Foundations and Development of Isogeny-Based Cryptography: From Origins to the SIKE Collapse - Naskar, Krishanu; Dey, Abhishek (International Journal of Computer Sciences and Engineering, 2025)
Isogeny-based cryptography represents a compelling direction in post-quantum security, distinguished by its exceptionally small key sizes and solid theoretical foundation based on the computational difficulty of finding isogenies between supersingular elliptic curves. This paper traces the foundation and developmental trajectory of isogeny-based cryptography, from its early theoretical proposals to significant advancements leading up to 2022. Special attention is devoted to the period between 2020 and 2022, which witnessed substantial progress in isogeny-based signature schemes, key exchange protocols, and computational optimizations, alongside emerging cryptanalytic challenges. The discussion concludes with a concise summary of the 2022 attack on the Supersingular Isogeny Key Encapsulation (SIKE) scheme, avoiding in-depth technical details, and proceeds to compare isogeny-based cryptography with alternative post-quantum cryptographic approaches.This analysis affirms the ongoing relevance of isogeny-based techniques despite setbacks, while highlighting critical directions for future research.