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Fast elliptic curve point multiplication based on binary and binary non-adjacent scalar form methods

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Abstract

This article presents two methods for developing algorithms of computing scalar multiplication in groups of points on an elliptic curve over finite fields. Two new effective algorithms have been presented: one of them is based on a binary Non-Adjacent Form of scalar representation and another one on a binary of scalar representation method. All algorithms were developed based on simple and composite operations with point and also based on affine and Jacobi coordinates systems taking into account the latest achievements in computing cost reduction. Theorems concerning their computational complexity are formulated and proved for these new algorithms. In the end of this article comparative analysis of both new algorithms among themselves and previously known algorithms are represented.

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Authors and Affiliations

  1. Mathematical Studies in Information Security Section, Lomonosov Moscow State University, Moscow, Russia

    Denis Khleborodov

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  1. Denis Khleborodov
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Correspondence to Denis Khleborodov.

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Communicated by: Ivan Oseledets

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Khleborodov, D. Fast elliptic curve point multiplication based on binary and binary non-adjacent scalar form methods. Adv Comput Math 44, 1275–1293 (2018). https://doi.org/10.1007/s10444-017-9581-5

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  • DOI: https://doi.org/10.1007/s10444-017-9581-5

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