Twisted Edwards curves

D.J. Bernstein; P. Birkner; M. Joye; T. Lange; C.P. Peters

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

Twisted Edwards curves

D.J. Bernstein, P. Birkner, M. Joye, T. Lange, C.P. Peters

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

308 Citations (Scopus)

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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.

Original language	English
Title of host publication	Progress in Cryptology - Africacrypt 2008 (First International Conference on Cryptology in Africa, Casablanca, Morocco, June 11-14, 2008, Proceedings)
Editors	S. Vaudenay
Place of Publication	Berlin
Publisher	Springer
Pages	389-405
ISBN (Print)	978-3-540-68159-5
DOIs	https://doi.org/10.1007/978-3-540-68164-9_26
Publication status	Published - 2008

Publication series

Name	Lecture Notes in Computer Science
Volume	5023
ISSN (Print)	0302-9743

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

http://eprint.iacr.org/2008/013

Cite this

Bernstein, D. J., Birkner, P., Joye, M., Lange, T., & Peters, C. P. (2008). Twisted Edwards curves. In S. Vaudenay (Ed.), Progress in Cryptology - Africacrypt 2008 (First International Conference on Cryptology in Africa, Casablanca, Morocco, June 11-14, 2008, Proceedings) (pp. 389-405). (Lecture Notes in Computer Science; Vol. 5023). Springer. https://doi.org/10.1007/978-3-540-68164-9_26

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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.",

author = "D.J. Bernstein and P. Birkner and M. Joye and T. Lange and C.P. Peters",

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language = "English",

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series = "Lecture Notes in Computer Science",

publisher = "Springer",

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booktitle = "Progress in Cryptology - Africacrypt 2008 (First International Conference on Cryptology in Africa, Casablanca, Morocco, June 11-14, 2008, Proceedings)",

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Bernstein, DJ, Birkner, P, Joye, M, Lange, T & Peters, CP 2008, Twisted Edwards curves. in S Vaudenay (ed.), Progress in Cryptology - Africacrypt 2008 (First International Conference on Cryptology in Africa, Casablanca, Morocco, June 11-14, 2008, Proceedings). Lecture Notes in Computer Science, vol. 5023, Springer, Berlin, pp. 389-405. https://doi.org/10.1007/978-3-540-68164-9_26

Twisted Edwards curves. / Bernstein, D.J.; Birkner, P.; Joye, M. et al.
Progress in Cryptology - Africacrypt 2008 (First International Conference on Cryptology in Africa, Casablanca, Morocco, June 11-14, 2008, Proceedings). ed. / S. Vaudenay. Berlin: Springer, 2008. p. 389-405 (Lecture Notes in Computer Science; Vol. 5023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Twisted Edwards curves

AU - Bernstein, D.J.

AU - Birkner, P.

AU - Joye, M.

AU - Lange, T.

AU - Peters, C.P.

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.

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.

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

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

M3 - Conference contribution

SN - 978-3-540-68159-5

T3 - Lecture Notes in Computer Science

SP - 389

EP - 405

BT - Progress in Cryptology - Africacrypt 2008 (First International Conference on Cryptology in Africa, Casablanca, Morocco, June 11-14, 2008, Proceedings)

A2 - Vaudenay, S.

PB - Springer

CY - Berlin

ER -

Twisted Edwards curves

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