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Factorization of determinants over finite fields and application in stream ciphers

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Abstract

Binary sequences being generated by nonlinearly filtering maximal length sequences with period 2n − 1 are studied in this paper. In particular, we focus on two well-known classes of nonlinear filters, namely the equidistant and normal filters, and provide new improved lower bounds on the linear complexity of the generated keystreams. In order to achieve this, properties of certain determinants over finite fields, i.e. generalized Vandermonde and linearized determinants, are first analyzed in terms of their factorization. The value of the derived methodology is demonstrated by the simplification that occurs in the generalized version of the root presence test, which has been commonly used to obtain lower bounds on the linear complexity. Moreover, it is shown how these results can be applied to reason about the properties of more complex nonlinear filters.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their thorough comments and suggestions, which helped to improve the technical content and the presentation of the manuscript.

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Authors and Affiliations

  1. Department of Computer Science and Technology, University of Peloponnese, End of Karaiskaki Street, 22100, Tripolis, Greece

    Nicholas Kolokotronis

  2. Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, University Campus, Ilissia, 15784, Athens, Greece

    Nicholas Kolokotronis, Konstantinos Limniotis & Nicholas Kalouptsidis

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  1. Nicholas Kolokotronis
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  2. Konstantinos Limniotis
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  3. Nicholas Kalouptsidis
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Correspondence to Nicholas Kolokotronis.

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Kolokotronis, N., Limniotis, K. & Kalouptsidis, N. Factorization of determinants over finite fields and application in stream ciphers. Cryptogr. Commun. 1, 175–205 (2009). https://doi.org/10.1007/s12095-008-0005-8

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  • DOI: https://doi.org/10.1007/s12095-008-0005-8

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