Efficient group signature scheme using lattices

Abstract

Group signature scheme is a cryptographic primitive that allows its registered group users (or members) to generate signatures on behalf of the whole group without revealing their identity. An important feature of a group signature scheme is revocation, which allows an authorized entity called group manager to remove users from the group. Verifier Local Revocation (VLR) is a most commonly used revocation mechanism in group signature schemes because of its simplicity and efficiency. In VLR, the group manager maintains a publicly available revocation list that contains information about the revoked users. The cost of group signature verification is proportional to the size of the revocation list. To decrease the verification cost, it is enough to reduce the size of the revocation list. We use the notion of time bound signing keys for this and propose a dynamic group signature scheme. In the proposed scheme, an expiration time $\tau$ is fixed for the signing key of each group member. A user who is generating signature at time t must prove, he is a valid group member and his signing key is not expired, i.e., $t \le \tau$. Group user after the signing key expiration time are considered as ‘naturally’ revoked. Group users may be revoked before the expiration time if necessary, and it is considered ‘premature’ revocation. Hence, the revocation list needs to include the information about prematurely revoked users only. As a result, the size of the revocation list will be small, particularly in situations where natural revocation accounts for a large proportion of the total revocation.