Digital signatures are one of the fundamental security primitives because they provide authenticity and nonrepudiation in the broadcast/multicast communication networks. However, the current broadcast/multicast authentication standards are vulnerable to signature flooding because excessive signature verification requests exhaust the computational resource of victims. The situation becomes worse in the case of the energy-constrained networks such as wireless sensor networks and mobile ad hoc networks. As an essential variation of ordinary digital signature schemes, multisignature schemes enable a single compact signature to authenticate a message under a set of different signers. In this paper, we first propose an efficient identity-based multisignature scheme with three interactive rounds under quadratic residue assumption, which equals to the large integer factoring assumption. By using the technique of quadratic residue-based multiplicatively homomorphic equivocable commitment, an advanced identity-based multisignature scheme is proposed to achieve to reduce the interactive round complexity to two rounds. We give the formal security proof that our schemes are existentially unforgeable under adaptively chosen message attacks and chosen identity attacks in the random oracle model. Compared with the previous work, our schemes are very efficient. In particular, our schemes are featured by the weak assumption and the efficient signing and verification procedures. Copyright © 2012 John Wiley & Sons, Ltd.