Randomized encryption techniques, where randomness is used for security enhancement, are considered. We focus on the case where the encrypted data experiences noise, e.g., is transmitted over a noisy channel, within the encoding-encryption paradigm, where the data is first encoded for error correction, before being encrypted for security. We assume that the ciphertext is subject to a corruption equivalent to its transmission through a binary symmetric channel with known probability of error. The enhanced security is based on a dedicated wire-tap channel coding that introduces extra randomness, combined with that of the communication channel noise. The encryption is based on a block-by-block modulo 2 addition between an encoded message vector and a pseudorandom vector. The goal is to enhance the protection of the secret key employed in the encryption algorithm. Security evaluations of the model are performed employing an information-theoretic approach. Assuming both a passive and an active attacker, we show that there is a threshold before which the wire-tap encoder guarantees an information-theoretic security (during which the equivocation of the secret key is increased), and after which the uncertainty reduces, entering a regime in which a computational security analysis is needed for estimating the complexity resistance against the secret key recovery.

NRF (Natl Research Foundation, S’pore)