Efficiently computable distortion maps for supersingular curves

Katsuyuki Takashima*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationAlgorithmic Number Theory - 8th International Symposium, ANTS-VIII, Proceedings
Number of pages14
Publication statusPublished - 2008
Externally publishedYes
Event8th International Symposium on Algorithmic Number Theory, ANTS-VIII - Banff, Canada
Duration: 2008 May 172008 May 22

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5011 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Symposium on Algorithmic Number Theory, ANTS-VIII

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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