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IEEE Access

An Efficient Strong Designated Verifier Signature Based on $\mathcal{R}-$ SIS Assumption

Jie Cai, Han Jiang, Pingyuan Zhang, Zhihua Zheng, Guangshi Lyu, Qiuliang Xu

Published Jan 1, 2019• 16 citations
Publisher

Abstract

The designated verifier signature (DVS), introduced by Jakobssonet al., has the property that only the designated verifier can verify the generated signature. In order to prevent an eavesdropper to get the signature on-line before the designated verifier receives it, they also proposed strong designated verifier signature (SDVS). In this paper, according to an efficient SDVS proposed by Saeedniaet al., we present a post-quantum SDVS in the random oracle model based on lattice assumption. The unforgeability is based on the hardness of the average-case hard problem$\mathcal {R}-$SIS$_{q,n,m,\beta }$, which is at least as hard as worst-case SVP$_{\gamma }$over ideal lattices. In addition, compared with existing lattice-based SDVS schemes, our scheme cuts by more than 50 percent repetitions and the size of signature is shorter with 256 bits security.

DOI
10.1109/access.2018.2889242

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An Efficient Strong Designated Verifier Signature Based on R−\mathcal{R}-R− SIS Assumption
The designated verifier signature (DVS), introduced by Jakobssonet al., has the property that only the designated verifier can verify the generated signature. In order to prevent an eavesdropper to get the signature on-line before the designated verifier receives it, they also proposed strong designated verifier signature (SDVS). In this paper, according to an efficient SDVS proposed by Saeedniaet al., we present a post-quantum SDVS in the random oracle model based on lattice assumption. The unforgeability is based on the hardness of the average-case hard problemR−\mathcal {R}-R−SISq,n,m,β_{q,n,m,\beta }q,n,m,β​, which is at least as hard as worst-case SVPγ_{\gamma }γ​over ideal lattices. In addition, compared with existing lattice-based SDVS schemes, our scheme cuts by more than 50 percent repetitions and the size of signature is shorter with 256 bits security.
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.
Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital communication. However, in scenarios involving sensitive interactions -- such as e-voting or e-cash -- there is a growing need for more controlled signing mechanisms. Strong-Designated Verifier Signature (SDVS) offers such control by allowing the signer to specify and restrict the verifier of a signature. The existing state-of-the-art SDVS are mostly based on number-theoretic hardness assumptions. Thus, they are not secure against quantum attacks. Moreover, Post-Quantum Cryptography (PQC)-based SDVS are inefficient and have large key and signature sizes. In this work, we address these challenges and propose an efficient post-quantum SDVS (namely, LaSDVS) based on ideal lattices under the hardness assumptions of the Ring-SIS and Ring-LWE problems. LaSDVS achieves advanced security properties including strong unforgeability under chosen-message attacks, non-transferability, non-delegatability, and signer anonymity. By employing the algebraic structure of rings and the gadget trapdoor mechanism of Micciancio et al., we design LaSDVS to minimize computational overhead and significantly reduce key and signature sizes. Notably, our scheme achieves a compact signature size of O(nlog⁡q)\mathcal{O}(n\log q)O(nlogq), compared to O(n2)\mathcal{O}(n^2)O(n2) size, where nnn is the security parameter, in the existing state-of-the-art PQC designs. To the best of our knowledge, LaSDVS offers the \textit{smallest private key and signature size} among the existing PQC-based SDVS schemes.
In this paper, we propose an ID-based strong designated verifier signature (SDVS) over R - SIS assumption in the random model. We remove pre-image sampling function and Bonsai trees such complex structures used in previous lattice-based SDVS schemes. We only utilize simple rejection sampling to protect the security of our scheme. Hence, we will show our design has the shortest signature size comparing with existing lattice-based ID-based SDVS schemes. In addition, our scheme satisfies anonymity (privacy of signer’s identity) proved in existing schemes rarely, and it can resist side-channel attacks with uniform sampling.
Among post-quantum alternatives, latticebased cryptography is the most promising one, due to its simple operations, reduction from aver-age-case to worstcase hardness, and supporting of rich functionalities. Ring signature enables a user to sign anonymously on behalf of an adaptively chosen group, and has multiple applications in anonymous e-voting, anonymous authentication, whistle blowing etc. However, most lattice-based ring signature schemes were constructed in the random oracle model from lattice basis delegation and they suffer large verification key sizes as a common disadvantage. This work proposes an efficient ring signature scheme from lattice basis delegation without random oracle based on the extended split-SIS problem, whose security is approximately as hard as the worst-case SIVP problem. Our scheme is proved to be anonymous and existentially unforgeable under latticebased assumptions. Finally, the verification key size is significantly reduced to a small constant, instead of increasing linearly with the number of ring members.
Digital signatures are unsuitable for specific applications that are sensitive on a personal or commercial level because they are universally verifiable. Jakobsson et al. proposed the Designated Verifier Signature (DVS) system, which only allows the intended verifier to validate a message’s signature. It prohibits the disclosure of a conviction to a third party. This functionality is useful in applications that require both authenticity and signer privacy, such as electronic voting and tender calls. The vast majority of current DVS schemes are based on difficult number theory problems such as integer factorization or discrete log problems over various groups. The development of a large-scale quantum computer would render these schemes unsafe. As a result, it is critical to develop quantum-resistant DVS methods. In both quantum and classical computers, signatures based on one-way functions are more efficient and secure. They have several advantages over digital signatures based on trapdoor functions. As a result, hash-based signatures are now considered viable alternatives to number-theoretic signatures. Existing hash-based signatures, on the other hand, are easily verifiable by anyone. As a result, they do not protect the signer’s identity. In addition, they are one-time signatures. This paper presents a hash-based multi-time designated verifier signature scheme that ensures signer anonymity. The unforgeability of the signature scheme is also tested in the random oracle model under chosen message attack. The properties such as non-transferability and non-delegatability are investigated.
Universal designated verifier signatures can be used to resolve the conflict between authenticity and privacy in some applications. However, all of existing constructions for this primitive are based on hard problems in number theory, and will be ultimately broken in quantum era. To address this issue, we construct the first lattice-based universal designated verifier signatures as a post-quantum candidate for this primitive. Our construction is obtained by directly extending a ring-based variant of the Gentry-Peikert-Vaikuntanathan signature scheme with some additional algorithms, thus the existing key generation and signing implementation can be used without modification. We also show that our construction is provably secure under the Small Integer Solution problem over rings, in the random oracle model.