Binary Edwards curves

D.J. Bernstein, T. Lange, R. Rezaeian Farashahi

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

86 Citaten (Scopus)
2 Downloads (Pure)

Samenvatting

This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formulas for binary elliptic curves, i.e., addition formulas that work for all pairs of input points, with no exceptional cases. If n = 3 then the complete curves cover all isomorphism classes of ordinary elliptic curves over F2n. This paper also presents dedicated doubling formulas for these curves using 2M+ 6S + 3D, where M is the cost of a field multiplication, S is the cost of a field squaring, and D is the cost of multiplying by a curve parameter. These doubling formulas are also the first complete doubling formulas in the literature, with no exceptions for the neutral element, points of order 2, etc. Finally, this paper presents complete formulas for differential addition, i.e., addition of points with known difference. A differential addition and doubling, the basic step in a Montgomery ladder, uses 5M+ 4S + 2D when the known difference is given in affine form.
Originele taal-2Engels
TitelCryptographic Hardware and Embedded Systems - CHES 2008 (10th International Workshop, Washington DC, USA, August 10-13, 2008, Proceedings)
RedacteurenE. Oswald, P. Rohatgi
Plaats van productieBerlin
UitgeverijSpringer
Pagina's244-265
ISBN van geprinte versie978-3-540-85052-6
DOI's
StatusGepubliceerd - 2008

Publicatie series

NaamLecture Notes in Computer Science
Volume5154
ISSN van geprinte versie0302-9743

Vingerafdruk

Duik in de onderzoeksthema's van 'Binary Edwards curves'. Samen vormen ze een unieke vingerafdruk.

Citeer dit