New pseudorandom functions based on SIS

Abstract

Pseudorandom functions are vital tools in the construction of cryptographic primitives.Under the hard assumption of SIS (short integer solution),two lattice-based pseudorandom functions are proposed.The first one has parallel structure by the ideal of tree-like pseudorandom synthesizer,and the second one is serial structure whose public key size is reduced.Both constructions have small modulus and provable security.Compared with A Banerjer,C Peikert and A Rosen’s construction (EUROCRYPT 2012),their key sizes are asymptotically smaller,and efficiency are improved by avoiding the “rounding” technology.

Keywords

• pseudorandom function;lattice;short integral solution problem;hybrid argument