Cryptology ePrint Archive: Report 2003/257
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Mathieu Ciet and Marc Joye and Kristin Lauter and Peter L. Montgomery
Abstract: Recently, Eisentraeger-Lauter-Montgomery proposed a method for speeding up scalar multiplication on elliptic curves. That method relies on improved formulae for evaluating S = 2P + Q from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulae save a field multiplication each time the operation is performed.
This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling or quadrupling a point, and present a ternary/binary method to perform efficient scalar multiplication.
Category / Keywords: implementation / elliptic curve cryptosystem
Publication Info: accepted for publication in Designs, Codes, and Cryptography
Date: received 16 Dec 2003, last revised 16 Jun 2005
Contact author: klauter at microsoft com
Available formats: PDF | BibTeX Citation
Note: minor changes throughout
Version: 20050617:000431 (All versions of this report)
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