Improved Method of López-Dahab-Montgomery Scalar Point Multiplication in Binary Elliptic Curve Cryptography

Abstract

As elliptic curve cryptography is one of the popular ways of constructing an encoding and decoding processes, public-key algorithms as its basis provide people a comfortable way of exchanging pieces of encoded information. As the time goes by, a lot of algorithms have emerged, some of them are still in use today; some others are still being developed into new forms. The main point of algorithm innovation is to reduce the number of processed operations during every possible step to find maximum efficiency and highest speed while performing the calculations. This article describes an improved method of the López-Dahab-Montgomery (LD-Montgomery) scalar point multiplication in terms of working with binary elliptic curves. It is shown in the article that the possible improvement lies in reordering the set of operations which is used in LD-Montgomery scalar point multiplication algorithm. The algorithm is used to compute point multiplication results of the curves over binary Galois Fields featuring the following m values: