Twisted Edwards curves

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

doi:10.1007/978-3-540-68164-9_26

Twisted Edwards curves

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

University of Illinois at Chicago
Eindhoven University of Technology
Thomson R&D France SNC

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-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 language	English
Title of host publication	PROGRESS IN CRYPTOLOGY - AFRICACRYPT 2008
Volume	Volume 5023
Publisher	Springer Verlag, Berlin
Publication date	2008
Pages	389-405
ISBN (Print)	978-35-40-68159-5
DOIs	https://doi.org/10.1007/978-3-540-68164-9_26
Publication status	Published - 2008
Externally published	Yes
Event	1st International Conference on Cryptology in Africa - Casablanca, Morocco Duration: 11 Jun 2008 → 14 Jun 2008 Conference number: 1 http://www.informatik.uni-trier.de/~ley/db/conf/africacrypt/index.html

Conference

Conference	1st International Conference on Cryptology in Africa
Number	1
Country/Territory	Morocco
City	Casablanca
Period	11/06/2008 → 14/06/2008
Internet address	http://www.informatik.uni-trier.de/~ley/db/conf/africacrypt/index.html

Series	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	5023

Access to Document

10.1007/978-3-540-68164-9_26

OpenUrl availability

Check availability in DTU Findit

Cite this

@inproceedings{5fbb47c42d2d4c188141e04bbce42c39,

title = "Twisted Edwards curves",

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",

author = "Bernstein, \{Daniel J.\} and Peter Birkner and Marc Joye and Tanja Lange and Christiane Peters",

year = "2008",

doi = "10.1007/978-3-540-68164-9\_26",

language = "English",

isbn = "978-35-40-68159-5",

volume = "Volume 5023",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag, Berlin",

number = "5023",

pages = "389--405",

booktitle = "PROGRESS IN CRYPTOLOGY - AFRICACRYPT 2008",

note = "1st International Conference on Cryptology in Africa, AFRICACRYPT ; Conference date: 11-06-2008 Through 14-06-2008",

url = "http://www.informatik.uni-trier.de/\textasciitilde{}ley/db/conf/africacrypt/index.html",

}

Bernstein, DJ, Birkner, P, Joye, M, Lange, T & Peters, C 2008, Twisted Edwards curves. in PROGRESS IN CRYPTOLOGY - AFRICACRYPT 2008. vol. Volume 5023, Springer Verlag, Berlin, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. 5023, pp. 389-405, 1st International Conference on Cryptology in Africa, Casablanca, Morocco, 11/06/2008. https://doi.org/10.1007/978-3-540-68164-9_26

Twisted Edwards curves. / Bernstein, Daniel J.; Birkner, Peter; Joye, Marc et al.
PROGRESS IN CRYPTOLOGY - AFRICACRYPT 2008. Vol. Volume 5023 Springer Verlag, Berlin, 2008. p. 389-405 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); No. 5023).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Twisted Edwards curves

AU - Bernstein, Daniel J.

AU - Birkner, Peter

AU - Joye, Marc

AU - Lange, Tanja

AU - Peters, Christiane

N1 - Conference code: 1

PY - 2008

Y1 - 2008

N2 - 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

AB - 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

U2 - 10.1007/978-3-540-68164-9_26

DO - 10.1007/978-3-540-68164-9_26

M3 - Article in proceedings

SN - 978-35-40-68159-5

VL - Volume 5023

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 389

EP - 405

BT - PROGRESS IN CRYPTOLOGY - AFRICACRYPT 2008

PB - Springer Verlag, Berlin

T2 - 1st International Conference on Cryptology in Africa

Y2 - 11 June 2008 through 14 June 2008

ER -

Twisted Edwards curves

Abstract

Conference

Access to Document

OpenUrl availability

Fingerprint

Cite this