Issue No. 11 - November (2005 vol. 54)

ISSN: 0018-9340

pp: 1454-1459

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2005.173

Vijay K. Bhargava , IEEE

T. Aaron Gulliver , IEEE

ABSTRACT

This paper introduces a new radix-2 representation with the same average weight as the {\rm width}{\hbox{-}}w nonadjacent form (w{\hbox{-}}{\rm NAF}). In both w{\hbox{-}}{\rm NAF} and the proposed representations, each nonzero digit is an odd integer with absolute value less than M. However, for w{\hbox{-}}{\rm 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{\hbox{-}}{\rm 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.

INDEX TERMS

Index Terms- Minimum-weight representation, left-to-right recoding, efficient implementation, point multiplication, elliptic curve cryptosystems.

CITATION

Vijay K. Bhargava, T. Aaron Gulliver, Majid Khabbazian, "A New Minimal Average Weight Representation for Left-to-Right Point Multiplication Methods",

*IEEE Transactions on Computers*, vol. 54, no. , pp. 1454-1459, November 2005, doi:10.1109/TC.2005.173