On the optimal parameter choice for elliptic curve cryptosystems using isogeny

Toru Akishita, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingChapter

13 Citations (Scopus)

Abstract

The isogeny for elliptic curve cryptosystems was initially used for the efficient improvement of order counting methods. Recently, Smart proposed the countermeasure using isogeny for resisting the refined differential power analysis by Goubin (Goubin's attack). In this paper, we examine the countermeasure using isogeny against zero-value point (ZVP) attack that is generalization of Goubin's attack. We show that some curves require higher order of isogeny to prevent ZVP attack. Moreover, we prove that this countermeasure cannot transfer a class of curve to the efficient curve that is secure against ZVP attack. This class satisfies that the curve order is odd and (-3/p) = -1 for the base field p, and includes three SECG curves. In the addition, we compare some efficient algorithms that are secure against both Goubin's attack and ZVP attack, and present the most efficient method of computing the scalar multiplication for each curve from SECG. Finally, we discuss another improvement for the efficient scalar multiplication, namely the usage of the point (0, y) for the base point of curve parameters. We are able to improve about 11% for double-and-add-always method, when the point (0, y) exists in the underlying curve or its isogeny.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsFeng Bao, Robert Deng, Jianying Zhou
PublisherSpringer Verlag
Pages346-359
Number of pages14
ISBN (Print)3540210180, 9783540210184
DOIs
Publication statusPublished - Jan 1 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2947
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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