Unconditionally Secure Ciphers with a Short Key for a Source with Unknown Statistics

Abstract

We consider the problem of constructing an unconditionally secure cipher with a short key for the case where the probability distribution of encrypted messages is unknown. Note that unconditional security means that an adversary with no computational constraints can only obtain a negligible amount of information (“leakage”) about an encrypted message (without knowing the key). Here, we consider the case of a priori (partially) unknown message source statistics. More specifically, the message source probability distribution belongs to a given family of distributions. We propose an unconditionally secure cipher for this case. As an example, one can consider constructing a single cipher for texts written in any of the languages of the European Union. That is, the message to be encrypted could be written in any of these languages.

Keywords

• cryptography
• unconditionally secure cipher
• entropically-secure symmetric encryption scheme
• indistinguishability
• data compression
• universal code