Insider attacks on multi-proxy multi-signature schemes

In 2004, Hwang and Chen demonstrated new multi-proxy multi-signature schemes that allow a group of authorized proxy signers to sign messages on behalf of a group of original signers. Later, Lyuu and Wu pointed out Hwang et al.’s schemes were not secure and then proposed a modified scheme. They claimed that their modified schemes were secure. But in this paper we show a new attack on the Lyuu–Wu et al.’s schemes. Moreover, the original Hwang–Chen’s schemes are also vulnerable to this insider attack. Furthermore, we point out some improvements for the Lyuu–Wu scheme and Hwang–Chen schemes according to Wang et al.’s methods [Wang GL, Han XX, Zhu B. On the security of two threshold signature schemes with traceable signers. In: Applied Cryptography and Network Security (ACNS 2003). Lect Notes Comput Sci (LNCS), vol. 2846, Springer-Verlag; 2003. p. 111–222]. These improvements can resist our insider attack.