A conditionally anonymous ring signature, first studied by Komano et al. (RSA06) (termed as a deniable ring signature), is a ring signature except that the anonymity is conditional. Specifically, it allows an entity to confirm/refute that he generated a signature. A group signature also has conditional anonymity since a group manager can revoke a signer’s anonymity. However, the group in this case is fixed, unlike a ring signature where a group is ad hoc. In this paper, we construct a new conditionally anonymous ring signature. Our signing/verification algorithms are asymptotically most efficient, compared with all known schemes. Our confirmation/disavowal protocols are non-interactive with constant costs while the known schemes have a cost linear in either ring size n or security parameter s.