Zero-knowledge Identification based on Lattices with Low Communication Costs

Abstract

In this paper we propose a new 5-pass zero-knowledge identification scheme with soundness error close to 1/2. We use the hardness of the Inhomogeneous Small Integer Solution problem as security basis. Our protocol achieves lower communication costs compared with previous lattice-based zeroknowledge identification schemes. Besides, our construction allows smaller public and secret keys by applying the use of ideal lattices. We allow the prover to possess several pairs of secret and public keys, and choose randomly which pair is to be used in a given round of execution. We also dealt with nonces in zero-knowledge schemes in a new way, lowering the number of values exchanged between the prover and the verifier. Hence, our scheme has the good features of having a zero-knowledge security proof based on a well known hard problem of lattice theory, with worst to average-case reduction, and small size of secret and public keys.