(2026-03) Survey of isogeny-based signature schemes resistant to Castryck–Decru attack
2026-03-04
In 2022, Castryck and Decru introduced an attack that broke several isogeny-based schemes, including SIKE, which had advanced to the final round of the NIST Post-Quantum Cryptography Standardization Competition. Despite this attack, research on isogeny-based cryptography has continued, primarily due to the compact key sizes offered by these schemes compared to other post-quantum approaches. There are now many isogeny-based schemes that are resistant to the Castryck-Decru attack. These schemes typically involve advanced mathematical structures that may require significant time and effort to study.
In this paper, we provide a structured survey of isogeny-based signature schemes that are resistant to the Castryck-Decru attack, aiming to facilitate an understanding of the current landscape and the most practically relevant schemes in this area. We categorize these signature schemes into two main classes: those based on the CSIDH group action and the SQIsign family. For each class, we discuss their fundamental design principles, security assumptions, and specific constructions. We also compare their performance and compactness. Additionally, we describe one representative scheme from each class that is particularly relevant in practice due to its efficiency or compactness. In conclusion, we compare the performance of the schemes discussed in this work with other post-quantum signature schemes.