Improved Supersingularity Testing of Elliptic Curves Using Legendre Form

Yuji Hashimoto, Koji Nuida

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

抄録

There are two types of elliptic curves, ordinary elliptic curves and supersingular elliptic curves. In 2012, Sutherland proposed an efficient and almost deterministic algorithm for determining whether a given curve is ordinary or supersingular. Sutherland’s algorithm is based on sequences of isogenies started from the input curve, and computation of each isogeny requires square root computations, which is the dominant cost of the algorithm. In this paper, we reduce this dominant cost of Sutherland’s algorithm to approximately a half of the original. In contrast to Sutherland’s algorithm using j-invariants and modular polynomials, our proposed algorithm is based on Legendre form of elliptic curves, which simplifies the expression of each isogeny. Moreover, by carefully selecting the type of isogenies to be computed, we succeeded in gathering square root computations at two consecutive steps of Sutherland’s algorithm into just a single fourth root computation (with experimentally almost the same cost as a single square root computation). The results of our experiments using Magma are supporting our argument; for cases of characteristic p of 768-bit to 1024-bit lengths, our algorithm runs 43.6% to 55.7% faster than Sutherland’s algorithm.

本文言語英語
ホスト出版物のタイトルComputer Algebra in Scientific Computing - 23rd International Workshop, CASC 2021, Proceedings
編集者François Boulier, Matthew England, Timur M. Sadykov, Evgenii V. Vorozhtsov
出版社Springer Science and Business Media Deutschland GmbH
ページ121-135
ページ数15
ISBN(印刷版)9783030851644
DOI
出版ステータス出版済み - 2021
イベント23rd International Workshop on Computer Algebra in Scientific Computing, CASC 2021 - Sochi, ロシア
継続期間: 9月 13 20219月 17 2021

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
12865 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

会議

会議23rd International Workshop on Computer Algebra in Scientific Computing, CASC 2021
国/地域ロシア
CitySochi
Period9/13/219/17/21

!!!All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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