This paper studies the security level expected by the canon-ical 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 (PRF) are used as filtering functions. In this case, it is shown that the security against chosen-ciphertext attacks (IND-CCA security) cannot be reached for the canonical form of the SSSC, but it is however secure against chosen plaintext attacks (IND-CPA secure). This result guarantees the existence of SSSC that can be IND-CPA secure although till now, the SSSC proposed in the open literature had be broken against IND-CPA attacks. The security proof lies on the property of indistin-guishability.