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Mathematics

A Hash-Based Quantum-Resistant Designated Verifier Signature Scheme

P. Thanalakshmi, R. Anitha, Neelamegam Anbazhagan, Chulho Park, Gyanendra Prasad Joshi, Changho Seo

Published May 11, 2022• 12 citations
Publisher

Abstract

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.

DOI
10.3390/math10101642

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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.

Malaysian Journal of Computer Science•Mar 1, 2012•10 citations
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.
Abstract Designated verifier signature (DVS) schemes can be applied in many scenes, such as E-voting and E-bidding use DVS attributes to protect the secret of participants. Most traditional DVS schemes are vulnerable to quantum computer attacks. Then, an identity-based semi-trusted third-party quantum DVS (STQDVS) scheme is proposed, which is safe for quantum means of attack. In new STQDVS scheme, the third participant prepares entangled Bell states and allocates them to the signer and the designated verifier (DV). The signer uses the identity information as her public key and the measurement results of corresponding quantum sequences as her private key to generate the signature. The DV applies the identity information as his public key and the measurement results of corresponding quantum sequences as her private key to verify the signature. Non-transferability and hidden origin are guaranteed by the fact that the DV can generate the same signature as the signatory by means of a simulated signature step. Security analysis has shown that attacks such as forgery, inter-resending, and impersonation are ineffective for the proposed scheme and that even third-party cannot forge signatures. On the other hand, the whole process of the scheme does not require any quantum key distribution protocols, quantum one-way functions, and quantum state exchange tests, which makes the STQDVS scheme relatively simple and more efficient than similar schemes.
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.
A digital signature with designated verifier (SWDV) makes that only the designated verifier can verify its validity. It can be used to protect the privacy and economic interest of the signer. So, the SWDV schemes have many applications in e-voting, auction and some other fields. To make the SWDV secure against the quantum forger, a quantum signature with designated verifier signature (QSWDV) scheme is proposed. Our QSWDV is robust due to its strong security against forgery attack, inter-resending attacks, impersonation attacks and Trojan horse attacks. Its properties such as non-transferability and hiding source can be guaranteed by the signature simulation of the designated verifier. What is more, our scheme can be proved to be information-theoretically secure, which can guarantee the secrecy of the signer’s private key and the unforgeability of the QSWDV. In the proposed QSWDV scheme, the partners neither need use quantum one-way function nor need perform quantum state comparisons, which can reduce the complexity and improve the efficiency the QSWDV scheme.
As a standard digital signature may be verified by anybody, it is unsuitable for personal or economically sensitive applications. The chameleon signature system was presented by Krawczyk and Rabin as a solution to this problem. It is based on a hash then sign model. The chameleon hash function enables the trapdoor information holder to compute a message digest collision. The holder of a chameleon signature is the recipient of a chameleon signature. He could compute collision on the hash value using the trapdoor information. This keeps the recipient from disclosing his conviction to a third party and ensures the privacy of the signature. The majority of the extant chameleon signature methods are built on the computationally infeasible number theory problems, like integer factorization and discrete log. Unfortunately, the construction of quantum computers would be rendered insecure to those schemes. This creates a solid requirement for construct chameleon signatures for the quantum world. Hence, this paper proposes a novel quantum secure chameleon signature scheme based on hash functions. As a hash-based cryptosystem is an essential candidate of a post-quantum cryptosystem, the proposed hash-based chameleon signature scheme would be a promising alternative to the number of theoretic-based methods. Furthermore, the proposed method is key exposure-free and satisfies the security requirements such as semantic security, non-transferability, and unforgeability.
Abstract We propose a quantum designated verifier multi- signature (QDVMS) scheme. In this scheme, multiple users can generate a valid signature by simultaneously signing the original message, and the designated verifier holds the exclusive capability to verify the signature’s validity. This scheme applies locally indistinguishable orthogonal product states to generate signatures, simplifying the preparation process in contrast to entangled states. Furthermore, our scheme does not require quantum one- way functions (QOWF), quantum state swapping tests (SWAP), or entangled states, which enhances its practicality and efficiency. Additionally, the absence of a third party (TP) in the entire process enhances the scheme’s security. The security analysis and comparisons with similar schemes indicate that our QDVMS scheme satisfies the security properties of DVS, and achieves information- theoretical security. Moreover, it offers higher efficiency and robust resistance against diverse attacks.
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.