A Compact Post-quantum Strong Designated Verifier Signature Scheme from Isogenies

Fuente: arXiv
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Main Author: Renan, Farzin
Format: Preprint
Published: 2025
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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
id 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