Cryptanalysis and Improvement of a Ring Signature Based on ElGamal Signature

The concept of ring signature was first introduced by Rivest et al. in 2001. In a ring signature, instead of revealing the actual identity of the message signer, it specifies a set of possible signers. The verifier can be convinced that the signature was indeed generated by one of the ring members; however, the verifier is unable to tell which member actually produced the signature. A convertible ring signature scheme allows the real signer to convert a ring signature into an ordinary signature by revealing secret information about the ring signature. Thus the real signer can prove the ownership of a ring signature if necessary, and the the other members in the ring can not prove the ownership of a ring signature. At WASA 2006, Jian Ren and Lein Harn proposed a ring signature based on ElGamal signature scheme. The authors claimed that the proposed scheme had the following advantage: the proposed ring signature is inherently a convertible ring signature and enables the actual message signer to prove to a verifier that only he is capable of generating the ring signature. Through our analysis, we find this ring signature scheme can't satisfy this advantage, i.e., it isn't convertible. In order to realize the advantage: convertibility, we improved the original scheme. The improved ring signature scheme can satisfy the advantage and is secure.