Quantum Resource Optimization for CSIDH

Yan Huang; Yongjie Li; Xiuyu Qiu; Zijian Zhou; Fangguo Zhang; Chao Chen; Wei Yu

Paper 2026/1707

Quantum Resource Optimization for CSIDH

Yan Huang, School of Mathematics and Statistics, Hunan University of Science and Technology

Yongjie Li, School of Mathematics and Statistics, Hunan University of Science and Technology

Xiuyu Qiu, State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences

Zijian Zhou, College of Science, National University of Defense Technology

Fangguo Zhang, School of Computer Science and Engineering, Sun Yat-sen University

Chao Chen, College of Big Data and Statistics, Sichuan Tourism University

Wei Yu, State Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences

Abstract

The quantum resource analysis of CSIDH has remained an active research topic. At Eurocrypt 2020, Peikert raised three open problems concerning the optimization of the corresponding quantum resources. In this work, we primarily focus on the first two: optimizing quantum resources for ideal class groups and choosing the collimation arity. Specifically, we reduce the T-gate complexity of class group actions for CSIDH-512 from $2^{52.6}$ to $2^{51.7}$. Furthermore, within our four-way permutation construction model and under a specified classical memory budget, we provide a detailed analysis of the classical and quantum resources associated with different collimation arities $r$. Among the evaluated configurations, $r = 4$ emerges as the optimal choice. By incorporating the hidden-shift quantum algorithms proposed by Peikert, we achieve a T-gate reduction of at least 85\% for solving CSIDH-512.

Note: no

Metadata

Available format(s): PDF
Publication info: Preprint.
Keywords: Isogeny-based cryptography CSIDH Quantum circuits
Contact author(s): huangyan116 @ hnust edu cn
17871139211 @ 163 com
qiuxiuyu @ iie ac cn
zhouzijian122006 @ 163 com
isszhfg @ mail sysu edu cn
chench @ sctu edu cn
yuwei @ iie ac cn
History: 2026-08-18: approved; 2026-08-17: received; See all versions
Short URL: https://ia.cr/2026/1707
License: CC0

BibTeX

@misc{cryptoeprint:2026/1707,
      author = {Yan Huang and Yongjie Li and Xiuyu Qiu and Zijian Zhou and Fangguo Zhang and Chao Chen and Wei Yu},
      title = {Quantum Resource Optimization for {CSIDH}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1707},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1707}
}