Optimized Method for Computing Odd-Degree Isogenies on Edwards Curves

Suhri Kim, Kisoon Yoon, Young Ho Park, Seokhie Hong

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

3 Citations (Scopus)

Abstract

In this paper, we present an efficient method to compute arbitrary odd-degree isogenies on Edwards curves. By using the w-coordinate, we optimized the isogeny formula on Edwards curves by Moody and Shumow. We demonstrate that Edwards curves have an additional benefit when recovering the coefficient of the image curve during isogeny computation. For (formula presented)-degree isogeny where (formula presented), our isogeny formula on Edwards curves outperforms Montgomery curves when (formula presented). To better represent the performance improvements when w-coordinate is used, we implement CSIDH using our isogeny formula. Our implementation is about 20% faster than the previous implementation. The result of our work opens the door for the usage of Edwards curves in isogeny-based cryptography, especially for CSIDH which requires higher degree isogenies.

Original languageEnglish
Title of host publicationAdvances in Cryptology – ASIACRYPT 2019 - 25th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
EditorsSteven D. Galbraith, Shiho Moriai
PublisherSpringer
Pages273-292
Number of pages20
ISBN (Print)9783030346201
DOIs
Publication statusPublished - 2019 Jan 1
Event25th Annual International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019 - Kobe, Japan
Duration: 2019 Dec 82019 Dec 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11922 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference25th Annual International Conference on the Theory and Applications of Cryptology and Information Security, ASIACRYPT 2019
CountryJapan
CityKobe
Period19/12/819/12/12

Keywords

  • CSIDH
  • Edwards curves
  • Isogeny
  • Montgomery curves
  • Post-quantum cryptography
  • SIDH

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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