New threshold-proxy threshold-signature schemes

A new (t, n) threshold-proxy (c, m) threshold-signature scheme is proposed in this paper. In this scheme, only any t or more original signers of n original signers can authorize a proxy group of m proxy signers and then only c or more proxy signers can cooperatively generate threshold-proxy threshold-signatures. Our scheme provides the fair protection for the original and proxy groups. So original signers cannot forge the proxy signatures while the proxy signers cannot forge signatures on behalf of the original signers. Moreover, our scheme satisfies the seven conditions proposed by Mambo et al. Further, in our scheme, the verifier has to verify the correctness of the threshold proxy certificate before checking the correctness of the threshold-proxy threshold-signatures. To meet the practical situations, the proxy agreement is reached not only the original group but also the proxy group. To realize this new kind of agreement, the scheme provides two options for the generation of threshold-proxy certificates: threshold and total agreements. The total agreement option provides the flexible for the proxy group that the members cannot trust with each other. The best way to agree on the proxy authorization is the common view reached by all members.