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An Analysis of Reordering Algorithms to Reduce the Computational Cost of the Jacobi-Preconditioned CG Solver Using High-Precision Arithmetic Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Linear Models for High-Complexity Sequences

Authors : Sara D. Cardell, Amparo Fúster-Sabater

Published in: Computational Science and Its Applications – ICCSA 2017

Publisher: Springer International Publishing

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Abstract

Different binary sequence generators produce sequences whose period is a power of 2. Although these sequences exhibit good cryptographic properties, in this work it is proved that such sequences can be obtained as output sequences from simple linear structures. More precisely, every one of these sequences is a particular solution of a linear difference equation with binary coefficients. This fact allows one to analyze the structural properties of the sequences with such a period from the point of view of the linear difference equations. In addition, a new application of the Pascal’s triangle to the cryptographic sequences has been introduced. In fact, it is shown that all these binary sequences can be obtained by XORing a finite number of binomial sequences that correspond to the diagonals of the Pascal’s triangle reduced modulo 2.

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Metadata
Title
Linear Models for High-Complexity Sequences
Authors
Sara D. Cardell
Amparo Fúster-Sabater
Copyright Year
2017
Book
Computational Science and Its Applications – ICCSA 2017

Print ISBN: 978-3-319-62391-7

Electronic ISBN: 978-3-319-62392-4

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-62392-4_23

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