That's why I said "almost" :) AFAIK, cryptography without P != NP is an open question. BTW, quantum encryption is not encryption as we know it (a purely functi

That's why I said "almost" :) AFAIK, cryptography without P != NP is an open question. BTW, quantum encryption is not encryption as we know it (a purely functional deterministic bijective transformation of the message), as it requires special hardware, optical fibers, etc... As of EXP etc... I am not aware of any (theoretical) encryption schemes that use problems harder than NP (actually most use circuit complexity, so NP/poly, but it is related). In designing encryption you often want polynomial verifiability (for decryption), and that implies NP membership.