2025/07/20 by Farzin Renan, Renan, Farzin
Computer Science · #11T71 #14G50 #68P25 #81P94 #94A60 #Advanced Authentication Protocols Security #Cryptography and Data Security #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2507.14893
openalex publication_date 2025/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 CSI-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 \mathbbFp-isomorphism classes of supersingular elliptic curves and is founded on the hardness of the Multi-Target Group Action Inverse Problem (MT-GAIP). CSI-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.