İZOGENİ TABANLI KRİPTO SİSTEMLERİN İNCELENMESİ

This thesis advances isogeny-based, quantum-resistant cryptographic constructions by designing and analyzing novel signature schemes with advanced functionalities, together with a verifiable delay function that extends capabilities beyond basic primitives. We address potential gaps in the literature—privacy-preserving authentication, efficient key revocation, blockchain compatibility, and accountable delay—by constructing protocols based on three central hardness assumptions in isogeny-based cryptography: the one-wayness of commutative class group actions, the computational hardness of endomorphism rings, and the path-finding problem in supersingular isogeny graphs. Our first contribution is CSI-SDVS, the first randomized isogeny-based Strong Designated Verifier Signature scheme. It provides compact authentication with designated verifiability, substantially improving upon the large key and signature sizes common in many post-quantum alternatives. Second, we introduce a generic framework for Key-Updatable Signature Schemes (KUSS), enabling efficient key revocation in identity-based systems via a single multicast message. The construction maintains logarithmic network overhead and constant user storage, and we present a secure instantiation based on isogeny-based group actions. Third, we present SQIAsignHD, first isogeny-based adaptor signature achieving post-quantum security at NIST Level 1. Built on SQIsignHD, it cryptographically links signature validity to secret disclosure, enabling quantum-resistant atomic swaps and payment channels. Finally, we propose µ-VDF, a watermarkable Verifiable Delay Function on supersingular isogeny graphs. It embeds a user-specific, publicly verifiable watermark into the sequential computation path, providing traceability without sacrificing efficient verification and deterring misuse in decentralized environments. Together, these results demonstrate that the mathematical structure of supersingular elliptic curves supports not only quantum resistance but also a broad range of advanced cryptographic functionalities, contributing toward post-quantum systems that are more private, manageable, and accountable.