If by pairing he can't decide... Craig Wright has lied! (again)

Today Wright claimed on twitter that the elliptic curve group used by Bitcoin is a pairing friendly curve as part of his ongoing effort to fake being bitcoin's creator by pretending to have special knowledge about it. (Then he went on to further embarrass himself by saying that he would somehow patent this 'fact' and make it available exclusively to his scammy BCH cryptocurrency...)

Unfortunately for Wright he has again blundered into making an easily proved claim.

On each line below are three secp256k1 public keys: A, B, C.

Exactly half of the lines are of the form A = aG, B = bG, C = abG; The other half of them are of the form A = aG, B = bG, C = H(a)G.

If you can compute a bilinear pairing in the secp256k1 group then distinguishing the two sets is trivial due to the definition of bilinearity:

The relationship e(A,B) == e(C,G) will hold only for the members of the first set, so you need only perform two pairing operations and check if they match to tell which set each line belongs in.

Wright claims that secp256k1 is compatible with bilinear pairing. He can prove his claim by simply identifying which 64 of these 128 examples the bilinear relationship holds for, something that would take only a few milliseconds of computation if his claim were true. This holds for any bilinear pairing, not just the weil pairing, it is a definitional property of bilinearity itself.

After he gives his answer I can prove or refute it by publishing the a and b secret keys behind each example and everyone can verify for themselves if wright got it right. His answer would reveal nothing about the methods he used to get the answer, only that there was some truth behind what he already claimed in public.

It's time for wright to show us if he's got a pair().

A correct answer would look like 00100110001111001101011001000111111000111101000000101010101100101011010100101000111000011100000110010000000100111111111101110111 (as an example)

 SHA256 of the correct answer: c78b98aec0401b12945428088d4ca93fcbbfed47da220f9410dd648682a8bfe1 000: 02050b1250dbc82596de1600581822248cd7bf1ef38c5a2810bb1b85d68a4580ea 02ce9dc182687c7ca13b48a0260a0e1547745b66b6021fa81eba20b619d3f750b2 0383a24eb1360635ba932be7797ad99a267a30548782713e1f8d59d2f9020062fa 001: 022fb3d0b902aa60511b83bc665099f84678856c7d8bbbd4322fec9a421ed801b4 02e5955925f250d4e2c189d082c0ec6fb0d3d537b85308be1a5fcb67ff13d49473 023c0c102f7bd014fb240e64b33b88978ec0d98ef17686c8f55e5133f09025b9d4 002: 027813da648632fad396ad849bf4af5d308385c3633d3a9f76482f29b7536135b8 02a6ae1fe5be383aa136c8b00e098d11b57a940736111d814d087fdac39f7b9a89 02c14f5bf150928879ed9b4b329e52105f140eb4665d711404c3d787a9c6a912da 003: 034431a903fb0d49efe3992f95af20c17993cc306c2b2330c5d59626b49cb30e7d 039ef80f5b70b084314f1adf2991353f9285bc162e0ca40eafbd8f6e42ebe62eea 03822e72862627e087ee7ba01c6f774ec694252e77672b6604c9e419678c85cda4 004: 0256c81b43dbfc47c62d2c5447a147ecc6b6554a3286fd6dc7da067977b94e4708 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The sage notebook used generate this challenge is available.

Submitted October 29, 2017 at 05:14AM by nullc http://ift.tt/2zfKw51