## Cryptology ePrint Archive: Report 2008/145

**Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System**

*Jithra Adikari and 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.

**Category / Keywords: **Elliptic Curve Cryptography, Double-Base Number System, Multiple Point Multiplication

**Date: **received 31 Mar 2008

**Contact author: **jithra adikari at atips ca

**Available format(s): **PDF | BibTeX Citation

**Version: **20080331:183219 (All versions of this report)

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