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comment What is the lowest level of mathematics required in order to understand how encryption algorithms work?
Yes, XOR is minimal (but does it provide a "good understanding" of encryption?). The perfect security of OTP doesn't matter in practice, since OTP requires securely storing a key that's the same size as the text (and only using it once) so its rarely used in practice (why not just store the text securely)? But the math I mentioned doesn't require devoting your whole life to it; learning modular arithmetic to understand RSA takes a few days at most if you take the time to digest each part and play around with toy examples. Yes, there's much more to learn after that, but its easy to start.
comment Is every output of a hash function possible?
@fgrieu - No its demonstratable. H(m) maps {0,1}^infinity to {0,1}^N for an N-bit hash function. So, H(H(m)) at the outer function call takes {0,1}^N as input and maps it to {0,1}^N. Thus if we assume one single collision exists (which we expect with overwhelming probability for any hash function -- they intend to attack as random oracles not as permutations), then by the pigeonhole principle the whole output space is not reachable.
comment LT codes with Homomorphic hashing
@makerofthings7 ⊕ is one customary way of writing xor (exclusive or).
comment Can I construct a zero-knowledge proof that I solved a Project Euler problem?
@poncho - yes edited obviously was not thinking clearly. (The answer I got is roughly 1/3 of that so that's a much more reasonable limit).