Paper 2008/145
Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System
Jithra Adikari, Vassil S. Dimitrov, and Pradeep K. Mishra
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
- Published elsewhere. Unknown where it was published
- Keywords
- Elliptic Curve CryptographyDouble-Base Number SystemMultiple Point Multiplication
- Contact author(s)
- jithra adikari @ atips ca
- History
- 2008-03-31: received
- Short URL
- https://ia.cr/2008/145
- License
-
CC BY
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} }