逆CM群作用的一种亚指数时间多项式量子空间算法

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Mathematical Cryptology Pub Date : 2020-01-01 DOI:10.1515/jmc-2015-0057

David Jao, Jason Legrow, Christopher Leonardi, Luis Ruiz-Lopez

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引用次数: 9

摘要

摘要提出了一种量子算法，利用次指数时间，在多项式量子空间中计算同质普通椭圆曲线上复乘法群作用的逆。该算法的一个应用是，它可以用于在基于等基因的CRS和CSIDH密码系统中从公钥中找到私钥。Childs, Jao和Soukharev先前对这种多项式量子空间算法的声明是错误的;我们的算法(以及同期Biasse、Iezzi和Jacobson的独立研究)是第一个这样的结果。

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A subexponential-time, polynomial quantum space algorithm for inverting the CM group action

Abstract We present a quantum algorithm which computes group action inverses of the complex multiplication group action on isogenous ordinary elliptic curves, using subexponential time, but only polynomial quantum space. One application of this algorithm is that it can be used to find the private key from the public key in the isogeny-based CRS and CSIDH cryptosystems. Prior claims by Childs, Jao, and Soukharev of such a polynomial quantum space algorithm for this problem are false; our algorithm (along with contemporaneous, independent work by Biasse, Iezzi, and Jacobson) is the first such result.

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来源期刊

Journal of Mathematical Cryptology COMPUTER SCIENCE, THEORY & METHODS-

CiteScore

2.70

自引率

8.30%

发文量

审稿时长

100 weeks