FC7AA5284DE94EDBDCAF9FA0D2E1F1C56341F1FBCC570B5612", "0EFD57AA3345E14F4F7F290C0FC924FA51FA2A069C8EC961999A2819C0ECCAFC"},
{"B9199737B6E6C3126BB68D37E938ECCE04F6ECBEEDA1E9CBF10AA6138B5C842F", "7943A0C63E51D571184B2469BB371F4D5A2A66BB32E7BB44EB4974882BAD8B76", "9387384D13291F8DF67EC5EC862F1F5372503771811D5DAA4EFE190D75DD1A39"},
{"4263B3E7A22922C05FFCE2E922CEEBC583B7E5C537C8A4F3572DA96BBA8813CB", "F1335E670E5CB076BA973C92B24C87BDA85B962416539B2111A4317B4BE9AE44", "106C70EE074A552FF61D885616003A1139D86A2845464F59C742677464DA2110"},
{"F750484A92E6ED351C6D5CC9738085F62C5389C11E7C6BDFA292EFAF20D0AC1C", "3CA82E74725ED3A9D359AE58D094D2E5C327B3F7B1671452C3517842538FF204", "9EBA56838328AD2FD2091050C8DB174B7952B28CCF9E322E2A006958DA3FB625"},
{"6E139E20DAF5E0F98D0F21B7648016579809019F9022DA7334EDD864E7916B3D", "46F45C0139653C58F80377522F5E43E53E16045A88053AC84A00FD5EA6BFEE7D", "743BA29A19E2F118037977B8A614D8DC2427D538C7198632AED237D48E6FE9DD"},
{"1B4B9E14EAB0F76F57B01E1155548FF0CA5AB75C7B28B0EAD962662D875C6B74", "A173D134375B449EED2D28B941FF935EC3FCF66255BD6FB10CFD52C219E48812", "133B122DA45CC3DDC3E2B5C02E9D86F0AAF4FBE564EF5FCBA59CE87858569EAF"},
{"098FF774AF194BEDF730A2E3E42D6BA9DCADA504B1610133296CFA4DEF20CE53", "3BA9C946D318B32252B212337E7DEAF1127FCE02210CD2E4487C28CE8E04307B", "4C5D9A560E8666AC90BCF88FD39A0BEB4D302D9B7AD0D5683A2F8D32ACD7C988"},
{"02B36516F5976CF6C3CBD5D5663DB4E1C93DD67383EE79627BE8A1F2A93ED0AC", "FD01FA210DB77F9126F7559B5E0AF8927D4A4C45AE5233BAF025E5596AA13C58", "B95C7D1519CD85E075AE293A0272A7AAF2CB97F29B64A351A2C512CFF7DF6B49"},
{"204FF2CC9F835A21B2FA49D7B3B712B6ACB2E3A98E1EF0326F7965DDE8E1133E", "9EDD38343D35B22C057D37199FBBC530B96E630BA7B4C9A7C5268CC38D626787", "2CCDAAEAE19F3A0A5FA1B2C3C03984DFAD390262DDE254832A1BFB5E4860DBE7"},
{"C1D10168789CB7EAEDB80BE73491B572E8866F9C6A8BE13A219611D203E96DB4", "AED9D3D5B9DC1830A567A837F4ACC1A04EB5530BA7035A72C013F54E292834A4", "B967438FCEF87D8BE5EEBBDB336F7606E852E7229DC22DB14BA2B17FD7C9553B"},
{"C279603B48CEFC3BDFAAF80F5548B11612C4BCB0746B19915977BB9B21C5F718", "ACD33DFB09D55BE1A21729408DF603253B55087555E4012D677756A02278906B", "660650032DBCABA6CAC73027FF78277287A7FBCC6CB4B4A769F4FDD6EC5F5C11"},
{"7BCBA36D1148C7A5AC938CA14C19A947E69F230577C182E243EEA7539E5C544B", "7B5D4B743D6FA328DBE32D49C276B123C04887AEAEC01F117582E846F6F2255A", "35C32C24B0499A3968CBD609A32EB3627EA99A5798BF50BE8B28608BDBE5FACB"},
{"59B5E4509B28E1EA788C777C73337E4DC4F465C8772DAD204C8EE5FAFE2D4645", "51471C106EE9BC9E4D46ACF6409FA3C13787835080B2FE921BB2CCF9699636A9", "8272B678EB7E805A0725BC709E2BB2AEA7F10F3A53DAE3512D6DC8EEBF1D137B"},
};
for (const ThreeStrings &tc : cases) {
CurvePoint p(CurvePoint::G);
p.multiply(Uint256(tc.a));
p.normalize();
if (tc.b == nullptr && tc.c == nullptr)
assert(p == CurvePoint::ZERO);
else
assert(p == CurvePoint(tc.b, tc.c));
numTestCases++;
}
}
static void testMultiplyModOrder() {
const vector<ThreeStrings> cases{
{"00000000000000000000000000000000000000054C9DC1717D84540608A237D9", "0000158D3F4383CB7CAC54E74928B4BFDF58224F42A01A4C6318B0A3BB2BBD4B", "231F5FC63A0601A4931488454123D6461C58D63A0632C5705005B631A8FBC8A4"},
{"00000000000000000000000000000000000000305E992F03907F26B287500DB3", "000000000000195BC7202AFEB9CA33432E3E338DE729525CD336EA7D4A7B4DB5", "86035A47723E45D64472BF5785CFA256A6619271D0B3D3C3BE741FC4B0B84AD7"},
{"000000000000000000000000000000000000003A6032550A5D6324553E1B6F12", "0000000000000000000000000153212C248BF7D55E31087A3AA913546B645697", "4D54F31DF7C870DCA7CBB5643DB2E9841E2EDD8AD2E684D507119330C2868F9E"},
{"00000000000000000000000000000000000006B04BF966C3987BA141FD68C8A0", "00000000000000000000000001CD1FEDC181822A2DCBF8361C6EF8BB2B99A0CE", "0C4E5F95E31359063413213A10862D0770739338E6F4B747C30F2D146CCA61B4"},
{"000000000000000000000000000000000001C3640908994650F6D28B3DFAA264", "0000000000000000010104886AA2C7ACA649B976C442AA4CB24DED88312DF3ED", "3FAC44C0F58C2EA3D69EB77041356381503098168C3FA6CB559E3C9AD9CE2A63"},
{"00000000000000000000000000000000000324C8E1BAC6E3A45882124257AE67", "0000000000000000000000000000401BBD0120C2E48FE73946F913FA294C6131", "C9896BCA5AD974A301A035F01ABA482B9EDAE2BB186DF19CA006832E317168B7"},
{"000000000000000000000000000000000004FF3468B8C2727F1B989CDD24DFC7", "000000286B60CB514EF7E9DDD026ADBA6D066A7C9B281432ABC226948B0F6B83", "5D68BB266807CB927462D144B70EBBDB5D772FD235B1487B996FBE31B3ADDD3E"},
{"0000000000000000000000000000000000071EF7B5ACD4FEDB970E884A39261E", "000000000000000000000000000000530646098F12EE8BF4807FE13C7C29171C", "024F36FC711851731185E05AA0CF08B32B6E0EF8DD2DBD047762B438E37ADD48"},
{"0000000000000000000000000000000000081375508BBAB588591F5CB1734D66", "000000000000000000000000000000002716480EDE527453F069ECD2ACEFEEBB", "00013BAAD14B47FF0A6A957F6E32F38A832D4320D042B2303DCABE009B685D82"},
{"0000000000000000000000000000000000093F3BBE8B96205CD277189A1CA58C", "00000000000000000000000000000000000007A359D8675CFC557A14F3BB734B", "0000000046A1240CFF6FA694A1B3DA3C29D91F287C2E521D8F085C70D6066404"},
{"00000000000000000000000000000000000B913ABC721053C522DEAF59EDD912", "00000000000000000000332412BAF8C3CBB4731D7DF3824A3008B296F2AFCFBA", "1CC1A6B05AFEFFB9030DF5FDDEDF78E25B68E2FE1C757910893D0CE5061B391E"},
{"000000000000000000000000000000000017F80086B7998F0F69127C3355AE7A", "000000000000000000000001268A1E5C20E9234ACA25617E85F640AD48359DB9", "22AFBE2118052D25873986866A9B0CE6C48D8AC7C8DED8AA9A134D26B25FE5AB"},
{"000000000000000000000000000000000174C12B61D8A82D35A53A3F6BFB9E94", "00000000000000000000000000000000001EE0A9C5CD31F35A8430E18840C358", "00002CF5C34EF612ADD4685BA72EEC64094DC283B9E5839E6F9520480D493EE0"},
{"00000000000000000000000000000000067545C860A9B9B5B2D50598C83AE0BB", "0000000000000000006A62AD5E3537C65B526D7E057577A003A9C8336D132597", "6A0039A8CCED4D86840BC5CAC95A49C5C9E3505645A0CBD774A47D2078E98A4D"},
{"00000000000000000000000000000000B842E2E864157CEF8A5370455D4AC6D1", "00000008F245A84CFF0342DC1BD7DFAE1909F25E51EABB211C349807B2E96EBE", "D6CF6D1FA062CCF0768BE03D4DF216134AF2399D5ACCF10D135D3C079A7CBEA0"},
{"000000000000000000000000000000017F9235B60F284E6FC389F694FA385E99", "0000000000000000000001FFD13D83845D2C1ED68559AC13DAF2E2F136250774", "D4B02A359DB1DD32FCE933CECB55F1C6DCB4E2C398D61430510E93DEEB65DDAE"},
{"00000000000000000000000000000004895028EF3A2AF3AF82F8F7F1A1754A7C", "00000000000000000000000006CF999B8481BDC02DE736489821A355E8D4EE26", "19E6B05500BFE91B1695C0BFF2FEB4CA6C70F61241009555B3B0747E84BC758F"},
{"000000000000000000000000000000375CDCFF01F61EA2F8E108D1EF19AEE89F", "000000001C24F3255F17D0BA0996D5C1726E12D6E2D921EDD5334AF4B6D38959", "6744B7D3C9F85F78F4A227D879103A1F4EF3F83A3634E751C3EE3C0AAC9D97D1"},
{"00000000000000000000000000000047EB6388C2999EA61C6E01F31A22260A0E", "00000000000000D6062C69E6C0397F0265A3349AE3CC9FAA2E6FBB1891F1CDE1", "6FA5CBD67569D8568CFF6A2E163382F03A06CDD7499CCC0DAAD8619A8C86B39B"},
{"000000000000000000000000000001ACB971CCB56CF2B865B60E5B5BC9812817", "000000000000000000000000000F6E5251A0572C9579FC1181C7192D87F4BFAB", "FE3DCFBB382731B381E5B61A4BB1941E6416446CFB6F45270E1FC58758C10EE8"},
{"000000000000000000000000000006CA54E90D3827EA670E69D18B034119C4E2", "0000000000000001CDAED94C9DADC6E1F05D56CFF12F9F1A6AB01745C4B6072B", "F530AD2660DBA512E9840F69CBBBDBDBE67B97DC3F55AC3435FF19BDBCC6D794"},
{"00000000000000000000000000000D8528FA8BD09DA634EE13B37D8EDB142668", "0000000000000000000000672F106E7C374ECA623F7EA3D943E252862B3C6F05", "BE5A99B8FBE89A12E1D9FB90FE3627BFEEDA5DF20E0B2A6CF29BD488A3C3A43E"},
{"00000000000000000000000000007CCD4701D24F10FC1ADE727310A7B0D883CC", "0000000000000008BFC99A69DD3327EAD650D1D53BB1064DE16E1F5185E08744", "99209F9E30BF196FD668EB4871DFDC2334CEC425431B213784427BF2308638C0"},
{"000000000000000000000000000135A4ABDB0AB6C8903D1512C8CDB8BC37B803", "00000000000185F85F215EF6397DFE076F9B4CE41CDA55D80DAEE47D1301D692", "E998E6383CED4D946A789E6A53488E0540A2E9D90C29D746148067F117B6D65C"},
{"00000000000000000000000000013B32312519C8195F6CF5E317C062D185C155", "0000000019ED7F9C7F40A01B7EAD61AFEC321FFB39C83B238F2B297EA4B1ABB7", "037BEE84685E8A9839490CAA7030C76DAF9CDFF85574C5A97C3919D177796B5C"},
{"00000000000000000000000000017379C46D327959F966DBEEAAB778C7EB7AA0", "0000000548F499FE4E81F1459CAC8DCE325F9F5063B6A189CB988A2F498649E4", "106093AADE816610078EF0078E21A0268ED453C7CD656BB7B5A48929C15A1CE7"},
{"00000000000000000000000000071E6BAC01866A5FDE9C0D2CC2EBE286D42564", "00000000000000000000000000000000001FD134A46B01AF184A4DEE4EA1B1B0", "80567BF2331C84C614AF9292F034083D0F92F2CC96FFBA0EE94F986D8BB23D5E"},
{"000000000000000000000000000FDBE31A9E96BB03938AE179FDFEF01BDD8FED", "00000339BE5C78AE92D092EF62E06F34720F5273C26DCA7BB8F32A1172E13E94", "8C32A55227B39FEAD4FE13DF78D5AD7926FA2F4087F77AEC2787CD4A54FCA753"},
{"000000000000000000000000002DE6CFCBC1D4F3786F95BD17F2763039D35F58", "0000000000000000000000328376858CA07E6F8FB1E5AF38D0CDF6AC812B8DBF", "E0C02A64B2071F11E49E078F7C4F4EEE59237480F563956F9B2349AFE07615DE"},
{"00000000000000000000000000C62494C857D13446F3B370A6B03AC9BFD07596", "00000000156FD3391A93120734EEECA1548AA7C0C295627EC8EA5AF513BB8EA5", "67FC4F95ADCE0F7D5A1A86455B5DD3934E72FE40D6F0BCAA285CFEED28EC1E6D"},
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{"3CA00B8BACFCEA0D84D56BFF140E76687F004B35BC4E083CE9C8F5F8AEEDCF47", "07AC194E89B5191298E4C250761D2D60AE2A5E6708DDC21EE02A5F4B038EFF15", "3F4D24E6287A0E478E36DBD69FFC979354CC7FFE3342697E884C00275A9E8378"},
{"499C55147795257DF2CC8BFD407E24782B5025A7AB894B21742D3B2D9F98D160", "6685B0E744F44153C0F3786A270C3C62434F59B6B6B525F6E6524FA61EB986A5", "242D1B1EBAADF4BCECF2BE7165AB268CC6B6270FF8835807B14D28BBE6C2C72A"},
{"5F1F4BFDEDD29F0689892A69507BF8C7D50D47ADCC7D9C2615298F30DE645137", "FB063F7500D7DD0219B9B9A19FD2196E58D1C9629232A75C9EEC38A8095E13D4", "942BAEBE9A49AEF24C13911FE4F213BC8A583C1B012D13060BCA1235FA4B3FE8"},
{"B70CFEC366E46390B39BB572D0511B88AA2AE6C5FD68D21368624696947B3869", "48FC042F64BCFE653CA2DEFB5E03BF91B6CC42093F0BF0E69A49286792C42780", "561AEAC7A8F80C950C9A0F864CC2FC4C35DFE546D2DC26BB6E4AA823B7E50652"},
{"DBD14AA6D37D93A19ED5F09178F1E02984B4C7FCB0235F55B7897CD3F143CAC9", "209AA16772271923D258A8EE1AC51E8E684FE89A841EBE9A5F72F07170B2F9AE", "8C149286067E400F21945AE21E0378268048BCADF6E7DDDE607F03D73C5659F7"},
{"E3E7D5BBA9E6BA0ACF981607FAD8004BEB31D99121F5AED271C2B31A22753341", "F754C7681141D64E70FD8C2DE1723FAE23DD9CC64E359210F7CE6E1A68B2FC58", "9E1BC1F3577B9DBA7F24E20CE23E3022A4074E0CD50B54F3F2C00E908EA70CB5"},
{"EE1AC7935818699AD1790FC415776484C6D3D8D90C4D8EBC3686C152B822D076", "9950DFB98E10659F3EA73A635A1B1547B9B54C1E9128A4B418E4BE938007F968", "B53E6A97998D2AF4B97AE947AEB4F308ECBE08B163C01BBB4CF33EDE2E6BF4D8"},
};
for (const ThreeStrings &tc : cases) {
Uint256 a(tc.a);
Uint256 b(tc.b);
CurvePoint p(CurvePoint::G);
p.multiply(a);
p.multiply(b);
p.normalize();
CurvePoint q(CurvePoint::G);
q.multiply(a);
q.normalize();
q.multiply(b);
q.normalize();
CurvePoint r(CurvePoint::G);
r.multiply(Uint256(tc.c));
r.normalize();
assert(p == q && q == r);
numTestCases++;
}
}
static void testIsOnCurve() {
const vector<ThreeStrings> cases{
// High and low multiples of the base point
{"1", "2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4", "2753DDD9C91A1C292B24562259363BD90877D8E454F297BF235782C459539959"},
{"1", "E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13", "AE1266C15F2BAA48A9BD1DF6715AEBB7269851CC404201BF30168422B88C630D"},
{"1", "F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9", "C77084F09CD217EBF01CC819D5C80CA99AFF5666CB3DDCE4934602897B4715BD"},
{"1", "C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5", "E51E970159C23CC65C3A7BE6B99315110809CD9ACD992F1EDC9BCE55AF301705"},
{"1", "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", "B7C52588D95C3B9AA25B0403F1EEF75702E84BB7597AABE663B82F6F04EF2777"},
{"1", "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8"},
{"1", "C6047F9441ED7D6D3045406E95C07CD85C778E4B8CEF3CA7ABAC09B95C709EE5", "1AE168FEA63DC339A3C58419466CEAEEF7F632653266D0E1236431A950CFE52A"},
{"1", "F9308A019258C31049344F85F89D5229B531C845836F99B08601F113BCE036F9", "388F7B0F632DE8140FE337E62A37F3566500A99934C2231B6CB9FD7584B8E672"},
{"1", "E493DBF1C10D80F3581E4904930B1404CC6C13900EE0758474FA94ABE8C4CD13", "51ED993EA0D455B75642E2098EA51448D967AE33BFBDFE40CFE97BDC47739922"},
{"1", "2F8BDE4D1A07209355B4A7250A5C5128E88B84BDDC619AB7CBA8D569B240EFE4", "D8AC222636E5E3D6D4DBA9DDA6C9C426F788271BAB0D6840DCA87D3AA6AC62D6"},
// Random multiples of the base point
{"1", "1B07DB98064918F5B2411F1466161F89B946743AFE2AA9325AB9C74AE0B60783", "171D8243BD690CF308BCC88627532714482396F044B0FE0AB29FE0F5665B01C3"},
{"1", "E1A0C178DC3F305A7EE7AE8BE81C2972DC624637E5EEBD9C2349C5485FD29995", "2AC409F0A89DEF3DCE8E223F38B861A1043697BA98CFD9F28F6ACFFEDBF58C1E"},
{"1", "5DF6035E2D94474A27779ECD2973AC52087974522AEE8D9D8373CA343B021AFE", "8CFA2CD8492347C2B1B37ED949512B741BF9E011ED63A6CD69576FD4EFED0A5C"},
{"1", "2D6A4711A41F6CD8EAB192E18C87D2D398990C914A71F8E059753C76D125EE42", "054BBD56DAE2C26CE3BEFE3274ADABCF8FDA0D410D8E79775EA2A43C27BFD214"},
{"1", "74146C93F5DF88C4E23105B15512D1E96BF975F85CB3C13D810DB4E32863787F", "E87A0EEE0108D550817D33C8A8B5D633B3C8980D3FC3C0E975EFB234F6D75CAA"},
{"1", "9E411FE9852B3378C971CE77C137E112D4B3F294ADE0673A1B7E4382E733B3AC", "52363849D9A49E0895B1D6A7AFDD9E60898A0E61BF9EA7E9E6056EDD8E90B3DC"},
{"1", "69F45B56C84A3B093EBAF7B57C15942D440A69859737FF8BE925E75706701594", "25E9009345D724AE44B239C1251411EC69C246A240C38206B238CBC4F063A4F4"},
{"1", "2311A5B686449D6E06ED292472D1444E386A7019E5FE12C14F50B18999A8761A", "91A583E277AFADE81128789A16718E96DEE2597C353F4A046111D919AC3BFD5A"},
{"1", "FF3E4BECE347F4BA604935DBAFAE85CA84179F97AD6BF9EA43E6D7D70A9BE495", "17A23B1EF3DB4373E89858F9310395C87EF02B1ED6EAB37450CEA0D1BE08D061"},
{"1", "2CC1132A4C3CC780E1E641773479CFBBA7F34CBC6C4B6F5D83D85B8A7BE56234", "175308D20EE4D36666AD21A9D997D543192E8E73A7D5568C821AF7CCDC12750C"},
{"1", "E99D7A6F04D3A206AD58BFDFD49BCFAF4846BF2369D34D1E54EDD14D52E53B59", "9C0CC36913998599A88F5B78D6F6A89F886B07300B243EB26CDBE0D0FBCD1003"},
{"1", "158FF6C43956FBBC94490D24B1F067C1D8B7D707A545781C312DB99444E2106B", "D9D34972E95DAB933365F0B8FB52D1B3815F0029D298C1CBB8EF69D3A1B3D8A3"},
{"1", "EA35D9EFBB4AB6D4FA100558DEEF87D0AAC4EFFC4A6C306646199DF00623A963", "07371782579F24C7ABDBA23FC2ABB4442432D8F4EE79C2EC37044046D7F847B3"},
{"1", "76FC3DF567F43F11FAF19D1CB673091CFF202410A0AA0EC00914FD32A80EA49F", "3459213E660178A1FDB1350A07DB98E27A8D0B9B271340902A1DB2A3684478FD"},
{"1", "50226B17E18C518AC6D391207D4421F481D6E60A04A150703B0F654472B0349E", "1C8552623C12584B87AC0E5E6C807F7544C9B0D8859DE2E99E939C1BFAC1E224"},
{"1", "03CEC9E4C36DA5BE1F65E5FC1DFE5718D23E38C327FFFB74BD1D538CE9503F52", "7AF9972E733BC0A7AB1B53435FDFAB3839FFB9FE1A18D67F516D1EE613622D4D"},
{"1", "B2F9ED7A97417A33C808427D2674A6F041E8F7288456EAD3C92ECE34A852265C", "4F8FD1D2CAD81E1C1FACC5B7F00F7B8969AB6176EF264A5D6DAA7D670EFAE5F4"},
{"1", "8E65E50F478C028446BF011573C42220146EECB6D7F93516B39065B8643D03BB", "7E55A908C293D6E2939F5DB57D97300678391BBFAE864BC939E9FB3CE874A1C5"},
{"1", "F3B97D10C5833C1F1CA056934C38A1941C16A6F4B3B315AAA06A39C7E8ABCA75", "E5BD7D2DC0894545F5375F97A9D4C93062B603BEE8F50BEFA8658C9BEC9A0CFE"},
{"1", "AADD5405B6E0D471C3D462BD46E5C912F86D40D4F12B25972AA69DCBD06F4412", "2709283EADEE6D6E71C01D0499EAECE2C6D5C607FE3FE8AD9EB5AC7749C90500"},
{"1", "344DDD0662591E4CEE695CA8DE97045693527ED759B671FB2ABA74EAE1FF409D", "4224A8B0A5B1C0E629AB9AF5890074156B38F983B738496EEA8832822202246F"},
{"1", "82089EF1B2F67B32537901FD772EBAD9F43791DBFE4CD90FC3CFAB59F0D45835", "BC8BCD53E2D9E51202048B004BACCD068E6BF143234DCB238C63AF1681004051"},
{"1", "88AADA0E12789AE0E7EAA2953D75FFFEC63E80F1434E1AFD1DE9402E9E4599C5", "D2E552C448732E03C592248EBA82F6AFA925C78ADC9619E7A5C87BB969CDC993"},
{"1", "91B4B4282D05952EA9A19AC99B828209E6CEC433B26D56A9934B264AD1E21798", "5F3ACF3802648CC1E6B70F81A01E19C466736BEDBA73255AFD42673E130DAF8C"},
{"1", "9B1D96376C4020C5A28EF2E625C04BCB4F4E6092ADA7AD7B08B3AB132FA602C1", "DC1AEC33E5524552F6A992542EF6CC4F9C7B2D3073D88EC2E15F4F31827FCB25"},
{"1", "6C644E5D7AE8F0112A9B58C42D7DFBAE7B47FA2308F1A27374CD8AFE333F3DB8", "9D9DA2DCB562E000B6CC2D3D629FC58B92F2BB2619ED1112DED7A8595A1E0243"},
{"1", "5C52634E493A6C856B2E4381EE07BB2A8E73AF5A85B7DB439B7D43B1C4245AA8", "4B9A23EC9DF4227F8A8D22D2F9EA723460491DC12204E6E31785D9776C357C45"},
{"1", "51E6DE129E839DADDDC2F415659E689DD76636A416A27527D5CD29776C6A9D0D", "25AB4F6CD5BB592D200DE7BCC60EBE5697E45C4875806E6E96B80184EF5AD729"},
{"1", "D3D0DF40929982857872BD049D5B783040CEB7A9C40DCD7EB3903B33BE7F5284", "50E43C943F095CFEB2D276534BBD47703F29164D76981A6556959B65668714A3"},
{"1", "AD42FB7C2864DE444184404D61A4B2B0CEC2A1C2F9EB39C697B0073C3786C6EA", "B5ACA9AB815A0596D2D0771F38FEC253525385B7344A405F25918B9C78FFFD95"},
// Random x, successfully solve y = +/- (x^3 + ax + b)^((modulus + 1) / 4)
{"1", "205CE0382E887F0A4E6BBA1F7914D48B8AC476A155C725E2B8A36BFEDAD96823", "9045481A4172CA1182F1E375911B0F3424CE4D8C71E443D541CA636472A4CFFC"},
{"1", "BDD30A055DBC5815704102F2D3B055739E4890F9607A54EABBDA9769355B74A4", "E84759447CD60F81327AB6E44277B309CE10641C1F0CEB6D39504A9D708A01BC"},
{"1", "BADEA26791714B0192F3E27F382DF6BABB5663371F879D62FFCD414B9FD84029", "EEFAA93D7A571CE61849320ACE9A7C39811082D6D82D9360FBC3FE2F2F4B4D6A"},
{"1", "BEBC13196AD505E4087E450F29F780EE44913013814CE8C5D22CFC5D592A42E0", "7A7F496A8D01C0203B785F5D7A25E05CECF42CDD554AA5E2C3A57B41860D7E1F"},
{"1", "26C431B62410B5386D395489DEFC5E8B120852C69B2F9DD77F1E37667E4D9F29", "8B2D91C6AD528C7A7603BFB4136338321CC8A715B69C811D9A6731B3466F55B7"},
{"1", "51B4127EA2BC8643DEF12D59619F1B5D4D6B28C05061DFDFBCF4C96CBEB2561A", "51D3704A06CA7C8768F236B9F78017DB3D085FC6B888D49F5DE5E335B82F43D5"},
{"1", "C69F619A52E5F41936D3585DAAC6D262D2722E9CDA3B0FCEA6B5B122A7DCF90A", "8AD9B9C53D2FAE651835C61B672E4398CB6EFB2E44F5E79C6C64B54FF1B4B980"},
{"1", "7EFE4DDBF91480C28EEDBE4AC8730EEBADB51236049D7233130BC19890C23A78", "5CB032BFB8FA7B4E3EF033099294C669D9CACC948DE778945B6529B5DE22F81F"},
{"1", "B0D22ECF778DD6E819359D802EECC78266A5676A4F5F0BB136E2FF7B9580EF49", "FB5426DC2F6E1391D902FB18474251C684A6A6AB01886E884DEA4D598433779A"},
{"1", "B484C7E9D0085C07D67EEDE85B2E97448AEA7818465080D739B0F7448AA38845", "9D8CCBCFEF4D4257B33BB6F7F0DF4CFC5AE9A6482759D3005338BE7670036371"},
{"1", "B1F365069773AB801B1EA949D9E79487FE33DE511FF9492A4862AA7D20B9767F", "870056D65ED8ECDFE92062B85C0C6FDA56D159BEE7F5462B85868B864C19E911"},
{"1", "0410C81426ACE86AC458FA1EB901895730DD21C8BA3554100DD9820EB88DA39F", "5068FB184C4829C619B124681E513DA2268C49551F298E0CB4A9003BBBDE44FA"},
{"1", "351C43B9B919A22472D5BB8AD0CBB9EBDE0AE10E11B248C87422AA82F3B000C3", "2C42E543B35B743214F9E9EA8E2840932B07CE8FAB4D0EBFC4C76DFD0CD6F74F"},
{"1", "3C89F96587AEFB9DD7F3C41F68195F9B03085B2C9E08AC787242025B2A20DBC1", "5BAEB6F1A2AD52CCD97B77509F6959CE05F8C6336ADE9C9E9C4B3D57E2125685"},
{"1", "5D7132F55D80F8151EE0EA2F8080DCD0378C7A077838053DEA7F22F1449D975C", "7C7C02F28C903935966941BE7ED9618AA45376CF6D112D12DE1971AA286FBB61"},
{"1", "39FF0AE947BA7F0F754A62F5FB2167A70E6DAAEB329D2E340740C85A36518AC2", "8482DCEC448F5BF20CD85272F6F14E1F164702D076BDB9AD6374678EF88D7E5A"},
{"1", "11DC37C5114BC8510A128D3259CD55437B64D550C0C7FA80397446D8BCA4BBA1", "42806F227EDA31001E67ECEA0A9B69A967D34C78DE8A54E3A18D40D36801522E"},
{"1", "BEA47012C17073A3E3F9AC43D6B1CAA0142FA027BD4B7BBEFCBDCD0BC89B4FEE", "26C875362B00951468707106E319FCDA6BC86D8A351903AEE10BA7603E604AA9"},
{"1", "74C880449C9593ABF63EC18806D3F2D472232991D0B4B7BC331853CA943C1580", "F3ECABFCC51C0DD77302DC58C0A78EEC59F0A73FC6FBFE94B31BD0C5EBE3CF44"},
{"1", "6A6E2E2A64E7E135C25120AD041ED550321D97F8D306A04A53D6805193BF98FB", "12D1F5FCEFE88F12A449734627639596E02D512EA704EC426FCEAE95B2FB6814"},
{"1", "4ED137D5F11E4D680EE8C70D605FCEB0A398133FF3E851542B44760F21524528", "01A72C663F5E3033679CFCE7F18BEC2C4F8895EE0A2F542300A1BCEACE706AA1"},
{"1", "B9B91AC2C0646C943D056D2FD03728E3F38562D10D22B82E49B87964E01CABBF", "423AD60D920D7CDE50F1627937F568BCFCF55FE5FB977393BC36D0022F31D631"},
{"1", "A985008A1BA3479B253809CEB959499B5B4ED61AA383E584C619C868D557D8A5", "3B8801FA40673A3DFAA456CC44989A60624FD4217018008E730B432B524DA151"},
{"1", "03DAED51CD075D2F6B97F031D88ABFA2D82D2C2FF5801CFAF8736835C21CE2FB", "3C78A32A9D6EA3DD4A6E9DDB9AC498CB4BE3D8FA207FDF40D59306932E544806"},
{"1", "A917B0A1C82FDD71E7BD8501E43A4806D76C6335D86D9688057152A13DF33E91", "E8452A5DB2B4BF7F08E8E6AC1187A61FAEE8F830C05C1CE8D809EA14344959A7"},
{"1", "7EFB501BD53B4E33952F543F486F7FA329CB149B0649F1C5D181617BB79765A6", "7620005FFD2E19952B0FBDB1B848B6495EA685EA5F753E75211BA1A7567097A8"},
{"1", "A4AE47569A759B310074F26D7E5A9CCA47043EFBC04946A59B565BF46ABDD395", "592DDE42F2CD1F7E2931A22D186E77FD8C5EEAF6878409B636FC5C0FD36E0A01"},
{"1", "62CD081F5FADC222E90AA86A62A2E5171823E51399CD4AABCED029AE948DAA1E", "BCCC1A4B5B05451D4F963196DE5B947661F648CF9A7DB62383C1890F781AA0CB"},
{"1", "3C62EE9A02701890B17ECCEA7205AA89390A957C4B937A415FE828A085172DF2", "50B51798BA12C10FC76B6140BE8F4CEE6E92CA65822539DB5CA8BE4189E7E9F5"},
{"1", "7E44F0904F49CCAA589F62101C2E359A7746C6E5B2D76AEE501694EEF4FE94F7", "DED83CCDA2AB3A249DBD767A7F0281DB87858B3224B51530E25451F731AE7A79"},
{"1", "93DCE6EDC6265E5FFCC844ABCD45E1F1FFCC742CC61614696176B0F5E98C815D", "5F16EEFC9CF4167ED43AA6BBE38DD5F697092A0CDDE60C6D28312E3A03F2822F"},
{"1", "5A76E121D1B81668DC7563A3A40E274345E7CA3F8C45742FDACF36CACB7EF11E", "0284B38AA0606F6CDBE34F0C297480CDCCA17D4625F801D7AD6D888FCF33C3FB"},
{"1", "3FCBAC51509177F3E02BC262C4B2298A51906BA4895CB5B942595D5CB46A5853", "861EC6805EDF0DF293B2B46CF61CB346377BBE227C1B76F93592CCBB738D7D0B"},
{"1", "FC4B1C071AA78C25D342AADA30A3D7420C11070E62AEE8E817DBDD38191ACB38", "195A554B1862AC2B8DE23C5CD0B1499F6DF46060EDB2E6F059F9BC317559D8B6"},
{"1", "D3ABEFC478DFE388767FE70D2F4444358DAA284E816A378C9DAAF637B035DD55", "C6B71D878817BF78F70A483E59674680B71ECA6EFFE3AB999C31696B44540229"},
{"1", "4CD9C50120ABF2E6B8F243DB9C006C922EC88B067C1C85A597B9FDEB6FB8F7D1", "DA91B2A11921321F5151F16381D58E54C56F6D11F9752CC73A2D2C28DEE0BD01"},
{"1", "5EBEF23B8010D00B2FF74162F756D0B19D1CF8EEBA5D31A39847BBCD2A0F14D0", "43E10FA071E19D6E9F1B4D09680BDBBED6A765718C152614471D8DF65158719C"},
{"1", "B083009061E9B56917CAB652A8873A004BE8C43936AF6156E09E6DE57144A3E3", "19128998CB111F072B04CD1B51615F47A935235587B8987F9591680213EBCC49"},
{"1", "1074723E8521D5B20BC8C967FD2B536B23175F4FA958D139F401B63EEFA13E87", "50863719B62F3F8A7564BAF2F06F025804184ED18455B0EC4FB4A377E3CC6917"},
{"1", "7EFD1EDF65F05935243253ACC1E14D8CEF86F88895F094533F4D7A645422E55D", "8A883F0F354233E8D3126C48D7E08D6603B73BB099D8A3F5B6B0AEE0EC92EA17"},
{"1", "D79B7858C30FD140573ECC7F9513B0945099C7A57496833CE3629149FF129C98", "9DDA537F66BD5E9395EF642E9CC40390C118E3D5F4076AE0297982426D062FD8"},
{"1", "D03BFCE878FB7916220B11CAEB2677A2F26E382C75E5E688E491272E6F4386B5", "2A8A168CF9C36DC8E6D89582CD5AA2E9B67D53C8B4B0DCBC5B40357873B33F0A"},
{"1", "36E31B2FBD4D6AD286B38F2A126FB79B43E4B0499887C847EA0BB2C860EF40BA", "E41564DE93C85C575BC3CF04BC52A3C6B44E7B57044C84B7CC9BE9A00CDF50E4"},
{"1", "F3476B9722260A650BC4AD422232D11F4B19D985EE68937FA31A33C6976B9E0E", "995DFB4501DCF16CE7898D45F778E67BE09527B7C717F6201B2238D7ECC230A4"},
{"1", "8AE7069945A235743FAFFF200F654D33519FEC1762709904CB0EFFB11E6C3335", "68FD58E8D9804B4C997A233C3091D9CB09BBC3E715672B1174EB6BD6A231921A"},
{"1", "9D4946A98C38FFBD80547515DC61641E7B2E5E74503BD2ED1BDA29E111DA3A8F", "3EFB88F418FE04E2B396B6DB13E70F814E23E2CD6A77BB4CEC176CBFC7F9F2B8"},
{"1", "82AB723D708412F247120BBB977D0C5691FE6368A6ADCB75A70695E94CFFA3A9", "D3E23A08F90E590F6CF557646FC9C8A9696E6AFE5E7F75EB76D1206CF5E32831"},
{"1", "5AB31BAB3A795EC041777EB400443B52719646D4075047DBE534CE1E8D710E52", "C33142BD17C52D5A81836A1C24E2FDCD7C44F5A989A2875CB44B8E1557BC6AC2"},
{"1", "ED31FABAE06166233F8FA744BAA2599ABF27E3C9CCD7A8549BA1CA21F2AB6EC1", "409C70F2E1DA8CD51E3C4A7D1D28FA1D6016D1DD267189CDDACDBC94F52F16A3"},
{"1", "D8722EFADA483B0EA4BBA4DDD46EF2ECFA0C64738AEA6F73D48D7453B7C2BA4A", "B24E138B6B725AB17A3D1663CD8C0A5D40BE597CAC8E3E642715C5952C22721C"},
{"1", "EF1C1329FFBCB726CEA68875AEBE0169EBFBDE083BB4A8C76FDAE2C026DC308C", "15B6A56FAFDCB7D3DCCFE463E12635ABD26C2406B0D475EFB28ED65AF3415470"},
{"1", "FA53B0C9110B1EE70B36E998B71BED6EDCEAAC443912F9659D7A722D7F464855", "C8108300A5B73178B249C233EB4F215CD56FD4D0EE1BA3648E31CB0171A0F5BE"},
{"1", "06500140504AA1EA86ECDBA14AA823BCCAFD085E12DEFFAFA3286A15C9D8E220", "828A76378853C10D13AA2589312330344E135C8EA3C60FFBA2EDEDE9059E3FE8"},
{"1", "D5E66B1A54AD9588CA6E0D4F1ECD89EA9869E9AC3C292FF355BD75D2DB5557C9", "4F2A05107B892FC94B36BFDEE86BAC675F63D8EC587349A8FE4FB1AED759733F"},
{"1", "0A03EC068DB83D46D47756C9004D817D83AB297BA82B8D3EFF3C94E426F20861", "507B2130920346CE8700C06D9588972075DEFB1EFA8E495F127010A31855E4CA"},
{"1", "8CF780E3486691D7C8EB2B06C645071C66F9110B325E82E0847397A1C9B53F62", "67DA3AAEB6A249B367BA9609C615C9CE349BB54DD1BA94A1C662DE99A6C3C4E9"},
{"1", "03CAD72BE309A8EF2D42235696D30F7010CB3CFC87C67FFD87A993FD9ECAEBAE", "25632B9EBFF7CE26BBA55B4EEDB2C40BCCB5AF7C87565620F1FC7D85D373F7BF"},
{"1", "E910DF10B880B8B5B28F1E2245E1B0C8539C14C78889777F6BFDDA8DF7699D3F", "E3466D9904F322E66044D3AA37DB86FA3B3B8C1B4B3DB4F678456F3C7F0AFE1B"},
{"1", "F5E2EEF4C0204BB40EC6C6A3237533AEA7A00BB1305F86EE2C54527FE5EF6D44", "540DDA8AB8672050D5C13326C56A3B3EB9256A6103168FB319FA31DB83472158"},
{"1", "0325C20B25EDF52757A1FB42343BE46323D4578B3BC0BB407F216FCC46DDD866", "D547DC660F0DEAF17BB6C166C52440B5D83421AD76314558503BD990405C4B53"},
{"1", "C76679AF82DBEB5C552F2269454952CDCC3237C765D579F161E8A2A1E4CD5E40", "2DB94E7D039B54F9A4809278CAEC34984E56599C6422EDB37C9A68FB23A9C86D"},
{"1", "62F1EA342EAD95B2D9264989B9045C02A6EA964D1D6AECC39BFE51F91A44D2A3", "A659D998FDDAA9901D7FF418E1CFB0DAFE0FD63DA87EB17CA6387FDAAB8A4EA9"},
{"1", "6DDAF3030142BAF676E8ECC2CC743E268B9AB055958AC1D667EB6F0A5C742550", "3140671157C14AD4866BD81AA112B851868DF1794B2F8FD2F8D9F5296108F202"},
{"1", "FFE86CCE3B9049D52F77F73ED9869235D8F5705EAACA6E56DA6989BC91169694", "61CEBDCDB31850663D35F9F422A250D6D54B25347A78F3AC596898EF29E9E545"},
{"1", "3F285449D247F3A0CB9DF1D22C30E99EF89AFD2811369E89EA0B5BCB72B4845F", "C4E1B9B8FECF6898784BE480195267C7AADCB55B6DC10ABDC7305334FE426C04"},
{"1", "4659836C9C345E53609C3A484F8AA15DCEC3A3DA165CC06E54C8CD1387779C60", "D67E2D10121DBAF1590B3CF7329F956BEA79142C4671E9C82BEC9A64FED624EE"},
{"1", "B87B10FBFE40F966D176725666B1664015E7961BC6363D86E11B66325E9FBD81", "FFF23CB34AB413107A39CCE2B57990F7129CCB862B40DD6070CE658850D2EEB9"},
{"1", "F8D6DB07A59CF04814F51F01035D22E60CE049B843F3CAE94CC32AC67E74135B", "786E750C19992B011AB3C67044D926D8D8541EE1F0E5708002B6617AD5E6CF37"},
{"1", "FCF50CC9FCEBCBB30EE0A189DCF5061C47A92AD050CB04BA03C3AF1B8BB23097", "BF72792349F2531D69F17A8FAF0DF241E32110B7ADDBC8761EC57ABE5FD008DC"},
{"1", "72371C7FBBBB879C5A20B28AA163C087FBCC5B095D7B6832F7B66343166B5F3F", "EE622EC1CC468768EEFA1203F3D3F455E67677F777D04BA0FD080E69F183589A"},
{"1", "1D3F591AE358AED2970894E80F798DA46D33749C999D0289B672CD31B8FF3D18", "9E5BB6ADE34861DC7FDCB4055C72EDF07B186CD50109D3327A7D414FC338FE21"},
{"1", "6F7ECDCAE66BBE1756BD0A946EE74EF6A46B1225EA3AA754F6EC667677EBD7C0", "E36897BC486C2743935B73F377CBE2FA1EB92007CEB94CA5D1FF42B0AF9A2F82"},
{"1", "1BDB8D1E05300E063548E55FB97D0935D7FFA39F3521005F063C0E51AB4AADAC", "9C499663437E2DF756E04D18BFF24ABA1FA1CF0F5A58974D804EB8AECC31017E"},
{"1", "F1CB7912D4C12D367315ABFD642671DFD87C6AA331305CCC1FA3A0BF36BFCFB1", "87BEC8EB872D56AA47844941E50B7B76FDBA3A6C9A6AAEF49207B05CD0E551E0"},
{"1", "1C051AE979E4D7CFDD41E98EA1B233CD962F2D6AB337723A51D052EE0B6B1847", "802353C5078B432D322EA81D304C5BB93D4EA0D98BA54E86AF02CE9F0F55FDEF"},
{"1", "A781B8FEA637AE4099D2CE97B6BFAC7B6FDF77505EF9AA85F3002144D21634D3", "E351536CADE4BE8A30D2030AAD28BE56EFD2F427A326E01FD34CE43AD64A2F51"},
{"1", "F78C7AE45328BF4C9D604C6A2DE76B076E875A2234039DE92B9E4A455F3692F6", "CD035DAAF1E752D251C9DD73707AA654189340B71EB78AEF2972F3593380846A"},
{"1", "B6ABE3AB0B0CC0E329136C3066F688A5EC930A55337F286B36924312D740360A", "8FCB59331F74FB14DCE054652D165F67B280C90A6E7173DC34013B1AC1D0CE0F"},
{"1", "B8DD8BC92FAEEC2E61A9059B03370365867267AA43BF08E4DF0F075BEE5BA283", "52BA1E8C49D26D286975F0930A9108D10587F595D1DC3DAB29C8D1C57E3B44EC"},
{"1", "ACB1109DEE8C6E45E5C27A7FDA55F92A4F0866C63AFC2F197F9D61B3089C2ED7", "20D585F9FB96498A922C76BF070D40F680005FD53D22B839F4072BD4B9113E2C"},
{"1", "64B36BD204171436A55B9BD4D92F67B271069A5A2950D2AE604B4FF6A81A6ABD", "31A439C344EA23E5E98F6CF995B5B000767B7DF1FBD565EA0A74B28285AC61D0"},
{"1", "483BD23BF08D726543C9F220B8DC3960F0E25386262F2A3FF16E843FFFC2C8DD", "2C1EADDEE3E5BEF57AF2D4D8DC4B8C925D424A777E054BCBF067FCDD00F3C7DC"},
{"1", "C50A20F4D1FC74BBC5517F7AAF9018F6FF22D100FE3649CB900F3C409C80F7CC", "68B776893489900C62B66B41BD83C9198BE9040D775B311AB64B2F657E435C2D"},
{"1", "573AFF93432FDEDDC30A69453A17F0D1ADFD501CB655681C66E6861D8F72DD90", "AD71890DEF560FEF5C8FAAA94EB3A68E755FFF7D39C48524BC2AF29160C3E4D9"},
{"1", "4F6F0A3EFB65150BCB9ABA00B2194BA8CB2193266AD80755FF36A6BB776CA054", "6D36519415FCED4F92688E3BB4BB77149A21E6181BD0DF52E5CE10A0F8A9702B"},
{"1", "3712F9F60C749876AF0D272CB92860BEEDF18AD199B365E3A7806AC2EC1FE96B", "00808F1AD3E612507FFE9D31207F3C51A95D37E57125C352F31D44986F656269"},
{"1", "663FD51D0B48BED4964F75C189E6C221E6219860BB324429D545899EDFBD4EF6", "6AAAB938D85BDB8A5BE684BB432E3CA9485701F63D3EA47F45835F449CA7C6FA"},
{"1", "0CF74B66CD1B8DE691C6AD85FABF7E9D7267BECC27E6DB975AF659231E2C8AAD", "4530F8B1A1E2264856454CAA8F0C054ECEA7491530679047F36E155359EBDA94"},
{"1", "79AF3F049AF2411124906127EEDC9C5006CC372302CAEB37EFAC4ED75F39C316", "DD834D02A6D5BD9FDF6EC4F1B6051993DB578051443B3E829005662310B4B403"},
{"1", "29D56CA5BB390D21EEA4C8CE809D2BE791114D58F6A92A5FDD13755815FB67F4", "0CA87EAEE97E4A2A4124672B3D1B593DF029AA38137514C3FAF9E87EF898D58D"},
{"1", "3A1A4769028AC34C1CD73EE7C626548C3CA44B527617D41F533E40B95548B211", "809D58FBD79C3ACB1787D4E562B4DD41A5D4A20CC1BD64B667AAC012A994CA93"},
{"1", "35707F3F9B63D7F835F78F6D181F8F9ABB7925D9629422D75F22265C8761F3DC", "78A465F9FD4469B61ED4F24D3A31296F25892D9DF8B3EE594341D23988D6E6D3"},
{"1", "636B69BF4BDF7A5AA10795FEA327308721DD62FD2BD9BC2D2CE9A9E1CF1A6DA2", "E4763FA3464DA92D3DE05402D9F6C301DBB55A7BAEDFC03BFD27A4DFBB4728AA"},
{"1", "2505C8D62C0AAE544177B7B829E3DC85463191044FD8A55ECEB884487D148B91", "AFFE3C3A17E2F83374000D57A3435D9604D63031434262A06284A59D1F09E2C6"},
{"1", "D90705A8CA9E376C1BE3D203D655F69E92FEE14FB2F8749C99B33EF6437B7047", "FBD06D5A7639BFC15A03AE7AE861D232034DC2C5CD26721612991EA39B272855"},
{"1", "E585B8EEF2707D80591AB4C83777104EF08DAA6E206A7F3987F09134060B70AA", "1CE2BDE1A8DBAF64C507465849643ABA9872029D7CD786E30AE586728AD76ED9"},
{"1", "0131AEFD0EFF5B3E6E75248B4DC7BE1C86F57EB464528BF81621F8AAC98F4E36", "56578B191D93DDEBF7C7D5B0B211EECAD6B9CCDD0DC4803F2B76C33088F2375A"},
{"1", "2BADD9BC2EE0F3A72287523D8A0EB34311F34D1809E13C6316C239DF30F0677A", "2E3C217209E024EE12321A077C2CA51FAFDECCB4CE570DC55B45C810FBF0B1BF"},
{"1", "1B8E49615324B3C097E4F28726BCA785D6E3521EE576420B3741490323583C72", "AFC187FA1FE02ED4ADA9D5E5AC44AADF07B29F3CF27E7EA14A30479705F56507"},
{"1", "9D4277D34C8C5F20F8DD016F71739F3BE79EF26AE4454FDE5F0C0CD2C02C5829", "D571292D278F372E316E45A86F98F75B7116F5BA83E92B4AC8C00DE8A676C012"},
{"1", "DBFD7AF082B262C65E7DA3FE3A6A828AE424D09F5BCB2A240C12869476E2144B", "0CE3B37421421B18960F5F444F6A923730DEB6A51EF96A9277170A518109F025"},
// Random y, successfully solve x = {(y^2 - b)^((modulus + 2)/9), x0 * k, x0 * k^2} where k = 3^((modulus - 1)/3)
{"1", "216C0B2BC9D311B1251DC7A239B17AD8CADF3D0B0DEFF78708140DF1809F6195", "82C7EAC1595438CB1CADA438264E2008EA6AB86CA250AE4C86A44A4DB822F950"},
{"1", "D1436690F849E4CEED190526E510ECCA191D542450BE9821A66B779F05554812", "29EC63C3AEAE6A3EBB50DAC9AA8ED24854D15A73257879A2ABE48D33D3E88E3D"},
{"1", "5A0BF4D9CF4675EEAB04674D4E0EB615C976AAD14FE1E6249C58254A69F9E4CE", "E9040657D3F91EAA53BC1080D4440B5D66EE981E16C11B17E8C91147EEC19A27"},
{"1", "A2133AE955207A82EC06C621D73A24777DFE3BBA41BCAEBA0B4BF51DFFA3D36F", "3F8D29A1142DE3147BD236C18A202494600080298BFCA1030CEE9CC317501A36"},
{"1", "8B7EABAB9D063E0C3CE7B18DE4264858E8A9B045D354618579C48E88784A8623", "598EF068EE5138AF914993B54E5BF770B4FA3BCDCDCB03C160D716349C37995D"},
{"1", "FB53A93DAC9687E043954951FA1302CE27EC8DB7C3A554D864D2EF2D4E808FD9", "C2775BB8F3DE3CE4F2654F23A1B6121881EFC84FAF2E21A9DB423AE5309FC11E"},
{"1", "73FA36EAD4579678AD853772223A21DD580B36E7CA2A3089C48BAEA8A6EC623E", "933B27962A7193882B9C9C24B039D8035858EA8F5DD23EE9AED8DFF2068F86AB"},
{"1", "69B09667FAE6330840003EB44748A5F1F9EE5F7AB17DD0643DF5232F9557CBC8", "E6443027F3E9DC28AECE4BAD1364DDC279AB54D010C41F05E687F6201829C782"},
{"1", "A9F6185D7C6F9BB2B0029D1C1371541A9147E7FACD619CE295DE745F2542F0BA", "41EB63C2D5D17E421399E470285ED9BB8367F8E88E3C783B1E722CE5E670D95B"},
{"1", "50D70EAE474963514711CB47151BCBAE6B5900EBDFAA9100A946AE651C3C4CA1", "4F7AD09C6923C5EF6BD582FEE1FF52B71FBCB18926A26851A6291C054E6EB31F"},
{"1", "7BF7213B7C61BBC800C9CC16B722DE1F583948100BEA892BDC33125A979B917E", "A15C9936D1A127F757461747CAFCBEFB55128E8B85CD13C240FD2A82DF0BD9CB"},
{"1", "8BC9E812D9DC3C8604CD2516BC85E013B96D06B38F8AE4766A8BEBEC76EA197D", "F5C44518316911B4FD5B783E3EBE447EB5157A185C2DD6704C25B84B410A283F"},
{"1", "8AA9615C6090991CD8FE60D6773680B5AF1BF55278324D636E7EDA33456403D2", "F26739A6369E04303C62C374A2939DB0A86B8C64D2A0D5694B1842A2CA3EE4B9"},
{"1", "F99D02EF820496E437A5EF363602BE8A42B534788B1AEF70FB9B9BA4255DF4D3", "92C49945DA4F79364922B62DE48709449BF68FA81FE01EAC66C2C31696646523"},
{"1", "B9D9070EEA9728A4C563F1BFAE06C7EE8E89768EB099EA2C4B02ABECC5031842", "F8F8D733946B6DF6A47A9C8337D4B43D8400B513A6DA05E78063330B57D6E9DE"},
{"1", "C71B408AE8A9D7EF7BD56EFEBD4F4C46E583CBBD9C24C4BD5D1943456A0B2FB1", "EC8FE81CBE10FED574EA116E25069A59AAC98D9F3BA06EFD18B25DE942AC675B"},
{"1", "53D6A984A866AE70FC665086CBDCBD267D8BBABBB651B09109A7FAA26733AC0B", "1FB48FB5E88F9A9EAD4D058E2ECE6EB70731713ACAF735809872EC931B4B2FE2"},
{"1", "19CFD7B45B958B18158020B7F749583D563C3D55B5CBC57A58A5030E8E93223C", "E477678A5F3FEE8243E7B745B2D00F073B1A5309105D2D02A1E20C5E75FC8EC1"},
{"1", "71D18C4F72613AB6C6E0735D9064505CB06C9059E3708DDF49CBE35743EF4A58", "74F3061B2815BC14EE08472A3E09BE78FAD1F09CDF683B9985CAE52EA0690B99"},
{"1", "1C2C36541903DE36FB8D106324075AE7B4717014E8BC0AF770DAD1EA5FE26AAC", "B2B5616B86360CF41E2C15E75EC7A5DA73DA80B9321174CBFE40A7C90F859447"},
{"1", "FD8F682BC286100DDF858EE4F9F16837BAB6FF5EE011444024D620DC6A17363B", "D83FDF18977026F79CC183388FC5039ABFCC5E249D75A0DC91DB0B1A527E6E71"},
{"1", "749CDA4E445E88C296FFEA844C45EED0BCD74B61ADA0E40EF1AD5487E4B525A3", "27A80DC87F3B9C23FCBA835BA5A8DB07906AFC343EDB3AEE73FF284C1319D5BE"},
{"1", "3BD1460D551A0EFAC1F30EC2DE0ECE2DBE0F88F8505D84B3639B5E074BF2CF5A", "EAA399BF1F0F111F6FE7E372E4ACBEF2FB9AC0B9551CF3B778C0F0276F27EF18"},
{"1", "D964DA929BF46DDC5552585B4535648BDF9E5488D90CEA3A760D7C68710EC84F", "0F7D1BBD8CF7571B7ED79DCE1118B493556BF523CBC41771A39403896BBAECDC"},
{"1", "94818DFA81A617E79A167CFA26A7301C45F77D6811B64AEBFCFA10F3589319EF", "9170504AC1107C545E04E99274B1698E136640A6C34BE18A6AA70DF105D6A383"},
{"1", "099FD26FDBA5B5A79A862694B8700D8D480C8E80C8309843F3B217276A45A512", "CE3B8AB2188A77ED2C33825E6E1FF73EFFD7F35ED81E5C282C494DA2BED75D9B"},
{"1", "68840B635DB0CFAA11626516DEF0A30A533EA76820C1DB829B38195A06675AE5", "586D2EBD411C5ECBAF9B5240338FF5DEF9B8D1A8CE0123CBDAA9A44152C7594C"},
{"1", "85F3CDA7889AF7CE1866E75CCD0B3E52A4A3FDBC7B2971FA44123A2B43F85F60", "E4852CE27B8314568D1A26B4C9F38461FFF3AF65422654476A5B740B4A1AF5C4"},
{"1", "70E4FB0BC68F8F5F71468944E225713D49776B4ED5DA423A15AE3BDC21218404", "7981299D10C87CD5A6AABCF317701C9259D72E7EBEACE12670E4F383EDA70207"},
{"1", "B1A358B0635CC79151FAF889D396F2711679755FE9E8F2DDF1658AEFDEB33327", "F352E1435C63F606F1E4EC838B706888FDF14FCDA77109F2A4E14B586C9FE2A0"},
{"1", "2475D1BD2E4DA3FB8B5B49813A7B3A2519130D168013A82B2C3CBD6DD2473282", "64286CAE73734DF8ADC06205C648A8B5368123426309A47B2F21EDB15E289475"},
{"1", "8323DAC5C8278A7AD9B0D61541ADBB20D58B26AC6AE8F7B0D2EB4210F7F41623", "3A9C9FBC46D82DE1777FC10C457691289DEC16CB8AA59F155F04B9BAD1268690"},
{"1", "51A41A2887C575DB95E91C36AFD83795A3F9EFBFE5E38825AF9003565B97FBB8", "2E97536517D2EFF9349F96B791008C9E3D343795E076BBA6B322E0B4BCD46639"},
{"1", "933B2505FB4FEA2580079121851F208B9AD9D7977C60AA5FFB046BDD60DF9381", "368437169D0556CAC71FBA1E19F1C07E0CAA5BBFEF04DFBF46F339A1CEE72296"},
{"1", "784677EF6F72443C13A1FE55BDD2C5C997DF69C04CC9D0B7F4E8B721476C54A8", "E3444F62B66E00632513334B0F0BE530C0C41AFD1D85B5C26C488A640618DF9E"},
{"1", "242D1008EDFD623547251EB1F24A8E4EC559F6B1626FD2918141604C94BC4526", "5ED6147ED070874D9CBA2352A1A2E2EDE724B0D45A303CD224E0DE45B46776F9"},
{"1", "7EFA4E8E4C62EAF51A31E3B64AFB5C2A64594B7C14CEE2CF783C1F669145BDE5", "A0CA43AD63CD6D33AE6767A86D6C36A1AD329885DD9A04EF596835A7F10D7AFE"},
{"1", "F98736451F6E9D1AB8837C9FC6F8DBBC99B41B0BE27022BE08DE79C9D9209296", "7ED59163E1FB4AC3CCDFFED45BBC74EBD3BFAAAE8D15A9AD5D787A5C3D45A6F3"},
{"1", "C3AEACB4EEECEE0556C91FB2A6D42C6EF7827C63D7373E9421023E6905D3F03C", "3D0509995B00BDA5A8879558BCAB6A0A9C8F85D08D9BFE02913FE28B53E65DE7"},
{"1", "AA82E6336F087FB227C2C1F9B452AA46A9FA1A8988C5AF6A4D9538E6A40D185E", "A63964F3FE441A4F0C7CD6036026E26FD176A8C88ECFCF8798BA6396F7EBDB42"},
{"1", "0B69635711825AB5E0D81E729026D52F637CEA376B84CA24EA1D45372314C1F2", "3E944EA2B4EE24BE2497A110A5E0DD468EE8FF80A3885839B73AB7DF455CB42E"},
{"1", "76327A332829B07BA8B783A8D51B35E077D782ED0DED719CF8BF157D5D6E4A8A", "CDCB3341510C16EBFA5E6AACFB055C2451B1FCDB52D935807647E60D5A17A335"},
{"1", "D11B7CF958DA377AEE102F7CC04AD9E63F237C79646C320111FC5932432FE0B9", "5DD167C669055E8A825CE5CAD840E47618070EC96BD920B657CEA4122741931E"},
{"1", "22CF3E1251EF6D8091D28665B8267A09A622A6C2DD31A8B6400D71ABE2F5D21D", "3BC06F65CFC21DFB43561E9F726C616133D5BA8AA68938953F643C16A98F5B1A"},
{"1", "943319363C901A8B3589072FC9E4FFDD61289421E6BA1B90F431A1BD07BEF070", "8728218EC4D2210CE44DEE873ADA9D3DFCBF93F205FCCC718A09A81CC4EBC624"},
{"1", "5828C87EEBD6CD656745FB7FBE402FB1CD991AE20283D02EE7DE1C30698A6B31", "F278C4B40673FF7EC54B341BABCDE23760CBF0813EAE7F36A92B570608D673AD"},
{"1", "7163748B032A100971DD7ED8B49C97B7B34436AA0164BB97C926F021C1FC8201", "EFEE0679F7B84259B5D03D5713DD188D147E25397A9FB9FF0E75FAB2BA27A954"},
{"1", "9B5116992CA8FBB84F7982F38D78A96765559F8AD0053E69226AD271F2A53CFC", "99B70D1F337A812F5A785BB4AD0C53AA81D3171170269FC0913B1AFB9F4A846D"},
{"1", "551DDBC2509A6E40410CFA3996A5390D4E3BFAE18325AA07BD618EEA461A0732", "53442046AD3033A7DB375D4867AE01ABBBCC845AC571524F2C73FFDA2056E3CD"},
{"1", "245EDA52D3918E0359433C83642862155ADFF6E37D286109127F32DB7285A95E", "4CD34878479270FA74C3E12A80FCC5BFAF27E8E3D34CDC6E00519B12C24E7F0B"},
{"1", "B925D118AB09FE0A11DDE11147F2317C58293898F1FCA1899AB10FCB6EC03AED", "7D096E5A734B1D9B324E49F6206C48E5EC5B75A9FEB2CD1BE4AE2D6511B93600"},
{"1", "97C16E98C621689CA1806AF7C6F86C6CDB985B70E25189172DD0E2C2F2D16D59", "965AAD9C04B8BB47B3C21C26B76E6AC395E035A403BA49E71DADE23DC22FB0C6"},
{"1", "FE989A2AEFF9BF1A5E7AB17CA3B2902771130EBA3A69BD1DF55DEB22D648FCA3", "2D50F83D59D88EBA646CFBA298618AAE888B24D956ABC119A159107C37CB183D"},
{"1", "319EEAA95C3A55D5FD27E25313F6702FF5313FF9AB707A1CEB2672DD445607BB", "7E11339C9D18AAA66D76579F90DAD47FD9725BAD825852CA56A105D09C036150"},
{"1", "F4B1722088D43A05F5FDCCF06C012717A2B1718F69B22EC960481A5E796BDE46", "A6CE465135D209731E5881AA7C38FEF87512B3D62B371C4BCDD0496984C81A28"},
{"1", "F255D2FA83FE8F7B3A9D4934A0449FEDDCA095859269A4F3C0567DA2FBD54585", "7E53DEA02DE6482D8ABED951DF1684FCB7280A701326670B35F646380F0C3C2B"},
{"1", "5ECE8045812F0472484A57DF988A1E8511C78230DA0F03641BE30423DE60674C", "04C5DEB88F5451255839CBB8B4CB7111DC348463E384386265D9077D91295553"},
{"1", "CD9D15EF5C5A915B962FE9CE748EA194A5D79C11D6BE276C559BDE8E8A61D7BD", "AD5B4451D36ADA85B8798337EB50CFBEB10BB73225D8E944AA03A91A8AC59477"},
{"1", "2379CB5F302D9ADC0A8D698AB550178CF223FD365568EB5246C1DFE0310A488F", "015E1BFBC9965ED731AE197BAD02DCEC1678B8676B0061E9B80372712ED5BBCC"},
{"1", "969CDF8B547BDBB48BD722B88911E2596B2647CBE49441DDC13FC1C5FB315979", "37EAADF90C936CFF0FA8C30823A5F294E257A92B51E1E89641759B2253ECCF83"},
{"1", "6AA285C988E333C59DC8226E67F9793012B3A065523C5A309125738BF81D2C10", "4DC7489EE406619677B5DCC46E810EAD90FF7BFAF97F08C3E818084FFAA2DEA4"},
{"1", "CFD3180F919943C105576A3A973D7086D62FD0441890B4A863963E9C58CCC446", "3D7D1D8C90F5D81D4D782AF7FB35CC0704BA32244B807C15EE32D7EE541102B6"},
{"1", "6413CECB0ADB671E2B3F47AE0A36177A61122E9D38247F5268E83593D1E3C77F", "3ABB9FBAC989C5E62192180D57E1A9CF0DDC1E5A9F57F91F355DBD4ACCECABC4"},
{"1", "A86D426FD63B8E7869AF1DDEA3A2A094EAF20AAF1AEA9B1B83B0A18E724D57BC", "59CA3407F69AB06CB340EF70BC24C997639264709E95FCF54C40EF00697C0A91"},
// Hand-crafted non-points
{"0", "0000000000000000000000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000000000000000000000"},
{"0", "0000000000000000000000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000000000000000000001"},
{"0", "0000000000000000000000000000000000000000000000000000000000000001", "0000000000000000000000000000000000000000000000000000000000000000"},
{"0", "0000000000000000000000000000000000000000000000000000000000000001", "0000000000000000000000000000000000000000000000000000000000000001"},
{"0", "0000000000000000000000000000000000000000000000000000000000000000", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2E"},
{"0", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2E", "0000000000000000000000000000000000000000000000000000000000000000"},
{"0", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2E", "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2E"},
// Randomly generated non-points
{"0", "01B99457023DCC54F6BDCF41EFC3D26CBF08D728F2C3852AE0F26EB180C95307", "13CDC5C9B68AA83347BD512C600120D295B762C7D829F95E0D910F48A16893BB"},
{"0", "0B611FF3796B16F9D474EDAFF30FCF0C04C26BF6F4151A6611ED2F8215611A5A", "CE0CD9279B7F909C8EE64E4C654105C5457D125ABCFA78631352E6AC253FE10D"},
{"0", "314FED93E643C1586C7BF3B52A2786402E7A91E7D3B02054DD1F07DA4F61BFA1", "838360450D481082E2C4560D3EFAF659E3B7FEC9315C8E4550246E3FBD4A561F"},
{"0", "3918FC25EFB44EF24FE24351974674FE4D8431AEBBE34C38254A505C6AE093B2", "C0D66270971D69E54990FB9127C531F032385198F47DC77E9167A9154E9FAFE6"},
{"0", "44F52919C321BCD639EDFDA43F7BA16CC60F1170F1B71B4C0955628D5D8AAD32", "EAA4F332698E62E7A8F03C2668418297533685F0DC965C4FA335513F2E1D4FB0"},
{"0", "4B17CC0EF863154F463E09C9F31531C99286C2CE8F77C7BFF5719D8917AB06AA", "72566847B15B36F01A4590F7F830F78BDB8C8DF9DECABF7682E55E000F46F68C"},
{"0", "52DED27E487D6A22E36073230C4F36CD5662E7224FBC149A25F6E39C2C740F64", "47AB8BD38FD28FD4D10EF4E4BC5EE34D5E75BEE890EB92096D808D25AD4F83C8"},
{"0", "601507D8D340A5B7E2AD2C1E72CC51C183533F8DAD6B7B053581D4BB528419DC", "CCDE603FDD229ADE8C2265D48D8C57CF703C56F03CFCC1D5A81F5445352AEE15"},
{"0", "64880AF0609F5B1B84BB2833075690E71733C6D90DFD4463D6342B8D47AD9889", "F5CB7ECED6872E7C426643FEEE68448BEE6DB4DB369B1D2517A05A669B0C1DD2"},
{"0", "65A1A26B96449DB45307E8B684C2C5AEC90B65795ED4D0DF2D0D9CC575587460", "9225BC6064E961F67A4C2024017318C687C2F31A5FF85826DD465C42F1654C7C"},
{"0", "7CD41FBB9B674022967E8F469D58BBAF1CC548C514D4E3588D7C66D6648451CD", "CE0AAC2CD1742BD92F197D272F45E572C44E8E31A9275F907182FD957CC07D60"},
{"0", "7E3F6069F79A51039857CE7F2A9A4A077781910E8B8490C5C23CCD9A5A5464CF", "6FED82855D64F9A56AC20DBAF63AE9D220A480DD13899DE75069DD985680E6C5"},
{"0", "940B2F3997D9930C28F1D4EA48FD3450224D67668A1C05339B00602182670A93", "2269CB84940E92669A8B6FB32265F259CD5447F906536F6EA19D3A9C99CAABB5"},
{"0", "96DED0959A9ADC375ECC672CC2EF892EFC36D37400E29FEA2495D6A0C68A0469", "D6E23B2E421DAAF9E16849CD410DDBE47F4744BA710714589AB4CEBDF5AAA236"},
{"0", "9A5065C0A0EE787CA1802FAA71B37DA27793F3AEEE1856E41454FE5826440E57", "E89D19467F61FF7DDBFC91CEEA790D11A633FCF9DEA5FEA8A5BA8E48FA24D723"},
{"0", "9C2502249662DB22D39B29B5E644943ACAA51AA2F0E0A96F6A5299A58C4033F7", "DD9C1C8D567351E45A7750CA0758C2EE37337BDBCA3EBBC947AE56B6C4916F67"},
{"0", "A556DC08D00DF71A1CE6368532CA3237622BABFB5D70134363035F9528371791", "438A3C5A588A5AFD23EAAA35E92349E825475FF3549FA827F53BF879A21C762E"},
{"0", "AAA610BF5A8998F5112B7BF9D77F2E5F5A6E0DD054EEA56CAB13E0CF9729F006", "1D3D3BFA99EDB555E7262D84C489A45215A8CE5447C883D89082A29425454EE4"},
{"0", "BF13F298989B6C040D15090DCA5CFBD22F22A682E20A07F5A4836EEC4BBE16E2", "EF5A8EB26944CADF085D83443F70D57FA97C90FA131C5C47E0ECCC9AD6A7522D"},
{"0", "C09E7C70562098E65AAD6FA00A3043D9AE0C62A1FDFF5069C470492BEC90A91E", "B38C3B14EF2E70AA71DFAEE17C3EE03E9906ADC9A8BC24FF09F535CDE6FCAFDF"},
{"0", "C1A913D1942654A2F32A989C68799D2DF52C017B525E82823C0129DEEFF659DE", "4FFA63608987F857EE17A8B55DFB282F5F19C2EBAFBCC2F3D0E3EF91C81A9D66"},
{"0", "C2A9E2D327B0BB377EFEDFC04B31470354C8C140530CC3B007942BB6993C93DC", "DD00BAECA9E79E46C404F71FB0625ABB0FBBBAAB3C83628E01A681CA1D16F5C3"},
{"0", "C4054C7B4368D6118059A06F019258E9A867CC815F4939585A581FFCB9AD505F", "5EA51B348D2E9760ABDA6555184908CE3578AB498899B449DC1F37B3C26E3603"},
{"0", "C85FDCDBC9418A4F6EAE8494AA3D2CC1EE24FE379E881A1663EDDBF3173A58EC", "9840F12E2BBFDF1EEAAD22BD10E96A42BB5B5721110BC601DBC404309DA7384A"},
{"0", "C8A4E959F70359456CCD41C90EFEA1D24CB7ADDC66D237F2CF9ABBAC6817F4A9", "08B742C24B333D3B4318044169FE08A282AC2C636AB275EDCA0E0672DE069DAF"},
{"0", "CE6C7FC7E60F5C3854013A5720F0427D22010CD2821FBBB02AF5326C1D688DCE", "E7530558B61EC95A5D2C386F64CD6D2F43D20BB3A59CF72533DC5F7CE3B22084"},
{"0", "D26F0ECBF74E896A9594F5217C8E52BEE514998B4CD02575B9020644D9D9B80E", "27325298B5CA448F934F03583ADE2D8A423C6CD08D6ED168A7E236A9C0D64618"},
{"0", "DCE4F91C72E71981E195FFB8A5DC7BBEC78D3D79B26752378872CA9A79EAB99A", "9D7770ADB0F5C1856FFC9D829C1BC0E530A6933C8DEFAD1ADDC074B9173FF387"},
{"0", "E276A17353B0F2945523276C8D0F1EFF9107E11C1D64D3435F843A54E81197FB", "B2063CA915BE04199958EDD321C5A0A575673C1A37CCEE0AECBBBA9FA77933AB"},
{"0", "FAA7F31272799FFEDDBFDF37FD2C64429215E6CAFDF6AA33F6FAAB34A19AA6F8", "D9D9416F7FDFDB96FD0EC9DC6C22B7EACD3E9143F8659238DDFE8459D6263D82"},
// Perturbed random multiples of the base point
{"0", "354FFFCBAC316E99B956FBA9E3AFD74DD0F402BBC37D1124CDE2AAC158D02DEC", "96155CE5DE35729AE28C1F859A8474BC1A12F2995A0787A21D6868F88200CA9B"},
{"0", "DD1BC9CCB5271C2939C77BF65C4EF3A9D2040E82836DD138FB934DFF7F92AB68", "355B0AE5C87C242934F48A8EC813131CE8375FBBD194078C48F73B1AE36B4D1A"},
{"0", "F464EAF9698F7DE0C7BB88A6AF899C9EEBDF19D2BE2EFC86DD98FF0AB72FDC8C", "2E4466C6EDC87FF948913EB6195987A6A238043C8460186BB58186C756EFFF85"},
{"0", "54D32842B1A96205E3B2D36427F80B0F6B4F0BD81D1F948F27DCA76123D33883", "B619D54820709EE416048309D5E8DCE7E458A3C592937E61190B3718B013D1A1"},
{"0", "FCA7043666610F149117C84EE1ED051C8D29CC2A77E924FEDD740076E8576BF1", "B5D5F03F7E3507DD57876ABED714798491BEFAAD1B81C7645921F5052226014F"},
{"0", "8D5D6075AD09948F57A1809D1AA2790AB68AFED8F4400AC405DE47F4667C078A", "8185E69E88C6C27D332B260302F6272354BFE2474DBEBEC1DD75FD01557F6137"},
{"0", "A154229FE6A296D419A150D0675384FCA702B96F02B6805264906F25116AC7FD", "81FA01913BA1DAD0F4F47210342B7742E6C0210EE735F8727A4837ABEAF6DD3E"},
{"0", "6E840A33279C950DA5F58F28A7A6716030994E6879F02CE108A3D41CC8E024EA", "402AA2986EEE8F06631D5F3D5B83329A7A5AD06195EB6A8F0A31A4EFFB199048"},
{"0", "2BBA764FAE35BBC7411348C4E92CB50EA09E22693D05073300AE63085F9EFB6C", "791B4FA8A583F5D064170B6B0F0C43C5469CBE5FB9DED7C5E65C8AB8F52C8239"},
{"0", "02E559E49832C9C76E3DFEEE3997333C085D799D05F1C6CADD730701AC2A5196", "D8ACAFCDF348BA79A3B3447C0D5507780A7813CBD0E91D7E26B4FC80F1EE9F59"},
{"0", "3653F2AF46CFC62001AD4F603CCDFF132F2C64F348EBB468B775BB2FB67A5D13", "B368EE7841FBBDF072B2F5F05903C03915423101249CF0B4F57A3D4A6448A729"},
{"0", "79F6EBADB77DF3F1A56513F51A626972671DE3DBB537CD7E650B92FF19545DA8", "6B75A65EA88ECE563AF996B52E7B7348B40EFA38D60B1BAE9FF0047C761C0066"},
{"0", "10CDE5E2D00EF3B4010F3DFEFD32F1CC1B5F2E48A826AACFC06A3BEBB9838679", "14A28D8C3FC3C7952C9A951B0D680A90ADAE64ECBB69ABEA681291C5E15945BC"},
{"0", "BCA32BC4B12BDE02A12574C96B594ED479D78DBE0E7D41E89A59DA1489FEFB89", "46EE22EEBB535BE54952C9D79AF5C5260C5A3DDD432F8DA08F5E6750C8E073DA"},
{"0", "93C8F8FDCA02F38D031A2FE80C5AC215D8A8DD49998E47A475958CA7028B9CD6", "7074761BFC3B52392ADBE35477D224C04A3C211EA8ED672106E43ED792AF6742"},
{"0", "658CC7AB3B89CC74AB2B923788ADE01F80E62927572744085722F0DAA93966C1", "B6F5D4EE6DC6E7F1AA177FE549B91C8AA05AAC8CFDB45EBAF254B46652084BFC"},
{"0", "1747BC12502FFAE54BF79EB4AA4C4C185BAFA604CBBB7F748FF5B59EA060E985", "C766A19D729EE794871EEB5C99589063395AD74841CED093A313B593613D2E76"},
{"0", "8D2FB42F4919DD809ED43F8021A330BCBB640D1FAAABB6CF018C7BC53A21D711", "ACC8CCAA2D5E3F80AA25354CABAAEA98D4240D11D39ECFD744205B294C4EDA20"},
{"0", "99680F5AED5D1A08B71A3C0370A8239143FC7F88B0B8CB3B5CEF65418ACBB4A5", "8C0800B490B1F991CDC4D7A4E25BE3F06AE4D7505FE23241C989CB9641AA80DA"},
{"0", "A2089CE613CEB1B63D36D02FF83A2980A2FB1E35C67F8E867511E2CCBEC18EC1", "D34FFBF2D1A4E9D6B352489C30C8E67CE3D4A7251215BB688309B2E962043868"},
{"0", "5C9248985893E74CF976CAEA03BF54CA17EA1137F800EC60F30834AF7AC88ECA", "FC775AFB13435FF61F5CF4C0C7D017868D1538A2DB703906D2C7AD58E7476824"},
{"0", "921635E4E374C3646BB94306E393CB210C54E456744C5E277736958E9883C6AA", "051622A92E4C98FFD4253EA32E4DBAEC3B37473F039687D4CB1812B346457A83"},
{"0", "B5264FF37BAD2B4EF3F15889E04AD1F0A09B9FB78EDF6576E4903341EDD14884", "748B00C4E4ABB7EC6FD3C2E277178C25CAECB4F16811C64D6E446A8DE2B64EFD"},
{"0", "D2DB96EC255529FE0D2047D30424DAEB773D5BE251A3E9D89E4A909344A01464", "6A65025319CB43C2832B3379B39EBA127DA75C732F8D6239A5D633573324E866"},
{"0", "7C1B2DBE4D340187DC5BB3813B070ABF8CE7EB1E32C281273F567DC19DBC356E", "AF65D1B5A62D35AF62C20DD2A82FED3ABF058262F0BE494FADF77600B12C983B"},
{"0", "5A449E43740B050F903F6FBAA79C3AACD07BE9F03B18A7FE28327E8C8B02D35B", "3205304699F6507A812AB1166AFBA67C9C0D45E5CF26CF0A17E44C398E212C06"},
{"0", "8F8336F3C2835FC40EED3459C16E53503113C96A799E89F3F790259DABBACD1D", "95FFADC66705FCBF47BC4B13F650DFEDAB7460518FF9712ED92AEC803653B336"},
{"0", "406CD86775E2FB81253CDD2C54FD139F7CD57272AAE576869EC8C4C8ECB632F4", "3DF8F07DE671BC44D5CD51422297E568F9C4F5F47E799702E13AC3E984D2BB3B"},
{"0", "30F94C767C7F444AB5D48F69B05D71C891A023F907C90DE63247C067E230AA10", "D21329977944A3F20D20A9EBEC688C9A729260900F3A34C6FC411FAF6DDD4340"},
{"0", "04F6D0720AB0B2C11B48DED928FA1861B4971D5E55A524080B0A299D65F171CC", "1D8777DE5FDCB78061BFCC12BD54C17091FFE44B221AFC38E420A03218D15561"},
{"0", "622B6E590734D441331318E7A8FEFBE36B5301A96359A6182DF24E56C19A417F", "F4E1E3040E45C51EB88E1782AD9E83A14C0B2E1090091900D0ADC080CAAF3007"},
{"0", "54EF9A68094BCC1FB74645531004395C396E0AFCAC001A9CEDA6809B7C8EEEEF", "62FFA8FC5BA78704E45471603194BD2CA75143E3E59A499B86BABD767251911F"},
{"0", "F02E69863D70560ED8376D0CD8C9754EF4E907E4D87CF3EA824C0D7854FDBC15", "192D9001D0A965D02DB5816D2A769CE0BAACEE1F3C8987CBE987504698978960"},
{"0", "B7A50153A982DECA6828D46B025EED89A7A27EB2899AA4A11DDB7DECC02EFD80", "861DCC1ECFDFAD3259A76B550D5803D7D9C1644C4B42E2B401AE86F707E0C4A8"},
{"0", "D9CD0358028C1681647E45F2F760F95F34B97388E3B4212740E41A03BE3480AE", "76D68D28231321989A5A408AABF46EE929AC3D990E8B999200F686C3B881BE92"},
{"0", "83499D943DFC910CF1E33096A27B7C6532647CB9BE54B8BC68678CA55E9B9C41", "D559D9D0FEF5944BA5502379DBA80FE8186FF6A154A6BCE272CBF64EA270CFAF"},
{"0", "36A3593758C69C456DED8CBB7A9F378FA5A7022B855B3BF6921E2E02DD763B09", "84A05E22B02C94ED59E7223A1EB51F6952EFC73235F845FC0BA96C9453C8F6A5"},
{"0", "35639640F4BA188B77AF3D251C4B618F2A365CB421622C258AC8007491536081", "0DBA60C5976BBB856CA5D2B2008309FEA6E11AE8565811CC98915EDFE1E67A71"},
{"0", "36463DEA2DC7C0997DC82887AA3C09ACEAC39E3AA0A79852DE7A7FE31A2281C4", "441A1A50765AC6181A4E4A3812EBCEB4B1E20AF959B509D4BF9607CC86ABBF1C"},
{"0", "BFB3FE141FD8AFE206848D8CF68E06DB43B42A6D416755C9C6998C1C11B463D1", "4AFA76BB63AB02E7E12595F688A4ACE773C4FB6A390DF14D9C31332096CFBA07"},
{"0", "D4572102D84A2B85803CDEAE88A82ECAAB8E76B338B441F76B9864B55185877F", "2A500C942D26ABEA60410A51651EBD2BC3818725ADF75BA923961323DCBF8F3D"},
{"0", "5956C66109B2A6201630A81F9114076239580EDAF524F1F5831DCC40D21660A7", "D289B7EABD39BE3A99575F22D13ACB4BE210F945B4177FFEDCDD3A86858E7778"},
{"0", "B51514855DCA3077773DEC2276D79A33BB15C7C6A0C2725165A7EF550B79A25A", "F7C7AEE4B553F50828CA1BDD4D3B3812B64646557E38D2F9E9C232AE3DE508F3"},
{"0", "1DB4449D87C95F8E21BD8B684460E14A9556E94617EB42574DEC500DFAC59245", "0A5A201028739A17D37E82182F1D6D9662ED5CC531637BE6E1758E21D86703CD"},
{"0", "8A33F6B8EB1556CB57FC7AC0C53DCCF43A26F5DBF29C4A196708802C89E4E618", "CB4E5891FD375242CC44FC966FA05C7B41740E21C81C922552EB3CD85C201082"},
{"0", "4A3E86B9B53526DC87997A8BE8FF72E4D5B16644C86928CE54F97CA3EF494B4F", "D24D4EE06D3496780D04CD44B14B010E81644307E943FCBC7923D0288AA1CA93"},
{"0", "D23C12A97A725495B350DE0E5B3E7F906AB406BB017BD483AC3DE37A86D14B8A", "D3D7FA50ACB9BA2625098362192E98F670EB26EEB121BE01E0C0A2AB73E1351C"},
{"0", "AE9365CE803314D86EADBD7FF5817C861DF21FF04802D5BB73AE0E01DF74738D", "99C860B56BC6B945BF48D40BC63A576081E6E1D01912BC26276F30D740E32513"},
{"0", "72FD8D392788DE36681E0D5F0BF3DAF82D957C21971E8770E8614538A4C2B5A2", "A3EEACC1D0B3A99CA1E8AD239E69D1F5F234FD8EA93C3E262683E16309003AAA"},
{"0", "1277E64E74AB9F5A6FCE6E6525252DAF96F7F263935B939913B2D312D3EDFB01", "5E3767E1EA0AC53645EFD865A116651A00186CD5565676950955B8F3455CDA69"},
{"0", "C1C9406F72C2B610EC139F8A8F5F4E3D70ACBA4AA856CD8EC6AA28CE29E5B37B", "A4878FEDE0795590D8251FCBAF6AEDD3FD4ECDF29B77501CBAF8FAEF615F3830"},
{"0", "7D9463F8428E811345EF5A2D66A2362AFE84E85E6EFAA697BBFC1F6C8757F23E", "B8E9B2E082855C0C42B9D07851D5F7CFAE51F20B97AD370A2F05BBD49939047B"},
{"0", "1BD45ACC1641E64785950D293F828A7A011DBEF33D688AFD7F8552D6CB9FB340", "0FF4EE7745B871E47A3A88E858E22D3B39229258BD64894024B8CB8ECACF1CAC"},
{"0", "390CE0BC1098B347210164543419BC902D44D06153052CDB92393BE66D5A98FE", "972B7087DBAB40E5803DD13DB2BBE577261EB27DA887C7A7CCAAEE57FB715CC2"},
{"0", "9CE71F82391FB6EE4E2ADC18989256A1F10641FDD7301286FC0B386CC616B2F5", "A1C923D30BAE10AA4E47307382EC141BBBCDAFC5862C7175D5990A7B201C0354"},
{"0", "19424A8ABC2153EC828BDCCA04B62686D3A596D5A63F27771CE237037DF5FC40", "3A1DED7169CBB0E24DADA27698EC7DCB65BBF262C3DF254B0EEC357C3E7B583B"},
{"0", "26DDE59893E2742ECE10C389009E7B4B7CC5FF4464DC7ED5B6090A00F6BF7341", "071C79EDD4DFB43394202E7CE93D59158FCA12E958DC3BE0EEF6E8999C02B2F1"},
{"0", "B6DC57E3E0EB5D0C569C23158D78EEBE65C1FAEEC7DE8A3393094FD244263385", "96C27E79EDFF2395DF7C5BDCBE5C17B999C2774E7A965D237DF82660510DEE52"},
{"0", "72FA40842BC51F2D8157F41CFFED3B5AD0D5819E25C301CC3D0DB5BEC475F82E", "D188F083640B2C2359663A0409FA697B7D483853DD4A005364D9E53D7FEC1EC8"},
{"0", "8E12D8550B2B1BC9B7723AB82C6853C4FD84E56821910384AC44C88129ABCBAD", "7205794CBAE650F60E90BFDF70D153BF83F3CB5F3871141C9F68B851DFFAF0DD"},
{"0", "1D52ECC862B52652CB2AC8DDC87679BAC612E64AC1EF5504C3E5BBCFAB516707", "AD26A9AC52382F0C437311F7C8ACBC95B99FF8D20B12D416D3B45B641E54375F"},
{"0", "DEF0572197C6B8825840D115F5C195FF03D12AF3B0C6FAEFC658A444B7A0B5E2", "C5827F8393E3C272C1808904970551F0D1767FD15CB9F5774DE33069007149C6"},
{"0", "76BB8816AA780F0BF545411CAFBAE69B3DF62D1EBA26EA6E70888EE6A8B47452", "053EA5A230724D1365B7050AAB37845BEAC615C18C24E17A447DC8B63C734C9E"},
{"0", "5828913B67CC5AA3252ABA98D649B771E6B2C6E9B211B134F4D2DD12069B0F9F", "8B4F9780210B4E290658A303018C7E9E5BDE653265569C18D31C1480F01627C6"},
{"0", "E9779485441CBE07C3ECDB6D13440EABCFFAE0EF5E0D52DF45355F8985F2D302", "76B6C5B9202A5906719C74FE18CD891698A726809C52783D67CA3714739B74CE"},
{"0", "87BEDDB8AD61040968A7939B3ADE5FF6EBD06D5A498FAC27D74D30ADA2F1CC87", "BAC8526279A8C1A5F9D95BC2333781B9B95A3D184CC702B514E81F6554AEC112"},
{"0", "ADD881C6E33D562BC6C8EC834817CB05B5B8B8ACA5543ADB65D9FB1F815C6E03", "252162DCA0E481D8713C78A2ECC5D71461DE4B1EA9CFF413ED8071A281959858"},
{"0", "EB6FBE327D9E36418BC58234421CE15EBC6A82B003ADD13D307C9F2AB6ABFF9C", "AA8388FD7B781ED2E68D1DD95A9067238539314461807889193AC329C8B14DFC"},
{"0", "293165A5E6500563ECAA7FC25A39B5351A87BFC089F326967179C4E0859BFA81", "A1D44E058268F1FC2FA12E806ABB1904D217CE4F47B54BA1048EA6B708FA3D20"},
{"0", "6D3367BCF7C5892A6D7406BB740EFFAB1ED2961ABDD1C501C19813B117D5AE00", "2651F1436206A0C68860EC12FB06C4E175BEFAC6566576C84F75461CFE8FBEA2"},
{"0", "7A56B2E8EFBA8B80D609CB1EA2D21488BB37D5DDD732F809E7E835D58E01D296", "9CE7BB70F0C7BCE8A79B02BD39165EBBBF0A1BBAAE7A2C2454C2834F486FEA96"},
{"0", "E5042DC20B5F6F7B1DC7BA09A4641C1D44E3D495CDA5FCB1607EE1CDC89C6A29", "F54AED1FFF7EC6DE2A1F0E9951F60B73D559EE397AF01EB9C5F8E9F78A7D4978"},
{"0", "A5B81CB59ACF5E35CA5BFA558792065D2D33ACE4475A7E228A993EBE5A7BAB59", "520622ACC1BB9626E713EA578E7DFCA9F92737D924A841A50AF069EE97A5EA3E"},
{"0", "B8BEEA911B4A547ACC661FD2F823182328FD258B5463E1BA75B5672510972A36", "8BD176E46F897574BEE713533C8A10E825BC8BC99369C8D9585A10C3ED059676"},
{"0", "8D3180FF4883DC5AA28B24968D902070BDFE70064566B8FCAD1764D69F808107", "133E7CC6A5A73F8A449FA67403D5C9A5C39038B8AD7068908D1AF05D8DDCA763"},
{"0", "D4228B042AD3ED361959EAB7877E6879A1D79BA249CA496AE7D8AD257F26BB8A", "86E9482443E39E1BF1F6794A2B41CD14AF81E3D1E0B9EE85FB7F3A3A4930B2F8"},
{"0", "CAB36D5C895B5BF531820D6583302318F02D67777E6DF7005ED6B1BD040658D1", "DDA24453430C3C0693F98ECE25A3A94788A4699FAA512E5714C671C01EABBF77"},
{"0", "AE4F4A4400BF6C3B0E2314075FF5D80B0A2663A1C19EF5DBD75D68C8558A34FE", "3ECC8D7E5BAD15FDB29DAA8B6CAEB965216F34ED879C088033051A5E835FB538"},
{"0", "87348C58B899D79C1937A51CE9B9A8584A8F95F038FA3A7FD926352E5440F329", "B4390C1AA4EAC86E2789D1A03FADDF4A84C4134A7BCC6EB5251DBA74C1400FE0"},
{"0", "3CC8BAB6CAF9827387DD2127BCE2B1B42AE767842C6A73CC4BC7B80EBAFBF6D3", "FA9D4C576228ECD07787778C96CC29D393F5BB74334A92E75E7D0A80A3EACC8B"},
{"0", "C8D02D9035FF0D18E5A4E2D6C8E67CB307AE4A11C6834402671E0D46DBCE68B0", "3696D9B01B072F4F28C101ECC2942A11F06EBC35916674659CE26E4604F30D5A"},
{"0", "8CF64E22552CF89635D9CCF54EB4248E82EF495430AA619BC5FD75CD553CF9DB", "63233CE796346CB07A31036A99D61651AF7D66C9CB2A8A6E3CFACD52718C8379"},
{"0", "A56B34F919CB1361E97A8786B378EED78D56D022C391939B73575DF9595DFA6F", "FB530FB1320AD26995D018ABC1AF8C2EDE716278EDE771EF7F13F24C112D10E8"},
{"0", "0CB4CDA546C4383F1703C152C43CD72216C02C482712B75A0B34D8376FE9BB21", "161EFE06C4C2E033F43BB987D5A01886551FEEA0AE5A73367FC29469A658D72E"},
{"0", "6FFA10CD3A53135A86BFE67977CCE41ACA9D2FD93F00530C8D4AD8E9C592FD90", "001BD061779DA3540C3F554F459A0EED3F41D87ED8C007C1C9FE470F89000C83"},
{"0", "2D64792F6491079E9951F303D22D5327684B16E455E4EA89C5AEEBB1BFED43CA", "EAD44A4C84B88FDCBB339A7A710729E86F58CD9232E05EF4F09CB1A800733D4A"},
{"0", "878A9CE42876EE5E8130F16DEFE439A36FAC8F06A826AD62DD1926B62D69C3B9", "7C19B953FA53F5D48CC3403B7B8D807CEDB0C86413E5ED7314552315EFB91942"},
{"0", "F16A317D5BBDD3F0C74A4CC9D13F6CBA7F4771EBCF0F8DA867E863AE91237155", "163A9A9E9088C7445A184100743985D78E08DE382A7408DECF9CD48C2A53F480"},
{"0", "AC997CE260E454BFA0E106EB981D1B7262D69B2631E3F2B3F9A3B22E5AFF73AF", "5D79FAF02297740A31DD18CABC77994E8C30CF232F195A12DBE56867FB9947FD"},
{"0", "663EF05CC02936A6331EC9BA693022A752ABDF3F6A5C29F84AFBB58B7401E2C9", "70821A9928C42A52935BF023976035528F257BEBF57A587510AFF64A8CA12FFC"},
{"0", "3A893BB94B7B9188A8FF78D474414210375F7662ABD2306CAF3C83C70B8709C7", "BE3D39A56B455D9DBBA47C489E42CA101E92DD5EFA88970A1BB214B9162025E6"},
{"0", "06612190E62678CD21CD8CDA7F99336965822742100DB7218084BFDA603ECF68", "61F2152B060C06761AF337774DB8B6D5F74A19A1BA7910C0CDE6392300EFC4C1"},
{"0", "E7EAEFA1D7E473CF741FD7AB196E12A1BAE6E783CC692BF8A0E5975BF22EC5C5", "057D09A9FDEF5A0F44C9C0E40A2F743601B08CCC162E884EAB895C3BFCECA581"},
{"0", "B909083760AE7EA582E90D075E41A35A0CD3BCF2C6C56A67DB04726CAED987F7", "469FAB1708F21192A4FB6D9A8513842203899BCCAF943884048823549613E4E0"},
{"0", "C8AF77278AB19BE50F9468EDC29CA66EDAA958B131EC304EA81F3A7F784FFF07", "387D521B23C8CF6CE08C288C8D4D7830178B4851FCD6F9084D7CD857EF5CC52C"},
{"0", "5089C6F1D3AA699206F9799AF9402E42324E947C31EE1A4F15F3DEEB8729A7F3", "A88CD70B486E27AE947341D03D94CF47A47BCB3605FEF11B83A1A8BB2EEFEEE5"},
{"0", "44B3DE1DA377AEAC5DA62BB59DCE3EA0CD82A21EA4740B42CDA2C85D4A22D9BC", "88E502D23BCA6D60E667647BE1EA962713DA8E79C4364762DEA0A4118BF76A39"},
{"0", "A5A8731805DFDBDC98D27C5A2E38C11D42217CFD5465DC51A2A82B7D42E21E7B", "637500824501E34FA9B11A65610776A0A36B871A0C210CB0E56932C1A026C236"},
{"0", "DBAF2A6B077EEDF73DD7361D7B4DF96BA68D9C5BFBD37D0F97A4A537E6BAE4AA", "011DB0C79D1E69EDC2B4DD23ECCCC3C5D588E783B237366C3D26345E2DA7EED0"},
{"0", "BC5939BDC1C9001FC9B529669814EB64185F1992EE6C460D93DD1840916A7A01", "7D1199C9D704D732829198E080A0A0EEEFD595E0004B71C62E64CD6A17EFA777"},
// Random x, unsuccessfully solve y = +/- (x^3 + ax + b)^((modulus + 1) / 4)
{"0", "5C355384A5C69C59C0BBD4072145A3908B0CBCA5D58E193282B7B43DB42E102E", "8F93C8F38FC452A85699E839C253AAA8C0D68507B82B02C8DBCC4B2664A723BE"},
{"0", "FFCFE33C36E2ADF5304C58F15F24C65B4498FB8EF5B48220AA9EE2443686DAE4", "3C746D1FC8FDB9BC370949EF3B917D5190C4A6940D8494374662B83EDFFCB2E8"},
{"0", "323617FFA986D869CFF92451C98EBE7E6F8A3E886AA62AADAC11E73F00291C18", "619B75B51B9E8D6B3B2768B9E9B3737B9F616A5A25E116778CA6C316057A5392"},
{"0", "E2470F6D011021A96411DD74A3FB79EE5B5031178A2694E80F7E27791D679011", "D45F0342DEA4502F27E393266F38F0B99C353A9B87EA71EFC9FFAE5F2E8512A7"},
{"0", "702C4E4A4B642E4027CD7A6EB130A5033D61B3F04D600015C63BEA8128A51813", "F03EEF55D4E101AC197F913533FD8E98BF348576A10AE6BCE6097D727DF96BE6"},
{"0", "58C6A4E6DE976E7C8E8201D0226F4F361D77E1D464D1CE20C255EFBD316FEE60", "FD397191527C1D21CB6F1ED766EDA5A2725389E603EB57360521CB5E07BC5208"},
{"0", "331DD3465CE6268776A10BC64A1B2A86581857DD4460F680C1ABD5B3D675CFC0", "FDDAC5B2110A0B14828267813A21476FF859D57EEB6A2DFC426A382EDA694403"},
{"0", "B3BAC1CE7071D37D66AEDE4CA5517B561F588BF5E9EB9CE48BF28E6C0B3E6482", "509015BFCFB2E897AA3FA7434D9BB77FA73E5F293BA20474B17F2C0E77F75BF8"},
{"0", "C5B239D074808E24D065C47C8957DB85E6A3223DE0E86C76520407E0A90770CA", "04C9D4FDA111D345871D68120E9054BE37313D83110DAE20B5EDEC723A5BD319"},
{"0", "92E77454E935969A820E53B2AD7DB46580D335BF4733C494505F12F7F10DE79D", "7175953DBF295D5749985E4589D90834DC4617F07DC1EA204625CC9D0E91B90D"},
{"0", "03845F71FEDAD34DFCB7F5D4B557E2A911AF91E7232C570821EFD327AD2719E1", "87D5448DF57BF7528E05EE321120013D482518A648615229B066741516B41366"},
{"0", "38AE6C0054A07FE1AE827676DB704872BEADC94B4E323FA350BAB0D72B97D2D4", "402F53AEB179426DFDC20D9BBD73903A5AFE3F5CEF28B0018B07EB12387B41BE"},
{"0", "6576F26C80093CD378E04EA87B63DD80020D65E424B72218FBA7D10D964F1D58", "B1FD939FD62ABED47B9289F0144330DF377E2D39F0056EA9839C8818A891341E"},
{"0", "E4A6692620341E54EE9DE2177FF888C285836248461FEE4F997DBFBBB0A932BE", "47C638C92416A96F180024398909DE2ADFACC67D02ECFE6DF8A519E0C7B4135E"},
{"0", "93874B9C039236C7DE094BAF566AB64C1ADD47CFC83787B478A1C3515CD11A82", "B13C87567ECE2293FDCE71DFF98FC184B4B9D269D3011CD4C1C476D11D9C8EE2"},
{"0", "51A49FE4CBFA5CABDEC93C3F820AF48189B6EB722A6D5A2FE2C07ABFDD4BEF52", "8624BAFC2CFC7DE672F7B6C5D4156203A519931DED11DBF4B6C840B674EBBF54"},
{"0", "9436E8A0117BFAA5D45AF115BEB9FDD2B7D9E523AEE0B3645A5A383B86661F7A", "A69F6E71077FBAC7B22E5C0C947F022F5996DA63B4FE816BEB1C664EF149E34B"},
{"0", "01231CF7F4AB759CC1BE17970CDFBC789AC00F24A1EE3176AEDD35ADFF40C025", "38836A4D862E39CF190A40A1B60E3069A7EC0C573550C80794C2F86738AD75AB"},
{"0", "6913E1C50AE1B6F1B5D4DAB658156F41E2A96F85139C024729C22E302085D4B0", "79D506C9CD56E408A217F60212B774557C3645156F2D8FBD032EFF678DDF1E70"},
{"0", "CA68780C50EC1C9AF2EB9F8D1BD91586181DE8005307EB5A8265E1D5FD93E76F", "58B82ABB31EB8E751CDFAA9977FAD6BAEF8B893F3DECA4827B457FAEDCB3A0C3"},
{"0", "AF97C1F1C2507B185A34F1CFC50B96FB510838DE8743E241EB3C25D9463C9CBE", "FC7909B4B7F82CFA983E88F33A00072FDCC5D3B9FA32EAED9023C92FD6E7A1C1"},
{"0", "8C18802E4E28D4D737E578B05FB71AE4C6A1329E8C042804BE9A53369E165469", "6711419F7951669973F7896C52193FE1CCE246BA1885B1D92C2C67755DB3FE30"},
{"0", "118659CE1EBD01BBE120E7706A78A99D0721FBAF4D25281DBBB4B025B0DE28A6", "37FFCE206320D01BFC545343C072E34BFC8053EF17B57C1C7C36DF4DE5E2E377"},
{"0", "2A6BB428F3A0969798CB5461D9A1268C427AA8190A2895F8C61244A228FE195A", "5EA4BE1C71C8CC83D6ECBBECB5E05406D447683FB4011D6EEC631BB5A1CC4F89"},
{"0", "D47105AA5917BCDB885D8E3BC137FE0D98AD4FD7ABA23DBC5F56E22A056D4451", "ECB0D561F875DA23EA2B9F10DA2F084F180412F921D13E0C701E53D690DDC635"},
{"0", "E0F6C747A9BE7C749B518196BCA7DC6E7ACE025968968FBD7FA083A0C4C2C649", "549B54B60965E5E187C9FB587322833F9257B52E1B321AF435805B705A1CF733"},
{"0", "90F71EEB7EAEE991673FB1BA9DB4B92DD39A36220E98D23B51D847F595D7B9DB", "A2B39D28655C4BF1F41784548B2849E6987888F1D7EAA6D6762B0067810DE1A3"},
{"0", "48DF25C129BB17CF06C38D27012551B6B33ED6484D419E202678D0031A618603", "AF01AD13D352DD9B1F767FFE9D210C8AF469BFEB632174942513EAFF2FFC11B0"},
{"0", "36CDA1EF47FF595CA408D14968F725413928DF1D0DA7A7ABE15E915C86CE02BA", "0FDD4FC4015EE14B5B19695F6698843723CEA04E80064FE6CD03E161DEBB120A"},
{"0", "8D7342A6E6A0D43326F6E8546727A9F4965EC2B0684740524224EA1A5E1FF0A8", "8457358C422795134990478C5F640742325322A3B796B738EFF91CDC0FB02E73"},
{"0", "F7AA3EC9B565E411D202273C692BD50541E4BC279E88EC662A0A6D93887412DB", "A0EE386BBBCF4E859E2F32108123251EDCA6B1EA15D5C7A87D81B9487919AA94"},
{"0", "C5014BABDBD1B98F059B9D75551B9660EF624E6F5AA9CD7F6188B8802AC5BED0", "6BFDD4B2BFEA44F985A94951A248A93945FD62ABA1E3116BA9A40FE9BF700B36"},
{"0", "CF91EBF863AE57DDB76B51DDC0D66853132C0667410B5CDB124E5D86430E5920", "2E48F15C664F610AF8774A909D08E1DDA05B1D4500D4BC27BA64ED7526BDE7D5"},
{"0", "962BD62CE8F40E8B3860FA1EE86780747CB4643C8295CF2C7BF5A7D3CD0F9C07", "21A9AB083E65E973F703B1565918F58748215E1F29BA496F3E644425F0D67730"},
{"0", "B3F69B3AF8C30B774263BEC60659EACA35308C20E236FF613C7F7EA7BE91B5EF", "9CDEC0B9C5206B76EB167D21DCA970AD550046CE677472D13A852F114673804B"},
{"0", "0B8A4F145517EC6992C8A60F947E38A60D684E70CBAD4472AD3F79B47DD858F9", "6E3081751BEFA3722BFF92809B47FF2E4CB580E6D6393A9A42944E3941CF76C2"},
{"0", "D21080372AB3F49B4A0DB89DB8C91DB039988A3AC6B199D918F46B59C63BBF69", "2528609AF74EF510BF29A255FAFE0B4EAD98094936591B0E1851AD2230B95B6A"},
{"0", "27DED2D6D142AAC00A84FE8142CC1DFAB530EC4720EF4421175C1F25E4A8EFE8", "C822E500FD74E5D0C04DE329D562973470BDA195A71373B40EA3080B72C41255"},
{"0", "56D2AE84AF15B5F61919027121DB71593AEB3BC828EB79DC37D050FEFBA49B29", "4465CD59AE4BD11757F7EA39E6FB4FC3E49E91E63409E540C51CC1A56F173B5E"},
{"0", "B90FC6617E781D3A96DDFD91A64C18700B4E2B1AC1D6EFDFE3F97A871E69454E", "B874F605B770121DB7F3C51B328F92623E29E2D47DE745370810E1E12E6CE5A3"},
{"0", "51E7098937CC0FCE805FB839855B23389045860BE7BCC4D72DB44975AB66C763", "2EFA8DECCCE9B5B6321D7D2A537E69462E2337F7C383E6121E045D012B885D1B"},
{"0", "7395F8610178BD1D4FB30F70670A462F04355BD000CBEA7314BB5D5B4E27B370", "4EFC4002611C39534C47E985912E1C6E9D9E9027BFD8B9E6EDCBB60FCA4F601F"},
{"0", "857A17AC605ABAC9E02D8563862252D55DC888D869F798E10727A876061440D6", "233549BD86D7A65F8F2AAE7C574A31CE39919F0FBC9258DC8FAD6064F4793869"},
{"0", "9649BEE247797C16EB4BDBC6F79D546A860A0AAAD82D9CBC73F9C2331A1B643C", "AE79681C3545AE994AF4ADBF32E72C78B88F848DCBF12445C426E42306A485D2"},
{"0", "7831442B8F779E01FBB3F5C6A918E0B4F9F98B6AA4AA7C979D54A9FEB43A92B5", "C5A5AF80ECE64821979A18DF8A54BD4E4C66EFD521A81A8071C9030659096D90"},
{"0", "EA4AFB17B60C2A368C5CAD2CBBCEE853A865C07BC74A5A082780DC083EC2F14E", "84BCDFBBD15534FEE1CF854089EB6392B50CB5D0AC82BAEAF5107BEB4B2DD185"},
{"0", "67EFE17A617EDB02F47AB4DFFE18E8A6B361A02A866EE515820A688C03CBD4D5", "7A22CCF4682FEDD26B93D8CF075B5D9688397969B732861DE0AE50390A3D824C"},
{"0", "407EB05DBE48DCF957F00233142BDA816DF59F18E86B77638FD92A286109F5F0", "FBE879CE9A2DAA5D97566EF9114C99C4AE982DEA4C9ED71A9AF1E197CBDFFEEA"},
{"0", "573D4485D2AE451B52B390E8FB02F6364A256A435FD68E79B9CE9992A3DB8F29", "3902609576F5CF7CF065B89E88DD2128F86E4F6E1CA1A1AD8979C87217E4424E"},
{"0", "122DBF9D289327FB4181228C12F97B840C91EF2DFD8D287A1A92BFBC032A2895", "D532731604951E764C51173386F9726F0958BA24EA89937BD893E92C4712F028"},
{"0", "BE43C176B936B6F581FA9A6F681D8D7733F9786778B362290693811633F1A71C", "75F9B32A8B7263073324E2E66D2BF5CFB8C0B9EC3E11F82027FD355ADB97E8EC"},
{"0", "D79DF76269B569A26959BFACE730519C326FCFDDD29F29A6427F0DFD5579AFC4", "74DF4C8534F8CD03926EEB4C16CF617BF47D371A0CCED3B974C1D6781B0FDB00"},
{"0", "6E700255C0407B90904855D66121F2BC000ED5217598D50C24A82187F7A9F731", "86E658FF96DBDA43D227047044A189D03D6513445CCFBA15259C9B9C3EC82E09"},
{"0", "75A8B5D627D8CBBE550C21E0AAE46B1491E80B6B2C51B24B5DDF729EE77C1809", "064D2B3118D1A352EA5530412508D25C099E62658BFA799457D35290E480899A"},
{"0", "4E6C01766E1E172AB4957CFEAF3433AB62C300959866F6EB074D44D209978378", "2BE2CE3006A4AE0FCF4CA0BB65AD090F4CA141E3D75E384A3255739FB82A465E"},
{"0", "CC6239636E34928576E32DA3E68B4EADE6235240B7C5C0EDA3BA149CDA4C20B0", "92308E741A6F2ACF3539F4584366AF3E285C6A2FFB2230E872848DE54717CA3F"},
{"0", "0270750B00B8E8B8899379919CAC40566A5BC7B9B0BD7256ADE320342AF8C7A6", "68088FE7ADFB9AD5888ADE912FBF4AF469BD0386DFE9295522310694EBE97744"},
{"0", "94D7196F5BB6FC279D7AC1341FD65DA92A32542E6D2284B090D6D24DFDEE3FD0", "59BAAEFF84AB0B6FA5EEE2349322FD9F16BF12F4308917B399D794E2C4675B4A"},
{"0", "8F2B28B9A4F01ABF456F0FC014F0A4B1E9808D593FD083CDC09EA69EC637CA88", "B191E42B9207084522AEBB17405CD4FF8175C51B6BD457A1923874CDBCC14CCF"},
{"0", "D99116BE132DADD521FFD33DDCE99800C99DE380B874CB1C0F72B0098037BB86", "5646D915BC25AD5A2C28CE496F29E425F2B35C3FDE948517492E46BA48E0A824"},
{"0", "766C22B55DD2EC6582B354DC1F05EE69495A658F43E840BD722DB10DF786BC50", "D8B4DF85E31F9FA8301DC3FC73EC239DB28FEB9C93C353FE11BDFBD4CF9D8C62"},
{"0", "D991B38CD908D89CD9244064749E9B3ED1CB1FA5BD3B609A78516F58A0898535", "E6D48958D04C976078821ABF1F66CF179229EFCF1251F5A5526B911BC0E08B2B"},
{"0", "4C4B6BCFDE9A6A3073FEBDB3B846B61D7398F249DAE082441BC4D15136809CB5", "54358A9D3C8B0BF2098A65D2A4FE17166722FE6D6609DF6EB7F3678CCF742309"},
{"0", "65CEF7050F80819A3B8320772D350F365D91D8620F72EC4400243BDFE9C9D1A0", "8E92B4E2DCDCCE1EA6560CCB2051819E813AFEF258BAAA93ACCB7A95ACD64EA0"},
{"0", "0154BCAD92BC591C7243D50C25B64BDB21347166946C4B76B7474FF5BD595762", "6CF16C8DE0D14577E99BDF29D81CEEF1F987992C03150E7A780769A003768D72"},
{"0", "49036B142E8B0DEF758A1E1CA9587DA6002F1501ACB2465DEFAA8D2475B3712E", "D602D844B0BE298F67BB009B50595F9CDEEDB48B6CB335E0E0FEC59A8E26100A"},
{"0", "364C139DB5280464CFE49D8657BBB08877ED2E5443A6E219BCC7EEF3E6898876", "6F22FFFF413AEFC89CF440DCE02E52E98E092639A5ED9BF824593C01BABE5C7B"},
{"0", "797CA09BF4A01FB5DF0C17C9611BF06FE6B65ADD8A066A13F0F39DD619BDE15A", "D740C63A35CB195D5370A2B98BECABF267DE8B9409F06ADC0DCB026357776ECC"},
{"0", "13A49E010397233032A1EDC450E0AD6C212EC6C2D4779745EE8916CB73B2259E", "A6C43CC1C9B8A709A2D6FB999F7931EFE80A14504380057A57B306968B9757A1"},
{"0", "7E3FD9A2848FB10D2907D5154DAC8ED9E3DC62FE914E13F6CBF9C5D5890D1506", "16034FC7FD17B892B6E3687879861DA7B2657ED1C36954447D92FF8993037544"},
{"0", "57D17A87F375F608A48028F04F275AE5373448764BE35A684142DB11BD0B4340", "76E5DB7D24E943681F1D234040300FAA843E649E61ADFFA12E8C0B7EAC1D4D3F"},
{"0", "20C4BF4CD8D274815DED0BE2D6F54C2BB90317C939B082A1D219201AF904B54B", "1AF3A74D62B916FF00184A18350F37A1370063563696F248CC9758352A7D8E9D"},
{"0", "B594957252A169C23F267E35C1304C8C05250DF064FAF4510139E1E9091F9015", "9E00B2FF6D6AF21213846DFECF8743F2977A8F5D5C6C30F2EA5A8CCCCEAA246E"},
{"0", "C8F1C34970B975FC682BBB01535054D94CDE461082EBB895132C90D6AE39773A", "4C3ADDCCE5DAD10858DEB5062569FF035FF10296C6CED15499D26FE9CC499875"},
{"0", "77A37179908E6EC8A53CC3602DB3BA0AAEC0D68A72C544B742F31460930FE060", "FBE70E3AB88345BC710C13F1499540C6FE413B5AE0396BC2B516ACC49493F9B6"},
{"0", "0D77D54B823EB42E59D800B2F4FEE628075CB13A58089246074A354B87C29B84", "CF719F60AD1B234AD50C25406FC3C371489DF31D59F211ED40B6B86286A3950F"},
{"0", "A4ADA87470AD529A6699E4AC0ABDD74458DA5DC136A30ECF94FB0761E528776D", "7914D917600AEDA93D9307F064E5820D9EB294E7A6D22F8E0DDBFA15ABF5B003"},
{"0", "07B77D28F2C22BAB325826BF39C4A12301F5D189D3FDB064FB0022F86050F97B", "F342EB799A4A82415691CCDE4E1E70FE67A3283D940FF9225178E8EBD9072B13"},
{"0", "9D7A6EC7B39EAE7F8F144CD0D1D790F80E4709E2390FFFAD1E0BD6DD38604C92", "426A0FA28FFAB2291FFC8993C9D23FD4C3FA980B71566F7D23E975C9B69FD8BE"},
{"0", "EC262CCA4203D0A563163ADF7A9FA638028C0F5B75CBBA1713CD60B2F523C5B6", "079C9AE2C361C03BB8FC7E3D99BAC6BBFB39FF9BA7174148BC8B66BDF583F259"},
{"0", "919E0573368A2EF5BF78D7890A9D5C86F582BF78E12B6331E119F2C00F946B32", "4446B21EBA289782417E2EADF2F2E7BC522C8477CAA726E3736F65196B156A26"},
{"0", "D54685BA54336CDA25164114703455D05278FEECD02C93B2C4F90C1DD7D1E59B", "1FD769D4DB66EE99EF5AC31E6B94D11498762238F6F908D2753437F74D950C0D"},
{"0", "693432193C831954E39129A51B4F62F89ECAC20F3FAB71B66BD6AD99A2FF51E2", "730A618B07438BA4C2ED7008597C33ECA51C9BE294E7971004A76FF56D65BB70"},
{"0", "6D5EE0D9EC7310A46F38AEF44D999AC3D8E923D7B60227F3BD65E02D51777C1E", "DBEAEE731126ABB5C8D942CCB9AF18D9A087F0A57CDBCAE1DC5DE0C52BA2C7BE"},
{"0", "4071CD03998C07FA94D7ABF33511A92C9415C2E528B25D2D3C82F2ABAB45FB69", "80BB9F16973662D6FDA0EE24E869C2983209FFC468559D1797DC7CC0BB97B7CE"},
{"0", "25862FAE0B86D2A32077BD6174B477829356C2DA3EB1B07E90BAF9DDD785CA00", "B3166DBB127E998C46834C505C8188AB53E48774AD94C6FBC4A261F5C95D9696"},
{"0", "ECC0844E782883195CE9EB0B0C4FBB4ACC90799FD2DE2D8A7184A7851A9AC580", "5440FC88218E6E3AEFCB97C303D417B570F7E370A4E3E9302BB9713100F3E913"},
{"0", "E5DE733BDF187F717B55246DFF32633D7B996118F50672069B0B7943D58314DC", "3F1CB377B6F925A42DD643954A793CBF98FA68E3C307E4EE0702D45A9115872B"},
{"0", "CE11B23F0C0A793FDF7276D5AD41E1894219D2225C16D930A90A5921AD59C1DD", "94B468CBABF0208356143CDB57690EB0AAF7DB989E4F5E3FFF3940242A79B5A7"},
{"0", "A8F28E8C4E24DDBAF450BFA5905F0333B7EFF0E05022DA08BD93A5070660C675", "758E688CA82DB2BBA54A00FD68785568D15EEC954395E274C5F2693CBFB235AC"},
{"0", "49CCEED2BA5F2CB00D15E874AFD86635504E786E57CB1136D73CFC41B3271C74", "722B35E7603E0C7AAFDD71AE9EFCB0D0ED2D7643938C77C3EE1CC80D52FA5724"},
{"0", "8420B584D4FB1E64B13D8ADAA91C8701DE61EEC2541213EE5E13A2AB40C593C3", "1334CCC9B2B55B79215415741483CF791EDDDCD723D1AA2A945D4D51FF1CB419"},
{"0", "45F1EB2C88B7C9CF4EBF3CB18F50275B0EBEA74B023968C54321FE0DA1F148F1", "843CE00E0762BEC9988315C60C66AD3A907D03769821E9B7FD04BCDF82A61DB7"},
{"0", "37EEA1E2A3CA43D808EA89658CBD2C8E06BAFDE3AD2F4777AAFA64F7483A7F80", "408BAECE92ACE2F6C50B7889F1314B9440405DCB8AE30A075D50EEF18E110F1F"},
{"0", "178E735C30007A2C7C2563A7FEA573C64A737BC7433AADC630C490DD634841AF", "19A2F7556C5611DA9FA2D58E6B1E8BCFEFE14D955B54A9995B665D5D27F36514"},
{"0", "DD321B8FC4627245081A2D6B28404AB1D485026FABB02CE74B7E3E471D2BCAAE", "19C0433C1398DDF2CF9D8A35AA5BCEDCD70A67DB8C1A9F93755C6F56B611799A"},
{"0", "B9EC3093D3507B59BE1FB29D87A3B0C51ADBD10AD949DB9058970AE8E0F9C42A", "2CCAC841E070B4C5E533834F83E880C4B7A20F0FC9AEA4F461F4062DB5329B05"},
{"0", "82E9F18167A2F50E81958F72E69AF780374B5C84E6828A901F808E8C6FE16D51", "1461032286244991C4222E493DEECE57B5D8BBDE178CCEB668D13D9E5BCFAB77"},
{"0", "5335CA7129FAD6826B8D8EB2A7B8DA3BB69D62E6B8FF8824556638956F547736", "A777355C01FEAE55C79EA6DCBF3BEDBFBB7CCDE944367F5167B14048C1DB36E6"},
// Random y, unsuccessfully solve x = {(y^2 - b)^((modulus + 2)/9), x0 * k, x0 * k^2} where k = 3^((modulus - 1)/3)
{"0", "45948014E0D46D303186CCD5AEA5B55B5859E6B5EC40A05C6B5B33BE6776DE10", "CB3949964CB61E5E71C12E5E22957E709B09E8601A1335916C67EBCAF5BA73BF"},
{"0", "D11077F4651D34C062EC7D89F6B6B9809915A90EF663F501FA59EDD8665AF1AF", "05AFB22E5CC69717013788E7FA369F543C3DFCF7CA33F7DD298C15F24D935522"},
{"0", "FA04AC1C1E2BBEA75B31194423B17D1D1C39BB9E614011B0740E8BA2C0876EFE", "A477042DD63612DB2B072F48D88D251F6A59D251DB8AD22A21D10B0D559671A7"},
{"0", "42075E66BB74472823C211E1FA2B20391AA68EE29670F96D333125840EC88017", "5BF2BF275FB043B03EC0715A83D0DAA14957C9B8157C82F53483B4D8DE238704"},
{"0", "3BC716499782ECBBC4C34B1323B9CD2F8E0218A2F33C90E76F86A1EAE5105B1F", "5A8EB691DF7B13C051ECBAF60F43B9493226AC482E7F3107311CDE9959620F29"},
{"0", "D83519ABCD7E7564399F1B57D71E491143ECAE68A49814F8C76EC7A2D0A278CE", "C73588A40177E086505447C3E33EC497785D854729A4E507ECCBEA25015D3D01"},
{"0", "69B17109FC0E894D3C75DE23AC61B5DDB46F5F8DDED732A6929DA46BE775C19A", "DB35114452309622AB83B34FD143674F1C31365D0F43CBB211411A2299E1D5FF"},
{"0", "F57EAFD1D123BC24A989AEFB4A1B18CF21124DB781C55C396ABD1C3D8333F32B", "80538B0FA9E2228EEEC0D7882D2F44AACE0C30811A8E937465B974FE4386DA8C"},
{"0", "79B81D752017B792A521F48BE4FF925FB2474E267CFBB2742BD11E6070CA71A6", "961281337AB519C84C6D57880350E56BB4D5978A6174A2F5346979CF3FAAA4E6"},
{"0", "AA9668316A6FD4E064C80E8933BF2DDED7C8DBA3BA7D77A23E21D78B7B6FA96F", "F82C685E6808BBFB32C0C88882BA7083A0759740FD84ECA7EBBE91F54D7A3C2F"},
{"0", "E77F3B9FBE87876F44D12526CBBB012A5314AC81A1225FAD98E4F590A3D98DE6", "773067989F5D239D41BE4E4C08797EA3FDAAD609BBBF74282F03712652944B6D"},
{"0", "194F2E3B8734B37CDEE3683563ED1007855210810B0E1E8FC19B626E0A3DD307", "0827449991187DB35A112B21E1E1E122BF50D61364DC20AE30B498F7C6EA62F8"},
{"0", "6DEC680BF48715651E30126193AA48334DBBCA2CF61BC4B33C84B1B3769BEBBF", "FA63CCDDA2F69BEDC2226EB8E95B3A66A3094BBD13120FF5EF4558251669C629"},
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