## CryptoDB

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

Authors: Jithra Adikari Vassil S. Dimitrov Pradeep K. Mishra URL: http://eprint.iacr.org/2008/145 Search ePrint Search Google 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.
##### BibTeX
@misc{eprint-2008-17822,
title={Fast Multiple Point Multiplication on Elliptic Curves over Prime and Binary Fields using the Double-Base Number System},
booktitle={IACR Eprint archive},
keywords={Elliptic Curve Cryptography, Double-Base Number System, Multiple Point Multiplication},
url={http://eprint.iacr.org/2008/145},