Efficient fuzzy identity-based signature from lattices for identities in a small (or large) universe

Abstract

Fuzzy identity-based signature (FIBS) is exactly like a traditional identity-based signature (IBS) except that a signature issued under an identity id can be verified under any identity id′ that is “close enough” to id. This property allows FIBS having an efficient application in biometric authentication and only four schemes on lattices exist, among which three constructions are existentially unforgetable against adaptively chosen identity and chosen message attacks (EU-aID-CMA) in the random oracle model, the only exception proved to be strongly unforgetable against selectively chosen identity and chosen message attacks (SU-sID-CMA) is constructed in the standard model. In this work, we first propose a new FIBS from the hardness of lattice problems for identities living in a small universe, i.e., {0, 1}ℓ, this new construction is proved to be SU-sID-CMA in the standard model. Furthermore, a new FIBS scheme for identities living in a large universe, i.e., (Zqn)ℓ, is proposed, so that it can capture more expressive attributes and this construction is proved to be EU-aID-CMA in the random oracle model. In particular, compared with the existing lattice FIBS schemes, both new constructions enjoy a smaller communication cost, and the faster signing and verifying operations, thus, they are more practical.