A Compact Post-quantum Strong Designated Verifier Signature Scheme from Isogenies
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911108884856832 |
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| author | Renan, Farzin |
| author_facet | Renan, Farzin |
| contents | Digital signatures are fundamental 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 present $\mathsf{CSI\text{-}SDVS}$, a novel isogeny-based SDVS scheme that offers a compact, quantum-resistant alternative to existing SDVS constructions. The scheme leverages the ideal class group action on $\mathbb{F}_p$-isomorphism classes of supersingular elliptic curves and is founded on the hardness of the Multi-Target Group Action Inverse Problem (MT-GAIP). $\mathsf{CSI\text{-}SDVS}$ achieves strong security guarantees, Strong Unforgeability under Chosen-Message Attacks (SUF-CMA), Non-Transferability (NT), and Privacy of Signer's Identity (PSI), in the random oracle model, thereby making it among the most compact PQC-based SDVS schemes and the only post-quantum secure construction based on isogenies. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_14893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Compact Post-quantum Strong Designated Verifier Signature Scheme from Isogenies Renan, Farzin Cryptography and Security Number Theory 11T71, 94A60, 68P25, 14G50, 81P94 Digital signatures are fundamental 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 present $\mathsf{CSI\text{-}SDVS}$, a novel isogeny-based SDVS scheme that offers a compact, quantum-resistant alternative to existing SDVS constructions. The scheme leverages the ideal class group action on $\mathbb{F}_p$-isomorphism classes of supersingular elliptic curves and is founded on the hardness of the Multi-Target Group Action Inverse Problem (MT-GAIP). $\mathsf{CSI\text{-}SDVS}$ achieves strong security guarantees, Strong Unforgeability under Chosen-Message Attacks (SUF-CMA), Non-Transferability (NT), and Privacy of Signer's Identity (PSI), in the random oracle model, thereby making it among the most compact PQC-based SDVS schemes and the only post-quantum secure construction based on isogenies. |
| title | A Compact Post-quantum Strong Designated Verifier Signature Scheme from Isogenies |
| topic | Cryptography and Security Number Theory 11T71, 94A60, 68P25, 14G50, 81P94 |
| url | https://arxiv.org/abs/2507.14893 |