International Association for Cryptologic Research

International Association
for Cryptologic Research


T. Aaron Gulliver


Partially Fixed Point Multiplication
A new technique is proposed in which bandwidth and memory are together used to reduce both the number of point additions and doublings required in computing random point multiplication. Using the proposed technique, we show that a significant speed-up can be obtained at the cost of slightly increased bandwidth. In addition, we show that the proposed technique is well-suited for parallel processing.
A New Minimal Average Weight Representation for Left-to-Right Point Multiplication Methods
M. Khabbazian T.A. Gulliver
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.