Paper 2003/257 Original: eprint.iacr.org/2003/257 ↗
Trading Inversions for Multiplications in Elliptic Curve Cryptography
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.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2005-06-17: last updated
- 2003-12-20: published
- Short URL
- https://ia.cr/2003/257
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2003/257,
author = {Mathieu Ciet and Marc Joye and Kristin Lauter and Peter L. Montgomery},
title = {Trading Inversions for Multiplications in Elliptic Curve Cryptography},
howpublished = {Cryptology {ePrint} Archive, Paper 2003/257},
year = {2003},
url = {https://eprint.iacr.org/2003/257}
}