Threshold signature schemes with traceable signers in group communications

Distributed and dynamic threshold group signature scheme

“…Note: Here employs the way in Wang et al's scheme [18] to identify who the signers are, but overcome the weakness in Wang's scheme, that is, the clerk or attacker can forge identity function, so the verifier does not know who the real signers are.…”

Improvement of the Miyazaki–Takaragi threshold digital signature scheme

“…That is, as compared to Eqs. (5) and (6), the verifier will be convinced that (r , v ) is a valid group signature for m . ✷…”

“…In the grouporiented applications, the group signature can be generated by one member, some members, or all members according to the group's signing policy. Among these signing strategies, (t, n) threshold digital signature [3][4][5] provides the most flexibility. Applying the (t, n) threshold technique to generate a group signature, any more than t members in the group of n members can collaborate to sign the message on behalf of the group, while less than or equal to t − 1 members cannot.…”

(t, n) Threshold Digital Signature Scheme with Traceable Signers against Conspiracy Attacks

“…Unfortunately, the above schemes [1,3] suffer from the conspiracy attacks and the secret keys can be revealed with high probability [5]. To avoid the attacks and to be able to trace back to find the singers without the revealing the secret keys, Wang et al [6] for the first time proposed two grouporiented ( , ) t n threshold digital signature schemes, one needs the assistance of a mutually trusted center, and the other does not need. However, Tseng and Jan [7] show that Wang et al group-oriented ( , ) t n threshold digital signature schemes are insecure under a forgery attack.…”