Paper 2002/112 Original: eprint.iacr.org/2002/112 ↗
An Efficient Procedure to Double and Add Points on an Elliptic Curve
Abstract
We present an algorithm that speeds exponentiation on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general exponentiation methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P + Q from given points P, Q on the curve. We give applications to simultaneous multiple exponentiation and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8%.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2002-08-10: last updated
- 2002-08-10: published
- Short URL
- https://ia.cr/2002/112
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2002/112,
author = {Kirsten Eisentraeger and Kristin Lauter and Peter L. Montgomery},
title = {An Efficient Procedure to Double and Add Points on an Elliptic Curve},
howpublished = {Cryptology {ePrint} Archive, Paper 2002/112},
year = {2002},
url = {https://eprint.iacr.org/2002/112}
}