E-voting is an important application of secure MPC (multi-party computation) and its achievement of security through verifiable MPC can be based on homomorphic encryption or shuffling. Homomorphic-encryption-based e-voting is often less costly than shuffling-based e-voting, but depends on validity of the encrypted ballots. Proof and verification of validity of all the encrypted ballots is the efficiency bottleneck to overcome. So homomorphic e-voting schemes still need efficiency improvements to support users with low-capability. In this paper, a novel e-voting scheme is proposed on the basis of an efficiency-improving technology, batch ZK proof of 1-out-of-2 knowledge. It achieves much higher efficiency in ballot validity proof and can improve efficiency of homomorphic e-voting to achieve an obvious advantage over the existing solutions. It is a good example to illustrate how efficiency of secure MPC can be improved by batch cryptology.