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

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Zhengbing Hu 1,* Ivan Dychka 2 Mykola Onai 2 Mykhailo Ivashchenko 2 Su Jun 3

1. School of Educational Information Technology, Central China Normal University, China

2. National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Ukraine

3. School of Computer Science, Hubei University of Technology, Wuhan, China

* Corresponding author.


Received: 26 Jul. 2018 / Revised: 15 Aug. 2018 / Accepted: 23 Sep. 2018 / Published: 8 Dec. 2018

Index Terms

Elliptic curve cryptography, binary elliptic curve, scalar point multiplication, finite field arithmetic, López-Dahab, LD-Montgomery scalar point multiplication algorithm


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: . The article also presents the experimental results based on different scalars.

Cite This Paper

Zhengbing Hu, Ivan Dychka, Mykola Onai, Mykhailo Ivaschenko, Su Jun, "Improved Method of López-Dahab-Montgomery Scalar Point Multiplication in Binary Elliptic Curve Cryptography", International Journal of Intelligent Systems and Applications(IJISA), Vol.10, No.12, pp.27-34, 2018. DOI:10.5815/ijisa.2018.12.03


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