An Information-Theoretic Security Evaluation of a Class of Randomized Encryption Schemes

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.