Many identity based signature (IBS) schemes have been proposed so far. However, most of the schemes are based on bilinear pairings. Only a few IBS schemes are with-out pairings. Up to now, there still remains a challenge to construct a provably secure and effcient IBS scheme without pairings. In this paper, we propose an effcient IBS scheme based on cubic residues, and we prove that our scheme is secure against adaptively chosen message and ID attack.