A new minimal average weight representation for left-to-right point multiplication methods

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 the time and space complexity of fast point multiplication techniques.