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 \(O(n^2\log ^2 n \log N)\)-bit group public key and \(O(n\log ^3 n\log N)\)-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 \(O(\log N)\) 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.