On the Security of the Li-Hwang-Lee-Tsai Threshold Group Signature Scheme

A (t, n) threshold group signature scheme is a generalization of group signature, in which only t or more members from a given group with n members can represent the group to generate signatures anonymously and the identities of signers of a signature can be revealed in case of dispute later In this paper, we first present a definition of threshold group signatures, and propose several requirements to evaluate whether a threshold group signature scheme is secure and efficient. Then we investigate the security and efficiency of a threshold group signature scheme proposed by Li, Hwang, Lee and Tsai, and point out eight weaknesses in their scheme, The most serious weakness is that there is a framing attack on their scheme. In this framing attack, once the group private key is controlled ( n-t+1) colluding group members can forge a valid threshold group signature on any given message, which looks as if it was signed by (t-1) honest group members and one cheating member. At the same time, all these (t1) honest members cannot detect this cheating behavior, because they can use the system to generate group signatures normally