Optimizing double-base elliptic-curve single-scalar multiplication

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

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

25 Citaten (Scopus)
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This paper analyzes the best speeds that can be obtained for single-scalar multiplication with variable base point by combining a huge range of options: • many choices of coordinate systems and formulas for individual group operations, including new formulas for tripling on Edwards curves; • double-base chains with many different doubling/tripling ratios, including standard base-2 chains as an extreme case; • many precomputation strategies, going beyond Dimitrov, Imbert, Mishra (Asiacrypt 2005) and Doche and Imbert (Indocrypt 2006). The analysis takes account of speedups such as S – M tradeoffs and includes recent advances such as inverted Edwards coordinates. The main conclusions are as follows. Optimized precomputations and triplings save time for single-scalar multiplication in Jacobian coordinates, Hessian curves, and tripling-oriented Doche/Icart/Kohel curves. However, even faster single-scalar multiplication is possible in Jacobi intersections, Edwards curves, extended Jacobi-quartic coordinates, and inverted Edwards coordinates, thanks to extremely fast doublings and additions; there is no evidence that double-base chains are worthwhile for the fastest curves. Inverted Edwards coordinates are the speed leader.
Originele taal-2Engels
TitelProceedings of the 8th International Conference on Cryptology in India: Progress in Cryptology (INDOCRYPT 2007) 9-13 December 2007, Chennai, India
RedacteurenK. Srinathan, C. Pandu Rangan, M. Yung
Plaats van productieBerlin, Germany
ISBN van geprinte versie978-3-540-77025-1
StatusGepubliceerd - 2007
Evenementconference; INDOCRYPT 2007, Chennai, India; 2007-12-09; 2007-12-13 -
Duur: 9 dec 200713 dec 2007

Publicatie series

NaamLecture Notes in Computer Science
ISSN van geprinte versie0302-9743


Congresconference; INDOCRYPT 2007, Chennai, India; 2007-12-09; 2007-12-13
AnderINDOCRYPT 2007, Chennai, India

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