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SQIsign2D\textsuperscript{2}: New SQIsign2D Variant by Leveraging Power Smooth Isogenies in Dimension One

Authors:
Zheng Xu , Hefei National Laboratory, University of Science and Technology of China, Hefei, 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
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Conference: ASIACRYPT 2025
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.
BibTeX
@inproceedings{asiacrypt-2025-35919,
  title={SQIsign2D\textsuperscript{2}: New SQIsign2D Variant by Leveraging Power Smooth Isogenies in Dimension One},
  publisher={Springer-Verlag},
  author={Zheng Xu and Kaizhan Lin and Chang-An Zhao and Yi Ouyang},
  year=2025
}