Cryptology ePrint Archive: Report 2004/266

A New Minimal Average Weight Representation for Left-to-Right Point Multiplication Methods

M. Khabbazian and T.A. Gulliver

Abstract: This paper introduces a new radix-2 representation with the same average weight as the width-$w$ nonadjacent form ($w$-NAF). In both $w$-NAF and the proposed representations, each nonzero digit is an odd integer with absolute value less than $M$. However, for $w$-NAF, $M$ is of the form $2^{w-1}$, while for the proposed representation it can be any positive integer. Therefore, using the proposed integer representation we can use the available memory efficiently, which is attractive for devices with limited memory. Another advantage of the proposed representation over $w$-NAF is that it can be obtained by scanning the bits from left-to-right. This property is also useful for memory-constrained devices because it can reduce both time and space complexityof fast point multiplication techniques.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem

Date: received 14 Oct 2004

Contact author: majidk at ece ubc ca

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Version: 20041015:202720 (All versions of this report)

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