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 without pairings. Up to now, there still remains a challenge to construct a provably secure and efficient IBS scheme without pairings. In this paper, we propose an efficient IBS scheme based on cubic residues, and we prove that our scheme is secure against adaptively chosen message and ID attack.