International Association
for Cryptologic Research

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 {\\it et al.} (Asiacrypt \'13)

and Langlois {\\it 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.