A novel fuzzy identity based signature scheme based on the short integer solution problem

Lattice-based cryptosystems have recently acquired much importance. In this work, we construct a fuzzy identity based signature (FIBS) scheme based on the Small Integer Solution (SIS) Problem. FIBS schemes allow a user with identity id to issue a signature which could be verified under identity id′ if and only if id and id′ are close to each other. To our best knowledge, no lattice based FIBS schemes were known before, and the existing security model of FIBS schemes is not correct indeed. We propose a modified security model and prove that our scheme is existentially unforgetable against adaptively chosen message and identity attacks in the random oracle model. To break the bottleneck of designing lattice-based FIBS scheme, the secret key of each identity bit is generated by employing the Bonsai Tree techniques in the fuzzy extract algorithm. We also use some techniques to prove its security. Then we show the performance comparisons of all existing FIBS schemes. Finally, we give its application in biometric authentication.