Twisted Edwards curves

Daniel J. Bernstein, Peter Birkner, Marc Joye, Tanja Lange, Christiane Peters

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

This paper introduces "twisted Edwards curves," a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and shows that twisted Edwards curves save time for many curves that were already expressible as Edwards curves.
Keyword: Heidelberg (CO),isogenies,Springer (CO),Montgomery,Finite fields,Cryptography,twisted Edwards curves,Cryptology,Montgomery curves,Curves (road),Microfluidics,international conferences,ELLIPTIC-CURVES,COMPUTER,elliptic curves,Explicit formulas,Edwards curves
Original languageEnglish
Title of host publicationPROGRESS IN CRYPTOLOGY - AFRICACRYPT 2008
VolumeVolume 5023
PublisherSpringer Verlag, Berlin
Publication date2008
Pages389-405
ISBN (Print)978-35-40-68159-5
DOIs
Publication statusPublished - 2008
Externally publishedYes
Event1st International Conference on Cryptology in Africa - Casablanca, Morocco
Duration: 11 Jun 200814 Jun 2008
Conference number: 1
http://www.informatik.uni-trier.de/~ley/db/conf/africacrypt/index.html

Conference

Conference1st International Conference on Cryptology in Africa
Number1
Country/TerritoryMorocco
CityCasablanca
Period11/06/200814/06/2008
Internet address
SeriesLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number5023

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