A CDH-Based Multi-Signature Scheme with Tight Security Reduction

Abstract

An efficient multi-signature scheme secure in the random oracle model is proposed, which is the first multi-signature scheme with tight security reduction to the hardness of computational Diffie-Hellman (CDH) problem. The scheme only needs the proof-of-possession (POP) key registration assumption to prevent the notorious rogue key attacks and obtain existentially unforgeable security against the adaptively chosen message and signing groupattack. Given current state of the art, it is as difficult to solve the CDH problem as it is to solve the DL problem in many groups of cryptographic interest. Thus the scheme with tight security reduction offers substantially better efficiency (for a given level of provable security) than other schemes in the discrete logarithm setting. Moreover, both the size of multi-signature and the computational cost of verification do not increase with the number of actual signers increasing. Therefore, the proposed scheme is efficient and can be conveniently implemented in the current public key infrastructure (PKI) environment.