A Lattice-Based Identity-Based Proxy Blind Signature Scheme in the Standard Model

Lili Zhang,Yanqin Ma

doi:10.1155/2014/307637

Abstract

A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice-based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice-based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity-based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS) and the inhomogeneous small integer solution problem (ISIS). Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice-based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice-based identity-based proxy blind signature scheme in the standard model.

Highlights

Digital signature schemes are the cornerstone of e-business, e-government, software security, and many more applications
In 1996, Mambo et al introduced the concept of proxy signature [2]: an original signer delegates his signing authority to another signer, who is called a proxy signer
The proxy signer can sign any message on behalf of the original signer and the verifier can verify and distinguish between normal signature and proxy signature

Summary

Introduction

Digital signature schemes are the cornerstone of e-business, e-government, software security, and many more applications. Many proxy signatures [21, 22] were presented in bonsai tree model based on the bonsai tree signature scheme Both the private keys and the signatures in these schemes become dramatically longer than general signature. In this paper, we will construct a new identity-based proxy blind signature scheme from lattices in the standard model, which is obtained from Agrawal et al.’s basis delegation algorithm [23]. The rest of the paper is organized as follows: the section gives the introduction of lattices, Section 3 explains briefly the definition of proxy blind signature, and Section 4 gives a detailed description of our identity-based proxy blind signature from lattice basis delegation.

Preliminaries

Proxy Blind Signature

Analysis of the Proposed Scheme

Conclusions