And that's why keys of one byte are a bad idea. Bad in symmetric, bad in asymmetric, just plain bad. This same attack is true for any block-level encryption - i

And that's why keys of one byte are a bad idea. Bad in symmetric, bad in asymmetric, just plain bad. This same attack is true for any block-level encryption - it doesn't make them insecure. And homomorphic encryption needs, if I remember right, enormous relatively-prime numbers. Like, gigabytes worth. We're not talking small keys here. This is incorrect. The key size has nothing to do with extracting one byte. As mentioned later in the thread, if the encryption is not randomized (and Craig's scheme is, like all "semantically-secure" encryption schemes) then the ciphertext leaks no information about the plaintext even if it were only one bit. However, if the encryption is not randomized then trivially, your encryption is only as secure as your plaintext space. Secondly, you say homomorphic encryption needs enormous relatively-prime numbers. This is not correct. Craig's sceme uses lattice-based cryptography. The keys are long because we don't have efficient reductions to hard problems and the best algorithms to solve lattice problems currently known are better than brute force (so we need to increase parameters to make the best algorithms known today take at least 2^80 time, if not more).