A new kind of proxy signature schemes is first proposed: multi-proxy multi-signature schemes. In multi-proxy multi-signature schemes, an original group of signers can authorize a group of proxy signers under the agreement of all singers both in the original group and proxy group. Then only the cooperation of all singers in proxy group could generate multi-proxy multi-signatures. To realize this new kind of proxy signature schemes, two multi-proxy multi-signature schemes are also proposed in this paper. The first scheme needs the help of clerks while the second does not. Both in these two schemes, the sizes of both the proxy certificate and the multi-proxy multi-signature are independent on the number of original or proxy singers. The verification of multi-proxy multi-signatures is similar to that of proxy signatures. So the new scheme is efficient. The new scheme also provides the fair protection for the original signer group and the proxy group. Further, there is no secure channel in the new scheme. This new scheme is secure against the insider attack that is a powerful attack on the multi-signature schemes.
Applied Mathematics and Computation 147(1), pp.57-67