Attainable Unconditional Security for Shared-Key Cryptosystems

Preserving the privacy of private communication is a fundamental concern of computing addressed by encryption. Information-theoretic reasoning models unconditional security where the strength of the results is not moderated by computational hardness or unproven results. Perfect secrecy is often considered the ideal result for a cryptosystem, where knowledge of the ciphertext reveals no information about the key or message, however often this is impossible to achieve in practice. An alternative measure is the equivocation, intuitively the average number of message/key pairs that could have produced a given ciphertext. We show a theoretical bound on equivocation called max equivocation and show that this generalizes perfect secrecy when achievable, and provides an alternative measure when perfect secrecy is not. We derive bounds for max-equivocation, and show that counter intuitively max-equivocation is achieved when the entropy of the ciphertext is minimized. We consider encryption functions under this new information, and show that in general the theoretical best is unachievable, and that some popular approaches such as Latin squares or Quasigroups are also not optimal. We present some algorithms for generating encryption functions that are practical and achieve 90-95% of the theoretical best, improving with larger message spaces.