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, we show 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). Then, a weaker property than pseudo-randomness is introduced in order to characterize the security of the canonical SSSC from its filtering function. A connection with the left-or-right indistinguishability (LOR-IND) is made. This property provides a necessary and sufficient condition to characterize the indistinguishablity of SSSC.