A new year's puzzle:
(We use a toy version of bitcoin in which the group order is 19. So notice that e.g. 1/7 is 7^-1 mod 19 = 11. If you want an easy way to do that, do pow(7, -1, 19) in python.)
Michael makes two Bitcoin transactions using taproot, so the signatures are Schnorr signatures. s_1 = 16 and s_2 = 18.
His transaction hashes (the H(P, R, m) values) were e_1 = 12 and e_2 = 3.
But Michael did something unusual. He used a secret nonce both times (so k_1 and k_2 are secret), but he made it known that each new nonce he uses, he will increment the value by 7.
What is Michael's private key?
#cryptography #bitcoin
Secret nonce you say?
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That's why Adam Langley at Google always used to pronounce it "N-once", to the confusion of some Americans :)
Wise, I don't think I could sit in a room with people saying nonce repeatedly without giggling.
