# $Id: ectab.in,v 1.2 2004/04/01 21:28:41 mdw Exp $ # # Standard ellipic curves #----- Curves from SEC2 ----------------------------------------------------- curve secp112r1 prime p 0xdb7c2abf62e35e668076bead208b a 0xdb7c2abf62e35e668076bead2088 b 0x659ef8ba043916eede8911702b22 r 0xdb7c2abf62e35e7628dfac6561c5 h 1 gx 0x09487239995a5ee76b55f9c2f098 gy 0xa89ce5af8724c0a23e0e0ff77500 curve secp112r2 prime p 0xdb7c2abf62e35e668076bead208b a 0x6127c24c05f38a0aaaf65c0ef02c b 0x51def1815db5ed74fcc34c85d709 r 0x36df0aafd8b8d7597ca10520d04b h 4 gx 0x4ba30ab5e892b4e1649dd0928643 gy 0xadcd46f5882e3747def36e956e97 curve secp128r1 niceprime p 0xfffffffdffffffffffffffffffffffff a 0xfffffffdfffffffffffffffffffffffc b 0xe87579c11079f43dd824993c2cee5ed3 r 0xfffffffe0000000075a30d1b9038a115 h 1 gx 0x161ff7528b899b2d0c28607ca52c5b86 gy 0xcf5ac8395bafeb13c02da292dded7a83 curve secp128r2 niceprime p 0xfffffffdffffffffffffffffffffffff a 0xd6031998d1b3bbfebf59cc9bbff9aee1 b 0x5eeefca380d02919dc2c6558bb6d8a5d r 0x3fffffff7fffffffbe0024720613b5a3 h 4 gx 0x7b6aa5d85e572983e6fb32a7cdebc140 gy 0x27b6916a894d3aee7106fe805fc34b44 curve secp160k1 niceprime p 0xfffffffffffffffffffffffffffffffeffffac73 a 0 b 7 r 0x0100000000000000000001b8fa16dfab9aca16b6b3 h 1 gx 0x3b4c382ce37aa192a4019e763036f4f5dd4d7ebb gy 0x938cf935318fdced6bc28286531733c3f03c4fee curve secp160r1 niceprime p 0xffffffffffffffffffffffffffffffff7fffffff a 0xffffffffffffffffffffffffffffffff7ffffffc b 0x1c97befc54bd7a8b65acf89f81d4d4adc565fa45 r 0x0100000000000000000001f4c8f927aed3ca752257 h 1 gx 0x4a96b5688ef573284664698968c38bb913cbfc82 gy 0x23a628553168947d59dcc912042351377ac5fb32 curve secp160r2 niceprime p 0xfffffffffffffffffffffffffffffffeffffac73 a 0xfffffffffffffffffffffffffffffffeffffac70 b 0xb4e134d3fb59eb8bab57274904664d5af50388ba r 0x0100000000000000000000351ee786a818f3a1a16b h 1 gx 0x52dcb034293a117e1f4ff11b30f7199d3144ce6d gy 0xfeaffef2e331f296e071fa0df9982cfea7d43f2e curve secp192k1 niceprime p 0xfffffffffffffffffffffffffffffffffffffffeffffee37 a 0 b 3 r 0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d h 1 gx 0xdb4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d gy 0x9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d curve secp192r1 niceprime p 0xfffffffffffffffffffffffffffffffeffffffffffffffff a 0xfffffffffffffffffffffffffffffffefffffffffffffffc b 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1 r 0xffffffffffffffffffffffff99def836146bc9b1b4d22831 h 1 gx 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012 gy 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811 curve secp224k1 niceprime p 0xfffffffffffffffffffffffffffffffffffffffffffffffeffffe56d a 0 b 5 r 0x010000000000000000000000000001dce8d2ec6184caf0a971769fb1f7 h 1 gx 0xa1455b334df099df30fc28a169a467e9e47075a90f7e650eb6b7a45c gy 0x7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5 curve secp224r1 niceprime p 0xffffffffffffffffffffffffffffffff000000000000000000000001 a 0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe b 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4 r 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d h 1 gx 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21 gy 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34 curve secp256k1 niceprime p 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f a 0 b 7 r 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 h 1 gx 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798 gy 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8 curve secp256r1 niceprime p 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff a 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc b 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b r 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551 h 1 gx 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296 gy 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5 curve secp384r1 niceprime p 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff a 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc b 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef r 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973 h 1 gx 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7 gy 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f curve secp521r1 niceprime p 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff a 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc b 0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00 r 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409 h 1 gx 0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66 gy 0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650 curve sect113r1 binpoly p 0x20000000000000000000000000201 a 0x003088250ca6e7c7fe649ce85820f7 b 0x00e8bee4d3e2260744188be0e9c723 r 0x0100000000000000d9ccec8a39e56f h 2 gx 0x009d73616f35f4ab1407d73562c10f gy 0x00a52830277958ee84d1315ed31886 curve sect113r2 binpoly p 0x20000000000000000000000000201 a 0x00689918dbec7e5a0dd6dfc0aa55c7 b 0x0095e9a9ec9b297bd4bf36e059184f r 0x010000000000000108789b2496af93 h 2 gx 0x01a57a6a7b26ca5ef52fcdb8164797 gy 0x00b3adc94ed1fe674c06e695baba1d curve sect131r1 binpoly p 0x80000000000000000000000000000010d a 0x07a11b09a76b562144418ff3ff8c2570b8 b 0x0217c05610884b63b9c6c7291678f9d341 r 0x0400000000000000023123953a9464b54d h 2 gx 0x0081baf91fdf9833c40f9c181343638399 gy 0x078c6e7ea38c001f73c8134b1b4ef9e150 curve sect131r2 binpoly p 0x80000000000000000000000000000010d a 0x03e5a88919d7cafcbf415f07c2176573b2 b 0x04b8266a46c55657ac734ce38f018f2192 r 0x0400000000000000016954a233049ba98f h 2 gx 0x0356dcd8f2f95031ad652d23951bb366a8 gy 0x0648f06d867940a5366d9e265de9eb240f curve sect163k1 binpoly p 0x800000000000000000000000000000000000000c9 a 1 b 1 r 0x04000000000000000000020108a2e0cc0d99f8a5ef h 2 gx 0x02fe13c0537bbc11acaa07d793de4e6d5e5c94eee8 gy 0x0289070fb05d38ff58321f2e800536d538ccdaa3d9 curve sect163r1 binpoly p 0x800000000000000000000000000000000000000c9 a 0x07b6882caaefa84f9554ff8428bd88e246d2782ae2 b 0x0713612dcddcb40aab946bda29ca91f73af958afd9 r 0x03ffffffffffffffffffff48aab689c29ca710279b h 2 gx 0x0369979697ab43897789566789567f787a7876a654 gy 0x00435edb42efafb2989d51fefce3c80988f41ff883 curve sect163r2 binpoly p 0x800000000000000000000000000000000000000c9 a 1 b 0x020a601907b8c953ca1481eb10512f78744a3205fd r 0x040000000000000000000292fe77e70c12a4234c33 h 2 gx 0x03f0eba16286a2d57ea0991168d4994637e8343e36 gy 0x00d51fbc6c71a0094fa2cdd545b11c5c0c797324f1 curve sect193r1 binpoly p 0x2000000000000000000000000000000000000000000008001 a 0x0017858feb7a98975169e171f77b4087de098ac8a911df7b01 b 0x00fdfb49bfe6c3a89facadaa7a1e5bbc7cc1c2e5d831478814 r 0x01000000000000000000000000c7f34a778f443acc920eba49 h 2 gx 0x01f481bc5f0ff84a74ad6cdf6fdef4bf6179625372d8c0c5e1 gy 0x0025e399f2903712ccf3ea9e3a1ad17fb0b3201b6af7ce1b05 curve sect193r2 binpoly p 0x2000000000000000000000000000000000000000000008001 a 0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b b 0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae r 0x010000000000000000000000015aab561b005413ccd4ee99d5 h 2 gx 0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f gy 0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c curve sect233k1 binpoly p 0x20000000000000000000000000000000000000004000000000000000001 a 0 b 1 r 0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf h 4 gx 0x017232ba853a7e731af129f22ff4149563a419c26bf50a4c9d6eefad6126 gy 0x01db537dece819b7f70f555a67c427a8cd9bf18aeb9b56e0c11056fae6a3 curve sect233r1 binpoly p 0x20000000000000000000000000000000000000004000000000000000001 a 1 b 0x0066647ede6c332c7f8c0923bb58213b333b20e9ce4281fe115f7d8f90ad r 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7 h 2 gx 0x00fac9dfcbac8313bb2139f1bb755fef65bc391f8b36f8f8eb7371fd558b gy 0x01006a08a41903350678e58528bebf8a0beff867a7ca36716f7e01f81052 curve sect239k1 binpoly p 0x800000000000000000004000000000000000000000000000000000000001 a 0 b 1 r 0x2000000000000000000000000000005a79fec67cb6e91f1c1da800e478a5 h 4 gx 0x29a0b6a887a983e9730988a68727a8b2d126c44cc2cc7b2a6555193035dc gy 0x76310804f12e549bdb011c103089e73510acb275fc312a5dc6b76553f0ca curve sect283k1 binpoly p 0x800000000000000000000000000000000000000000000000000000000000000000010a1 a 0 b 1 r 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61 h 4 gx 0x0503213f78ca44883f1a3b8162f188e553cd265f23c1567a16876913b0c2ac2458492836 gy 0x01ccda380f1c9e318d90f95d07e5426fe87e45c0e8184698e45962364e34116177dd2259 curve sect283r1 binpoly p 0x800000000000000000000000000000000000000000000000000000000000000000010a1 a 1 b 0x027b680ac8b8596da5a4af8a19a0303fca97fd7645309fa2a581485af6263e313b79a2f5 r 0x03ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307 h 2 gx 0x05f939258db7dd90e1934f8c70b0dfec2eed25b8557eac9c80e2e198f8cdbecd86b12053 gy 0x03676854fe24141cb98fe6d4b20d02b4516ff702350eddb0826779c813f0df45be8112f4 curve sect409k1 binpoly p 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 a 0 b 1 r 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf h 4 gx 0x0060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746 gy 0x01e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b curve sect409r1 binpoly p 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 a 1 b 0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f r 0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173 h 2 gx 0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7 gy 0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706 curve sect571k1 binpoly p 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 a 0 b 1 r 0x020000000000000000000000000000000000000000000000000000000000000000000000131850e1f19a63e4b391a8db917f4138b630d84be5d639381e91deb45cfe778f637c1001 h 4 gx 0x026eb7a859923fbc82189631f8103fe4ac9ca2970012d5d46024804801841ca44370958493b205e647da304db4ceb08cbbd1ba39494776fb988b47174dca88c7e2945283a01c8972 gy 0x0349dc807f4fbf374f4aeade3bca95314dd58cec9f307a54ffc61efc006d8a2c9d4979c0ac44aea74fbebbb9f772aedcb620b01a7ba7af1b320430c8591984f601cd4c143ef1c7a3 curve sect571r1 binpoly p 0x80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425 a 1 b 0x02f40e7e2221f295de297117b7f3d62f5c6a97ffcb8ceff1cd6ba8ce4a9a18ad84ffabbd8efa59332be7ad6756a66e294afd185a78ff12aa520e4de739baca0c7ffeff7f2955727a r 0x03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe661ce18ff55987308059b186823851ec7dd9ca1161de93d5174d66e8382e9bb2fe84e47 h 2 gx 0x0303001d34b856296c16c0d40d3cd7750a93d1d2955fa80aa5f40fc8db7b2abdbde53950f4c0d293cdd711a35b67fb1499ae60038614f1394abfa3b4c850d927e1e7769c8eec2d19 gy 0x037bf27342da639b6dccfffeb73d69d78c6c27a6009cbbca1980f8533921e8a684423e43bab08a576291af8f461bb2a8b3531d2f0485c19b16e2f1516e23dd3c1a4827af1b8ac15b #----- Curves from RFC2414 (Oakley) ----------------------------------------- # # oakley155 has too large a cofactor # oakley185's group has composite order; we double the generator to # produce a group of composite order curve oakley185 binpoly p 0x020000000000000000000000000000200000000000000001 a 0 b 0x1ee9 r 0x007ffffffffffffffffffffff6fcbe226dcf92105d7e53af h 4 gx 0x1bd555555555555555555555555554e8000000000000158 gy 0x14e999999999999999999999999998d7000000000001fe6 #----- NIST curves from FIPS186-2 ------------------------------------------- # # Most of these are duplicates of SEC2 curves. alias nist-p192 secp192r1 alias nist-p224 secp224r1 alias nist-p256 secp256r1 alias nist-p384 secp384r1 alias nist-p521 secp521r1 alias nist-k163 sect163k1 alias nist-k233 sect233k1 alias nist-k283 sect283k1 alias nist-k409 sect409k1 alias nist-k571 sect571k1 alias nist-b163 sect163r2 alias nist-b233 sect233r1 alias nist-b283 sect283r1 alias nist-b409 sect409r1 alias nist-b571 sect571r1 curve nist-k163n binnorm p 0x800000000000000000000000000000000000000c9 beta 0x715169c109c612e390d347c748342bcd3b02a0bef a 0x7ffffffffffffffffffffffffffffffffffffffff b 0x7ffffffffffffffffffffffffffffffffffffffff r 0x04000000000000000000020108a2e0cc0d99f8a5ef h 2 gx 0x05679b353caa46825fea2d3713ba450da0c2a4541 gy 0x235b7c6710050689906bac3d9dec76a835591edb2 curve nist-b163n binnorm p 0x800000000000000000000000000000000000000c9 beta 0x715169c109c612e390d347c748342bcd3b02a0bef a 0x7ffffffffffffffffffffffffffffffffffffffff b 0x6645f3cacf1638e139c6cd13ef61734fbc9e3d9fb r 0x040000000000000000000292fe77e70c12a4234c33 h 2 gx 0x0311103c17167564ace77ccb09c681f886ba54ee8 gy 0x333ac13c6447f2e67613bf7009daf98c87bb50c7f curve nist-k233n binnorm p 0x20000000000000000000000000000000000000004000000000000000001 beta 0x1499e398ac5d79e368559b35ca49bb7305da6c0390bcf9e2300253203c9 a 0 b 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff r 0x8000000000000000000000000000069d5bb915bcd46efb1ad5f173abdf h 4 gx 0x0fde76d9dcd26e643ac26f1aa901aa129784b71fc0722b2d05614d650b3 gy 0x0643e317633155c9e0447ba8020a3c43177450ee036d633501434cac978 curve nist-b233n binnorm p 0x20000000000000000000000000000000000000004000000000000000001 beta 0x1499e398ac5d79e368559b35ca49bb7305da6c0390bcf9e2300253203c9 a 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff b 0x1a003e0962d4f9a8e407c904a9538163adb825212600c7752ad52233279 r 0x01000000000000000000000000000013e974e72f8a6922031d2603cfe0d7 h 2 gx 0x18b863524b3cdfefb94f2784e0b116faac54404bc9162a363bab84a14c5 gy 0x04925df77bd8b8ff1a5ff519417822bfedf2bbd752644292c98c7af6e02 curve nist-k283n binnorm p 0x800000000000000000000000000000000000000000000000000000000000000000010a1 beta 0x31e0ed791c3282dc5624a720818049d053e8c7ab8663792bc1d792eba9867fc7b317a99 a 0 b 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff r 0x01ffffffffffffffffffffffffffffffffffe9ae2ed07577265dff7f94451e061e163c61 h 4 gx 0x3ab9593f8db09fc188f1d7c4ac9fcc3e57fcd3bdb15024b212c70229de5fcd92eb0ea60 gy 0x2118c4755e7345cd8f603ef93b98b106fe8854ffeb9a3b304634cc83a0e759f0c2686b1 curve nist-b283n binnorm p 0x800000000000000000000000000000000000000000000000000000000000000000010a1 beta 0x31e0ed791c3282dc5624a720818049d053e8c7ab8663792bc1d792eba9867fc7b317a99 a 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff b 0x157261b894739fb5a13503f55f0b3f10c5601166633102201138cc180c0206bdafbc951 r 0x03ffffffffffffffffffffffffffffffffffef90399660fc938a90165b042a7cefadb307 h 2 gx 0x749468e464ee468634b21f7f61cb700701817e6bc36a2364cb8906e940948eaa463c35d gy 0x62968bd3b489ac5c9b859da68475c315bafcdc4ccd0dc905b70f62446f49c052f49c08c curve nist-k409n binnorm p 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 beta 0x0dfa06be206aa97b7a41fffb9b0c55f8f048062fbe8381b4248adf92912ccc8e3f91a24e1cfb3950532b988971c23042e85708d a 0 b 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff r 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf h 4 gx 0x1b559c7cba2422e3affe13343e808b55e012d726ca0b7e6a63aeafbc1e3a98e10ca0fcf98350c3b7f89a9754a8e1dc0713cec4a gy 0x16d8c42052f07e7713e7490eff318ba1abd6fef8a5433c894b24f5c817aeb79852496fbee803a47bc8a203878ebf1c499afd7d6 curve nist-b409n binnorm p 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001 beta 0x0dfa06be206aa97b7a41fffb9b0c55f8f048062fbe8381b4248adf92912ccc8e3f91a24e1cfb3950532b988971c23042e85708d a 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff b 0x124d0651c3d3772f7f5a1fe6e715559e2129bdfa04d52f7b6ac7c532cf0ed06f610072d88ad2fdcc50c6fde72843670f8b3742a r 0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173 h 2 gx 0x0ceacbc9f475767d8e69f3b5dfab39813685262bcacf22b84c7b6dd981899e7318c96f0761f77c602c016ced7c548de830d708f gy 0x199d64ba8f089c6db0e0b61e80bb95934afd0caf2e8be76d1c5e9affc7476df49142691ad30390288aa09bcc59c1573aa3c009a curve nist-k571n binnorm p 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