A Review of Mathematical and Computational Aspects of CSIDH Algorithms

IF 0.5 3区 数学 Q3 MATHEMATICS
Luciano Maino, Marzio Mula, Federico Pintore
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引用次数: 0

Abstract

CSIDH is a post-quantum key-exchange scheme based on the action of ideal class groups on supersingular elliptic curves over prime fields. Its short keys and ciphertexts, together with its flexibility as a building block to construct complex cryptographic primitives, has motivated significant research on the efficiency of CSIDH and its resistance against side-channel attacks. In this work, some cutting-edge results from recent contributions are reviewed in a unified treatment, focusing on the mathematical ideas lying behind them rather than on cryptographic and low-level implementation techniques. In particular, we first describe ways to speed up the class-group-action evaluation, which range from the use of different models of elliptic curves to working with different ideal class groups. We then survey some constant-time variants of CSIDH, that make the time and memory consumption during the computation of a public/shared key independent of the secret key. Finally, we examine the computation of the ideal class action when the structure of the ideal class group is known, which is the case for a specific set of CSIDH parameters.
CSIDH算法的数学和计算方面的综述
CSIDH是一种基于超奇异椭圆曲线上理想类群作用的后量子密钥交换方案。它的短密钥和密文,以及它作为构建复杂密码原语的构建块的灵活性,激发了对CSIDH的效率和抗侧信道攻击的重要研究。在这项工作中,一些来自最近贡献的前沿结果以统一的方式进行了回顾,重点是隐藏在它们背后的数学思想,而不是加密和低级实现技术。特别地,我们首先描述了加速类-群-行动评估的方法,其范围从使用不同的椭圆曲线模型到使用不同的理想类群。然后,我们研究了CSIDH的一些恒定时间变量,这些变量使计算公共/共享密钥期间的时间和内存消耗独立于密钥。最后,我们研究了理想类群结构已知时的理想类行为的计算,这是一组特定的CSIDH参数的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.50
自引率
12.50%
发文量
226
审稿时长
4-8 weeks
期刊介绍: The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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