嵌入度为18的椭圆曲线建塔技术

Q4 Mathematics

Tatra Mountains Mathematical Publications Pub Date : 2023-02-01 DOI:10.2478/tmmp-2023-0008

Ismail Assoujaa, Siham Ezzouak, Hakima Mouanis

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引用次数: 0

摘要

摘要基于配对的加密是目前最受关注的安全解决方案之一。因此，为了使配对实用、安全且计算效率高，我们选择使用形式为k≥12的扩展有限域。本文主要研究嵌入度为18的曲线的情况。我们利用塔式构造技术，研究了2度或3度扭转的情况，实现了大部分的运算，这些运算分别是:第2、第3、第6、第9和第18，从而加快了最优解对的计算速度。

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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Tower Building Technique on Elliptic Curve with Embedding Degree 18

Abstract Pairing based cryptography is one of the best security solution that devote a lot of attention. So, to make pairing practical, secure and computationally effcient, we choose to work with extension finite field of the form 𝔽 p k with k ≥ 12. In this paper, we focus on the case of curves with embedding degree 18. We use the tower building technique, and study the case of degree 2 or 3 twist to carry out most arithmetics operations in 𝔽 p 2 , 𝔽 p 3 , 𝔽 p 6 , 𝔽 p 9 and 𝔽 p 18 , thus we speed up the computation in optimal ate pairing.

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来源期刊

Tatra Mountains Mathematical Publications Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量