Efficiently computable distortion maps for supersingular curves

Katsuyuki Takashima*

*この研究の対応する著者

研究成果: Conference contribution

8 被引用数 (Scopus)

抄録

Efficiently computable distortion maps are useful in cryptography. Galbraith-Pujolàs-Ritzenthaler-Smith [6] considered them for supersingular curves of genus 2. They showed that there exists a distortion map in a specific set of efficiently computable endomorphisms for every pair of nontrivial divisors under some unproven assumptions for two types of curves. In this paper, we prove that this result holds using a different method without these assumptions for both curves with r > 5 and r > 19 respectively, where r is the prime order of the divisors. In other words, we solve an open problem in [6]. Moreover, we successfully generalize this result to the case C : Y 2 = X 2g+1 + 1 over for any g s.t. 2g+1 is prime. In addition, we provide explicit bases of Jac C [r] with a new property that seems interesting from the cryptographic viewpoint.

本文言語English
ホスト出版物のタイトルAlgorithmic Number Theory - 8th International Symposium, ANTS-VIII, Proceedings
ページ88-101
ページ数14
DOI
出版ステータスPublished - 2008
外部発表はい
イベント8th International Symposium on Algorithmic Number Theory, ANTS-VIII - Banff, Canada
継続期間: 2008 5月 172008 5月 22

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)
5011 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference8th International Symposium on Algorithmic Number Theory, ANTS-VIII
国/地域Canada
CityBanff
Period08/5/1708/5/22

ASJC Scopus subject areas

  • 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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