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What you're asking for is akin to multiplication, which is just repeated addition. As we know from our grade school classes, these are reversible with subtraction and division. My understanding of the current state of the art is that in order to make it not trivial to reverse, it requires the input of previous state to generate next state--each subsequent ...


You might also want take a look at sponges function (f in the following image). your p0 ... pi is your input (absorbing phase), while z0 ... zp is what you get when squeeze it p times. for more informations : sponge corner Keccak (SHA-3) has been implemented using it. You could consider the compression function f as your hashing algorithm and squeeze ...


Q: Why do cryptographic hashes need to have a fixed length output? I know that the shallow answer is that an output that varies by key size or file size can leak information somehow, leading to cryptanalysis, but I would like some more intuition as to why this is the case. It depends on what you mean with that. If you mean that they need to have a ...


They don't, and in fact the sponge construction used in Keccak (SHA-3) allows for variable length output. In other hashes the Merkle-Damgård construction was used which has a fixed output length due to the nature of its design. But there is no reason to not allow for variable output length other than ease of development or use.

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