SQIsign2D$^2$: New SQIsign2D Variant by Leveraging Power Smooth Isogenies in Dimension One

Zheng Xu; Kaizhan Lin; Chang-An Zhao; Yi Ouyang

Paper 2025/920

SQIsign2D$^2$: New SQIsign2D Variant by Leveraging Power Smooth Isogenies in Dimension One

Zheng Xu, Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

Kaizhan Lin, College of Computer Science and Artificial Intelligence, Fudan University, Shanghai, China

Chang-An Zhao, School of Mathematics, Sun Yat-sen University, Guangzhou, China; Guangdong Key Laboratory of Information Security, Guangzhou, China

Yi Ouyang, Hefei National Laboratory, University of Science and Technology of China, Hefei, China; School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

Abstract

In this paper, we propose SQIsign2D$^2$, a novel digital signature scheme within the SQIsign2D family. Unlike other SQIsign2D variants, SQIsign2D$^2$ employs the prime $p=CD-1$ as the field characteristic, where $D=2^{e_2}$, $C=3^{e_3}$ and $C\approx D\approx \sqrt{p}$. By leveraging accessible $C$-isogenies, SQIsign2D$^2$ significantly reduces the degree requirements for two-dimensional isogeny computations, thereby lowering the overall computational overhead compared to other SQIsign2D variants. We also provide a proof-of-concept implementation of SQIsign2D$^2$, and give an efficiency comparison between SQIsign2D$^2$ and other SQIsign2D variants. In particular, the experimental results demonstrate that the key generation and signing phases of SQIsign2D$^2$ are more than twice as fast as those of SQIsign2D-East at the NIST-I security level, respectively. Additionally, the verification performance in SQIsign2D$^2$ exhibits marginally improved efficiency.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published by the IACR in ASIACRYPT 2025
Keywords: SQIsign Post-quantum cryptography Isogeny Signature
Contact author(s): xuzheng1 @ mail ustc edu cn
linkzh @ fudan edu cn
zhaochan3 @ mail sysu edu cn
yiouyang @ ustc edu cn
History: 2025-09-01: revised; 2025-05-22: received; See all versions
Short URL: https://ia.cr/2025/920
License: CC BY

BibTeX

@misc{cryptoeprint:2025/920,
      author = {Zheng Xu and Kaizhan Lin and Chang-An Zhao and Yi Ouyang},
      title = {{SQIsign2D}$^2$: New {SQIsign2D} Variant by Leveraging Power Smooth Isogenies in Dimension One},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/920},
      year = {2025},
      url = {https://eprint.iacr.org/2025/920}
}