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I think you have some misunderstanding here. Finding collisions when knowing the trapdoor is a required feature, but leaking the trapoor when knowing collisions is an undesirable "feature" (which some constructions suffer from). A chameleon hash function (aka trapdoor commitment) allows you given the trapdoor to find pairs $(m,r)$ and $(m',r')$ with $m\neq ...


1

As the other answers point out, output bits of a good hash function are uniformly distributed, so your substring has equal chance to appear in any part of the hash digest. However, in the case of Bitcoin, the address is not a random string. Not only it starts with a predefined number (1 or 3), but the string is the result of the Base58-conversion, which may ...



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