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Linear complexity of generalized sequences by comparison of PN-sequences

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Linear complexity is a much used metric of the security of any binary sequence with application in communication systems and cryptography. In this work, we propose a method of computing the linear complexity of a popular family of cryptographic sequences, the so-called generalized sequences. Such a family is generated by means of the irregular decimation of a single Pseudo Noise sequence (PN-sequence). The computation method is based on the comparison of the PN-sequence with shifted versions of itself. The concept of linear recurrence relationship and the rows of the Sierpinski triangle play a leading part in this computation.

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Authors and Affiliations

  1. Instituto de Tecnologías Físicas y de la Información, CSIC, Madrid, Spain

    Amparo Fúster-Sabater

  2. Instituto de Matemática, Estatística e Computação Científica, University of Campinas, Campinas, Brazil

    Sara D. Cardell

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  1. Amparo Fúster-Sabater
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  2. Sara D. Cardell
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Correspondence to Sara D. Cardell.

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An earlier version of this paper was presented at the Conference “Linear Algebra, Matrix Analysis and Applications. ALAMA2018”, held in Sant Joan d’Alacant on May/June 2018.

This research has been partially supported by Ministerio de Economía, Industria y Competitividad (MINECO), Agencia Estatal de Investigación (AEI), and Fondo Europeo de Desarrollo Regional (FEDER, UE) under project COPCIS, reference TIN2017-84844-C2-1-R, and by Comunidad de Madrid (Spain) under project CYNAMON, reference P2018/TCS-4566, also co-funded by European Union FEDER funds. Sara D. Cardell was supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), Brazil, and Sao Paulo Research Foundation (FAPESP), grant 2013/25977-7.

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Fúster-Sabater, A., Cardell, S.D. Linear complexity of generalized sequences by comparison of PN-sequences. RACSAM 114, 79 (2020). https://doi.org/10.1007/s13398-020-00807-5

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