Abstract. The problem of revocation in anonymous authentication systems is subtle and has motivated a lot of work. One of the preferable solutions consists in maintaining either a whitelist LW of non-revoked users or a blacklist LB of revoked users, and then requiring users to additionally prove, when authenticating themselves, that they are in LW (membership proof) or that they are not in LB (non-membership proof). Of course, these additional proofs must not break the anonymity properties of the system, so they must be zero-knowledge proofs, revealing nothing about the identity of the users. In this paper we focus on the RSA-based setting and we consider the case of non-membership proofs to blacklists L = LB. The existing solutions for this setting rely on the use of universal dynamic accumulators [20]; the underlying zero-knowledge proofs are a bit complicated and thus their efficiency, although being independent from the size of the blacklist L, seems to be improvable. Peng and Bao [21] already tried to propose simpler and more efficient zeroknowledge proofs for this setting, but we prove in this paper that their protocol is not secure. We fix the problem by designing a new protocol and formally proving its security properties. We then compare the efficiency of the new zero-knowledge non-membership protocol with that of the protocol in [20], when they are integrated with anonymous authentication systems based on RSA (notably, the IBM product Idemix for anonymous credentials). We discuss for which values of the size k of the blacklist L one protocol is preferable to the other one and we propose different ways to combine and implement the two protocols.