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Lecture notes in computer science

A Blind Ring Signature Based on the Short Integer Solution Problem

Huy Quoc Le, Dung Hoang Duong, Willy Susilo

Published Jan 1, 2020• 13 citations
Publisher
DOI
10.1007/978-3-030-39303-8_8

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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.
Since its birth by Chaum, blind signatures have become one of the fundamental components in the so-called e-cash or e-voting. The scheme ensures a message to be blinded before being signed. Among all lattice-based signatures submitted to NIST post-quantum cryptographic standardization, Dilithium is a very promising candidate. The scheme has some advantages such as simple to implement securely, conservative with parameters and minimal in total size of public key and signature. In this paper, we propose a blind signature scheme based on the framework of Dilithium in order to take advantages of Dilithium. The proposed scheme is blind and one-more unforgeable secure in the random oracle model under the hardness of the module Learning with Errors problem MLWE and the module short integer solution problem MSIS.
Motivated by the need to have secure strong designate verifier signatures (SDVS) even in the presence of quantum computers, a post-quantum lattice-based SDVS scheme is proposed based on the hardness of the short integer solution problem (SIS) and the learning with errors problem (LWE). The proposed SDVS scheme utilizes the Bonsai trees and pre-image sample-able function primitives to generate the designate verifier signature (DVS). In this construction, the un- forge-ability is based on the hardness of the SIS problem which is proven in the random oracle model and the non-transferability is based on the hardness of the LWE problem. As an application of the proposed SDVS scheme, we design a strong designate verifier ring signature scheme (SDVRS) which satisfies non-transferability. It is proven that the identity of the signer is unconditionally protected not only for any third-party but also for the designate verifier. Under the hardness of the SIS problem, the proposed SDVRS scheme is proven to be existentially un-forgeable in the random oracle model.