LaSDVS : A Post-Quantum Secure Compact Strong-Designated Verifier Signature

2025-04-23

AI Summary

Existing strong designated verifier signature (SDVS) schemes either rely on number-theoretic assumptions vulnerable to quantum attacks or adopt post-quantum cryptography (PQC) at the cost of low efficiency and large key/signature sizes. This paper proposes the first efficient, compact SDVS scheme based on ideal lattices. It leverages the Ring-SIS and Ring-LWE hardness assumptions together with ring-based gadget trapdoors. The scheme achieves strong unforgeability, non-transferability, non-delegatability, and signer anonymity. Crucially, it attains the smallest private-key and signature sizes among known PQC-based SDVS schemes: signature length is O(n log q), markedly improving upon prior PQC constructions with O(n²) complexity. This efficiency makes the scheme particularly suitable for privacy-sensitive applications such as electronic voting and e-cash.

Technology Category

• Machine Learning: Privacy
• Application Domains: Security
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

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 $mathcal{O}(nlog q)$, compared to $mathcal{O}(n^2)$ size, where $n$ is the security parameter, in the existing state-of-the-art PQC designs. To the best of our knowledge, LaSDVS offers the extit{smallest private key and signature size} among the existing PQC-based SDVS schemes.

Problem

• Proposes post-quantum secure Strong-Designated Verifier Signature (SDVS).
• Addresses inefficiency and large key sizes in PQC-based SDVS.
• Achieves compact signature size and advanced security properties.

Innovation

• Uses ideal lattices for post-quantum security
• Employs Ring-SIS and Ring-LWE hardness assumptions
• Minimizes key and signature sizes via gadget trapdoor