A New Fully Homomorphic Signatures from Standard Lattices

Abstract

Recently, Gorbunov, Vaikuntanathan and Wichs[6] propose a new powerful (fully) homomorphic trapdoor function (HTDF) based on small integer solution (SIS) problem in standard lattices, and construct the first fully homomorphic signature (FHS) schemes. Later Wang et al.[10] extend the notion of HTDF to identity-based setting with strongly security and construct the first identity based fully homomorphic signature (IBFHS) schemes. In this paper, we provide a new IBHTDF which satisfies claw-free and collision-resistant. Moreover, we find a homomorphic algorithm for our new IBHTDF where the noise level of multiplication gate is the same as that of addition gate. So, the noise level of IBHTDF for evaluating a circuit of depth d is reduced from to. Finally, we construct a new leveled strongly-unforgeable identity-based fully homomorphic signature (IBFHS) schemes based on our IBHTDF.