Identity Based Multi-proxy Multi-signcryption Scheme for Electronic Commerce

A new concept called multi-proxy multi-signcryption is introduced in this paper. In a multi-proxy multi-signcryption scheme, a group of original signcrypters can authorize a group of proxy signcrypters under the agreement of all signcrypters in the original group. Then only the cooperation of all signcrypters in the proxy group could generate a multi-proxy multi-signcryption. We propose a multi-proxy multi-signcryption scheme based on bilinear pairings. The proposed scheme has the following characteristics: (i) the size of multi-proxy multi-signcryption is independent of the number of original and proxy signcrypters. (ii) it provides the fair protection for the original signcrypter group and the proxy group.(iii) the key management problem is simplified because of using ID-based cryptography. Finally, we give an application of the proposed scheme in electronic commerce.