## CryptoDB

### Paper: Trading Inversions for Multiplications in Elliptic Curve Cryptography

Authors: Mathieu Ciet Marc Joye Kristin E. Lauter Peter L. Montgomery URL: http://eprint.iacr.org/2003/257 Search ePrint Search Google 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.
##### BibTeX
@misc{eprint-2003-11970,
title={Trading Inversions for Multiplications in Elliptic Curve Cryptography},
booktitle={IACR Eprint archive},
keywords={implementation / elliptic curve cryptosystem},
url={http://eprint.iacr.org/2003/257},
note={accepted for publication in Designs, Codes, and Cryptography klauter@microsoft.com 12951 received 16 Dec 2003, last revised 16 Jun 2005},
author={Mathieu Ciet and Marc Joye and Kristin E. Lauter and Peter L. Montgomery},
year=2003
}