CHide is one of the most prominent e-voting protocols, which, while combining security and efficiency, suffers from having very long encrypted credentials. In this paper, starting from CHide, we propose a new protocol, based on multiparty Class Group Encryption (CGE) instead of discrete logarithm cryptography over known order groups. We achieve a computational complexity of O(nr), for n votes and r voters, while calling the MixNet algorithm one time. The homomorphic properties of CGE allow for credentials that are shorter by a factor of 20 while maintaining the same level of security, at the cost of a small slowdown in efficiency.