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Oct 15th, 2019
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  1. points = ['0x898CB2616E46E8F01CB4C05732EB89D921543FE30000000000000000000000000000000000000000', '0x7631DC05F1954DA902E29FC8E2E7EC21A80C5CA474657D752620FD5E46628039AF3409C6CB209C5F', '0x161BBF1226F95B8774E1A36DECC20D9774099DCB487A327204565B2B10410681AD0F81367A8B8C9F', '0xD229562860D0DA42A3F40825812D3DB380FD4787957860E7C2F662C359863D0531271938CDE721F1', '0x48441C6F9D744D72D872E0BE9BA2B1DDBEF12B2E34AE26E93DBBA1AD366DED0E664AFD7EB1E9562B', '0x547F2D44BF42E61371D1478E5FC8C76764E4504108979358FEF026174CED242226C4B19EBAF03EF7', '0xE0061588ADAE4671E1D2C0B4A9E01340A3AD890801E048143B073AD21918EFDBB6ED525A6A3220BF', '0x50BC68926130E24542830B5A546C3F4690E370A3766BE509C344710FCB01A0F235EFEEBE464D93B5', '0x8686A07F6544B384B3AAA0FDA2344D6F8078BA1EDB52576D511BCE22159E3B48521AA7D124C03E26', '0x9598C16277BF6F9FD2AF1E1DFC3108AA4DBF35E0474D3D8170C6A2E7B3A6B7BAF1BC52EBAA2D90DB', '0xC97396948AE636D0012246750AA64A264DA6ADFA76B015CBD383B8FB3A36D26E8C599C734EF5E3A0', '0x19526078F8E4C3C33BECC466E256AD3FE1A58C18803065B138B88E5FB6835051C0E4C06B1C500AA7', '0xA2305767A4FD5A45D7520554C08F2F8AFFB0988C962CF4089B35767C7FF6D653FB080D8648F552F8', '0xE409901D98E3884B4E15C33982333A021124CD89025DC6EE4E99C1187BEB1F19E89397ED8D2845B0', '0x37B7F8658311F8A77C098AF6FCA4F111800CD8F5C21D090CBA9A7824889FC86B2691E7C22958CD32', '0xC24F6A8D82D5D9C6CBC4D24F9DB28E06D7B73C19115DFF8D8547B4BE1EDA04D2BFF0C576F0A5E5C3', '0xA0B31C3B2090D12DEAF87E65756DFB0850D6B60876E769561205B08CD5B67B1C2767326FEFDE6113', '0xE375ED0442A3B99276F200977088032E504FD1077E24693F99EAC1F2082F5AC5AB337E99473CFB5D', '0xB4BE47D0A516012DD76963F5CB60CA674B368735D9889300540867A495C3CE8F772C46DB49E70086', '0x3A33790B193974A2D085EC52D6BC530CF63B20AB61120114A378C64934E8C8401FD5C539EE20AF68', '0x85F567F520BE83C9E2F3432A331A0F9FA45E1C798707B631F09B36063401749AA5372899D1566218', '0xBA1D6A28988BBE44B78A9D800ADFA7CCA309A37B9430AFAA57D622D49189217F1D9780B336D84218']
  2. results = ['0x898CB2616E46E8F01CB4C05732EB89D921543FE30000000000000000000000000000000000000000', '0x7631DC05F1954DA902E29FC8E2E7EC21A80C5CA474657D752620FD5E46628039AF3409C6CB209C5F', '0x44F83E88F0F73DC921DF3D6B4A029B6B03EA7B8A4F69898B5B204BDB01974706A3EBF8C4B120DB9C', '0xD229562860D0DA42A3F40825812D3DB380FD4787957860E7C2F662C359863D0531271938CDE721F1', '0x170AB66B15E0098B371E1028135F415FD389E310AB7F9C16D9A485F0D74202B5F2E695BB820D033D', '0x9B1808809C73D0A3F65A531AFBA5583D4E449F56ABC4FF37C33504F414C769542CE040815625FAB6', '0x43381EA83509B33DB345D761F238A9256B0206A8BE623184FEBC236E13A948DDBF94ECD2132B48BB', '0x3980BBCE78DF7DB4FEF33C7EF5D9890D38A1720E5E1FE8D275B1461592B57D331882A3E40E4D8B07', '0xAB3CCC4B8D0E3216B8383EE7376FC93EA84517644B4077DBB69673DAF3AE3150D8128AD9DF380CB0', '0x7385972D154A7A1A9F0911A18C6689949F2657B13486C1B313C7AEB9BBC9415130BE8CFB47136F2C', '0xD17FC9A9BB05205821591158EB8425A6256B67EB5DC0A9DB5FF9C980E439B44AFC3B78944E1962A1', '0xA9D6B365DA91FA05B08B094D8C5BAC6612DD208DAEBA5DC083F43BE9EF431EC10AB809F3899D0FA6', '0x97B91F2CE1FE4BAC3AA39F0204F105DD2FC65A2F34C53297CEBB548791D027B90E3D5E9D72C0C23F', '0xA1A6E2B73DCC45EAC48783A4C6A78F0B2B06402D748D08924A7769DD9855EB9B0132B9D97C677A3D', '0x996F7B31B482C9A7C6C0BA638F4C39C4B378F82347448614C86462E32346CDAFE559287F5B767515', '0x52B7007DB336E70CD3DC8CA088A89BF0A2FE271813C6658B2721BB5BF9C6427F50A2625F14114D92', '0x5F60EBB6587A1D7358E5BB4A4EFF5DEA290A8D0A77725D8C6EB1C796D03CD9C451A0D1783BE035AE', '0x84045CBD05763F630F2535770C4B7F5D678DCCCCAC48DAB92896F45BF60B36C91BDA418ECED6E546', '0xA7CB2BB6BF19A9FC477BAD207146FD8EF4DB5BAC790D21C9ED9568C774734614DA3E5913E7A87810', '0x93B86DA1990B302C94FF40FE01938C77D4146418460D131080AF54DC342FEBD97162D5215BB028DA', '0x188CDFC6ED3FE42577CE2385187F7DA872F6AF04D966F7A0B1F6880CFCD326E4F71CA93E5F1048F6', '0x44BE5C0FBBA6ED5A56C9E684A9BCC9C8AEB9255F84E8AA81586BF751023F45FE2795C7B6A27FCB0F']
  3. p = 0xE95E4A5F737059DC60DFC7AD95B3D8139515620F
  4. a = 0x340E7BE2A280EB74E2BE61BADA745D97E8F7C300
  5.  
  6. E = EllipticCurve(Zmod(p), [a, 0x1E589A8595423412134FAA2DBDEC95C8D8675E58])
  7. g = E(0xBED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC3, 0x1667CB477A1A8EC338F94741669C976316DA6321)
  8. print "Order of the normal elliptic curve group:", g.order()
  9.  
  10. orders = []
  11. modulos = []
  12. for i in range(len(points)):
  13. gx = int(points[i][2:42], 16)
  14. gy = int(points[i][42:82], 16)
  15. newb = (gy**2 - gx**3 - a * gx) % p
  16.  
  17. E = EllipticCurve(Zmod(p), [a, newb])
  18. G = E(gx, gy)
  19. order = G.order()
  20. orders.append(order)
  21.  
  22. rx = int(results[i][2:42], 16)
  23. ry = int(results[i][42:82], 16)
  24.  
  25. R = E(rx, ry)
  26. m = discrete_log(G,R,order,operation='+')
  27. modulos.append(m)
  28.  
  29. print(orders)
  30. print(modulos)
  31. res = CRT_list(modulos, orders)
  32. print(res)
  33. print(hex(res))
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