Improvement on Tzeng et al.'s nonrepudiable threshold multi-proxy multi-signature scheme with shared verification

Tzeng et al. proposed a novel variation of proxy signature scheme called threshold multi-proxy multi-signature scheme with shared verification. However, their scheme has some security weaknesses. In this paper, by identifying some concrete instances and analyses, we will show that their scheme cannot resist frame attacks. That is, after intercepting a valid proxy signature generated by a subset of a proxy group, an adversary can frame new signatures, which can be authenticated as if they were generated by the subset of the proxy group on behalf of the adversary. Furthermore, their scheme needs a trusty share distribution center (SDC) for setting some parameters and initialization of the scheme. To overcome these weaknesses, we also propose our improvement with no SDC in this paper.