Elliptic curve method using complex multiplication method

Yusuke Aikawa, Koji Nuida, Masaaki Shirase

研究成果: Contribution to journalArticle査読

抄録

In 2017, Shirase proposed a variant of Elliptic Curve Method combined with Complex Multiplication method for generating certain special kinds of elliptic curves. His algorithm can efficiently factorize a given composite integer when it has a prime factor p of the form 4p = 1 + Dv 2 for some integer v, where −D is an auxiliary input integer called a discriminant. However, there is a disadvantage that the previous method works only for restricted cases where the class polynomial associated to −D has degree at most two. In this paper, we propose a generalization of the previous algorithm to the cases of class polynomials having arbitrary degrees, which enlarges the class of composite integers factorizable by our algorithm. We also extend the algorithm to more various cases where we have 4p = t 2 + Dv 2 and p + 1 − t is a smooth integer.

本文言語英語
ページ(範囲)74-80
ページ数7
ジャーナルIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
1
DOI
出版ステータス出版済み - 1 2019
外部発表はい

All Science Journal Classification (ASJC) codes

  • 信号処理
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 電子工学および電気工学
  • 応用数学

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