Security proof of the canonical form of self-synchronizing stream ciphers

Abstract

This paper is concerned with the security level expected by the canonical form of the self-synchronizing stream cipher (SSSC). A SSSC can be viewed as the combination of a shift register together with a filtering function. The maximum security of such a cipher is reached when the filtering function is random. However, in practice, pseudo random functions are used as filtering functions. In this case, we show that the security against chosen ciphertext attacks (IND-CCA security) cannot be reached but it is however secure against chosen plaintext attacks (IND-CPA secure). To relax the condition of pseudo randomness, a new family of functions with a weaker property is introduced. A connection with the left-or-right indistinguishability is made. This property provides a necessary and sufficient condition to characterize the indistinguishablity of SSSC.