Cryptanalysis and improvement of nonrepudiable threshold multi-proxy multi-signature scheme with shared verification

Recently, Tzeng et al. proposed a nonrepudiable threshold multi-proxy multi-signature scheme with shared verification. In their scheme, a subset of original signers can delegate the signing power to a group of the designated proxy signers in such a way that: (i) A valid proxy signature can only be generated by a subset of these proxy signers for a group of the designated verifiers. (ii) The validity of the generated proxy signature can only be verified by a subset of the designated verifiers. This article, however, will demonstrate a security leak inherent in Tzeng et al.’s scheme that any verifier can check the validity of the proxy signature by himself with no help of other verifiers. That is, Tzeng et al.’s scheme cannot achieve their claimed security requirement. Finally, we will propose an improvement to eliminate the pointed out security leak.