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

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

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