An identity-based signature scheme from lattices is constructed. The scheme is obtained from a modification of Agrawal, Boneh, and Boyen's lattice identity-based encryption scheme. In this construction, we use two distinct trapdoors for finding short bases. One trapdoor enables the real implementation to generate short bases for all lattices. The other trapdoor enables the simulator to generate short bases for all lattices. Furthermore, the generating short bases are used to sample short vectors as signatures. Our scheme is computationally efficient. The scheme's strong unforgeability is proven in the standard model and rests on the hardness of the small integer solution problem. Finally, we extend the basic construction to obtain a hierarchical identity-based signature scheme. Copyright © 2012 John Wiley & Sons, Ltd.