I. A. Dychka, M. V. Onai, T. P. Drozda


During development of many cryptographic applications, we need to perform fast algorithms of scalar multiplication. In this paper we
propose a modified window method of elliptic curve point multiplication over the GF(p). The object of the research are the processes of
performing operations in elliptic cryptosystems. The subject of the research are the methods and the algorithms of elliptic curve point
multiplication over the GF(p). The goal of the research is to develop and optimize the methods and the algorithms of performing elliptic curve
point multiplication operation over the GF(p) for improving the time characteristics. Existing and proposed algorithms were implemented
with C# programming language and integrated development environment – Visual Studio 2013. In this article we did an investigation of the existing algorithms of elliptic curve point multiplication and developed three versions of the window method LR-algorithm and generalized modification. Experimental studies of the implemented algorithms were performed according to the proposed methodology, which allows us to explore the impact of the multiplier and elliptical curve point on the results of the research. The experimental research of window methods and their modifications showed an increase speed of the modified algorithms compared to the existing algorithms in average of 13%.


computers, elliptic curve cryptography, scalar multiplication, precomputation table, elliptic curve, finite field.


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