Cryptanalysis of Several Linkable Ring Signature Schemes

The notion of linkable ring signature, introduced by Liu et al. in 2004, provides signer anonymity and spontaneity, but at the same time, allows anyone to determine whether two signatures have been issued by the same group member (linkability).In 2006, Liu-Wong capture stronger notions of signer anonymity and linkability than the original ones proposed by Liu et al. in 2004. And, they proposed a generic approach for constructing a linkable ring signature scheme. In 2007, Au-Liu-Susilo-Yuen proposed certificate based linkable ring signature. In 2005, Tsang-Wei proposed short linkable ring signatures for E-voting, E-cash and attestation. Through cryptanalysis, we found that all these three linkable ring signature schemes can´t satisfy the linkability. Anyone in the ring can impersonate other member to sign the linkable ring signature. In addition, most of the proposed linkable ring signature schemes can not also satisfy the linkability. To design secure linkable ring signature scheme is still an open problem.