Improvement of identity-based proxy multi-signature scheme

A proxy signature scheme allows a proxy signer to sign messages on behalf of an original signer, a company or an organization. A proxy multi-signature scheme is an extension of the basic proxy signature scheme, and permits two or more original signers to delegate their signing powers to the same proxy signer. Recently, Wang and Cao proposed an identity-based proxy multi-signature scheme. This scheme is very simple and efficient since it is an extension of the identity-based aggregate signature scheme due to Gentry and Ramzan. Though the identity-based aggregate signature scheme of Gentry and Ramzan is secure in the random oracle model, in this paper, we find that the identity-based proxy multi-signature scheme of Wang and Cao is not secure unless each proxy secret key can only be used to generate at most one proxy signature. Finally, we propose an improvement to overcome this weakness, which is more simple and efficient than the identity-based proxy multi-signature scheme of Wang and Cao. We show that the improvement is existentially unforgettable in the random oracle model under the computational Diffie–Hellman assumption.