Paper 2008/145 Original: eprint.iacr.org/2008/145 ↗
Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System
Abstract
Multiple-point multiplication on elliptic curves is the highest computational complex operation in the elliptic curve cyptographic based digital signature schemes. We describe three algorithms for multiple-point multiplication on elliptic curves over prime and binary fields, based on the representations of two scalars, as sums of mixed powers of 2 and 3. Our approaches include sliding window mechanism and some precomputed values of points on the curve. A proof for formulae to calculate the number of double-based elements, doublings and triplings below 2^n is listed. Affine coordinates and Jacobian coordinates are considered in both prime fields and binary fields. We have achieved upto 24% of improvements in new algorithms for multiple-point multiplication.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2008-03-31: last updated
- 2008-03-31: published
- Short URL
- https://ia.cr/2008/145
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2008/145,
author = {Jithra Adikari and Vassil S. Dimitrov and Pradeep K. Mishra},
title = {Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/145},
year = {2008},
url = {https://eprint.iacr.org/2008/145}
}