We describe the first efficient ring signature scheme secure, without random oracles, based on standard assumptions. Our ring signatures are based in bilinear groups. For l members of a ring our signatures consist of 2l + 2 group elements and require 2l + 3 pairings to verify. We prove our scheme secure in the strongest security model proposed by Bender, Katz, and Morselli: namely, we show our scheme to be anonymous against full key exposure and unforgeable with respect to insider corruption. A shortcoming of our approach is that all the users’ keys must be defined in the same group.

Proxy ring signature allows proxy signer to sign messages on behalf of the original signer while providing anonymity. Certificateless public key cryptography was first introduced by Al-Riyami and Paterson in Asiacrypt 2003. In certificateless cryptography, it does not require the use of certificates to guarantee the authenticity of users ’ public keys. Meanwhile, certificateless cryptography does not have the key escrow problem, which seems to be inherent in the Identity-based cryptography. In this paper, we introduce the notion of proxy ring signature into certificateless public key cryptography and propose a concrete certificateless proxy ring signature scheme. The security models of certificateless proxy ring signature are also formalized. The security of the proposed scheme can be proved to be equivalent to the computational Diffie-Hellman problem in the random oracle with a tight reduction.