Simpler efficient group signatures from lattices

Abstract

A group signature allows a group member to anonymously sign messages on behalf of the group. In the past few years, new group signatures based on lattice problems have appeared: the most efficient lattice-based constructions are due to Laguillaumie et al. (Asiacrypt’13) and Langlois et al. (PKC’14). Both have at least O(n2 log2 n logN)-bit group public key and O(n log3 n logN)-bit signature, where n is the security parameter and N is the maximum number of group members. In this paper, we present a simpler lattice-based group signature, which is more efficient by a O(logN) factor in both the group public key and the signature size. We achieve this by using a new non-interactive zero-knowledge (NIZK) proof corresponding to a simple identity-encoding function. The security of our group signature can be reduced to the hardness of SIS and LWE in the random oracle model.