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3

Yes, this should be secure, as it is largely compatible with KDF1 and KDF2 which basically use a 4 byte big endian encoding of the counter instead of a direct ASCII conversion to a byte. Note that this construct works fine for master keys (short length, high entropy) but may be vulnerable to length extension attacks if larger input is allowed. However, if ...


3

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 ...


2

Depends on what you mean by Keccak. There is actually a slight issue here that not all 256-bit Keccak variants have 256-bit preimage resistance. SHA3-256 (in the current SHA-3 draft) does have 256-bit preimage, but if you are using Keccak with 256-bit capacity it only has 128-bit preimage resistance. At least some of the earlier documents had 256-bit output ...


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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