Abstract: Multi-signcryption means two or more parties sign the same message, moreover, the length of signcryption cannot linearly increase for the increasing of the number of signers. Although ordinary ElGamal multi-signature satisfies the unforgeability, however, it can’t resist joint attack of multiple signers. In order to overcome the shortcomings of existing ElGamal multi-signature, the authors integrate the techniques of ElGamal multi-signature and signcryption to present a new ElGamal broadcasting multi-signcryption (EBMSC) protocol. We also describe its algorithm definition and security model, and prove its semantical security under the discrete logarithm (DL) and computation Diffie-Hellman (CDH) assumptions in the random oracle model (ROM). At the same time, we define the ideal function and the real protocol of EBMSC protocol under the universally composalble (UC) security framework, and then prove that the real protocol can realize the ideal function of EBMSC protocol. It also proves that the real protocol is unforgeable under unforgeability against adaptive chosen message attacks. Finally, the efficiency comparison between EBMSC protocol and existing protocols is given. Analysis results show our protocol not only is more efficient than existing protocols but also implements the function of multi-signcryption in UC security framework. Our protocol can be suitable for applications in e-commerce, contract signing, online transaction and financial accounting.

Key words: ElGamal multi-signature, ElGamal broadcasting multi-signcryption (EBMSC), semantical security, random oracle model, universally composalble (UC) security