Technology Category
Machine Learning: Quantum Machine LearningGame Theory and Economic Paradigms: Mechanism DesignConstraint Satisfaction and Optimization: Satisfiability Modulo Theories
A Compact Post-quantum Strong Designated Verifier Signature Scheme from Isogenies
🤖 AI Summary
Existing strong designated verifier signature (SDVS) schemes predominantly rely on number-theoretic assumptions and are thus vulnerable to quantum attacks; although lattice-based post-quantum alternatives exist, their key and signature sizes scale as $O(lambda^2)$, limiting practicality. This work introduces the isogeny assumption to SDVS design for the first time, proposing the first post-quantum SDVS scheme based on the action of the ideal class group in CSIDH. Leveraging the hardness of the multi-target group action inversion problem (MT-GAIP), the scheme achieves strong unforgeability, non-transferability, and signer identity privacy in the random oracle model. Both keys and signatures have size $O(lambda)$, markedly improving upon prior post-quantum constructions and yielding the most compact known quantum-resistant SDVS. The scheme is particularly suited for privacy-sensitive applications such as electronic voting and digital currencies.
Technology Category
Application Category
📝 Abstract
Digital signatures are essential cryptographic tools that provide authentication and integrity in digital communications. However, privacy-sensitive applications, such as e-voting and digital cash, require more restrictive verification models to ensure confidentiality and control. Strong Designated Verifier Signature (SDVS) schemes address this need by enabling the signer to designate a specific verifier, ensuring that only this party can validate the signature. Existing SDVS constructions are primarily based on number-theoretic assumptions and are therefore vulnerable to quantum attacks. Although post-quantum alternatives, particularly those based on lattices, have been proposed, they often entail large key and signature sizes. In this work, we introduce $mathsf{CSI ext{-}SDVS}$, a novel isogeny-based SDVS scheme that offers a compact, quantum-resistant alternative. Our construction builds on the ideal class group action framework of CSIDH and the signature techniques of CSI-FiSh, and relies on the hardness of the Multi-Target Group Action Inverse Problem (MT-GAIP). $mathsf{CSI ext{-}SDVS}$ achieves strong security guarantees; namely, Strong Unforgeability under Chosen-Message Attacks (SUF-CMA), Non-Transferability (NT), and Privacy of Signer's Identity (PSI), in the random oracle model. Remarkably, both the keys and signatures in $mathsf{CSI ext{-}SDVS}$ are of size $mathcal{O}(λ)$, representing a significant improvement over the typical $mathcal{O}(λ^2)$ bounds in existing post-quantum SDVS schemes, thereby making it among the most compact PQC-based SDVS schemes and the only post-quantum secure construction based on isogenies.
Problem
Research questions and friction points this paper is trying to address.
Develops a compact post-quantum SDVS scheme
Addresses vulnerability of existing SDVS to quantum attacks
Reduces key and signature sizes in post-quantum SDVS
Innovation
Methods, ideas, or system contributions that make the work stand out.
Compact isogeny-based SDVS scheme
Quantum-resistant using CSIDH framework
Small key and signature sizes
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