Cryptanalysis of multivariate threshold ring signature schemes

Abstract

Petzoldt et al. proposed the first multivariate threshold ring signature scheme extending the idea of a ring identification scheme in 2013. They claimed that their t-out of n threshold ring signature satisfies the security properties of unforgeability and source anonymity. Later, Zhang-Zhao in 2014 and Duong et al. in 2021 proposed other multivariate threshold ring signature schemes using different tools with the same technique. In this article, we cryptanalyze all these schemes and give an attack on their source anonymity which shows how the verifier can find the actual set of signers after some finite number of trials, viz., with at most N=(nn−t)+(nn−t−1)+…+(n1)+(n0) in t-out of n threshold ring.