Isogeny computation on Kummer lines and applications
Isogeny computation on Kummer lines and applications
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DOI：
10.1016/j.jisa.2023.103546
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发表时间：
2023-08
期刊：
影响因子：
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通讯作者：
Chao Chen;Fangguo Zhang;Changan Zhao
中科院分区：
文献类型：
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作者：
Chao Chen;Fangguo Zhang;Changan Zhao
基于等基因的密码学由于其抗量子计算攻击的特性而成为近年来的研究热点。不幸的是，效率是限制其加密应用的主要瓶颈。受Kummer线高效实现的启发，我们形式化了Kummer线上的等基因。特别地，我们导出了不同的2-同构的显式公式，由不同的Kummer线之间的几个变换组成，然后是一些吸引人的同构性质。另外，我们建立了奇次等同性的公式，并证明了三次等同性可以分解为三个相似的操作。此外，通过适当的优化，我们提出了计算F上的2-同质性的算法，并能够同时获得图像。对于可验证延迟函数和延迟加密的设置，我们的方法减少了操作次数，具有更紧凑方案的潜力。
Isogeny-based cryptography has been the hotspot in recent years owing to its resistance to quantum computing attacks. Unfortunately, efficiency is the main bottleneck that limits its cryptographic applications. Inspired by the efficient implementations of Kummer lines, we formalize the isogenies on Kummer lines. In particular, we derive the explicit formulae of distinct 2-isogenies, consisting of several transforms between different Kummer lines, followed by some appealing isomorphic properties. As an additional contribution, we establish the formulae of odd-degree isogenies and show that 3-isogenies can be decomposed into three similar operations. Furthermore, with appropriate optimizations, we present the algorithms of computing the 2-isogenies over F p with the ability to obtain the images simultaneously. For the setup of Verifiable Delay Functions and Delay Encryptions, our method reduces the number of operations with the potential of more compact schemes.