Pseudo-random Sequence Generation from Elliptic Curves over a Finite Field of Characteristic 2

Omar Reyad , Zbigniew Kotulski

Abstract

In this paper, the randomness of binary sequences generated from elliptic curves over a finite field of characteristic 2 is studied. A scheme of construction based on the haosDriven Elliptic Curve Pseudo-random Number Generator (C-D ECPRNG) is proposed. The generators based of this scheme are verified by using tests from the NIST Statistical Test Suite to analyze their statistical properties. An elliptic curve used in the numerical example is defined over F2 8. The investigations which made for the generated series of two output sequences of the lengths of 2 10 and 2 20 bits shown that 14 generators working according to our general scheme exhibit good randomness properties. Next, the binary sequences generated by these 14 schemes were used for encrypting a 256 × 256 grayscale Lena image as an pplication example and the security analysis of the ciphered images was carried out.
Author Omar Reyad IT
Omar Reyad,,
- The Institute of Telecommunications
, Zbigniew Kotulski IT
Zbigniew Kotulski,,
- The Institute of Telecommunications
Pages1011-1018
Publication size in sheets0.5
Book Ganzha Maria, Maciaszek Leszek A., Paprzycki Marcin (eds.): Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, Annals of Computer Science and Information Systems, vol. 5, 2016, IEEE, ISBN 978-83-60810-65-1, [ 978-83-60810-67-5, 978-83-60810-66-8], 1817 p., DOI:10.15439/978-83-60810-66-8 2016 fedcsis.pdf (file archived - login or check accessibility on faculty)
Languageen angielski
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2016 Reyad Kotulski Pseudo-random Sequence Generation.pdf (file archived - login or check accessibility on faculty) 2016 Reyad Kotulski Pseudo-random Sequence Generation.pdf 445.32 KB
Score (nominal)15
ScoreMinisterial score = 15.0, 27-03-2017, BookChapterSeriesAndMatConfByIndicator
Ministerial score (2013-2016) = 15.0, 27-03-2017, BookChapterSeriesAndMatConfByIndicator
Citation count*2 (2018-02-23)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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