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Nonlinear vectorial primitive recursive sequences

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Abstract

We discuss nonlinear vectorial primitive recursive sequences. First we consider the nonlinearly filtered multiple-recursive matrix generator for producing pseudorandom vectors based on some nonlinear schemes and give lower bounds for their componentwise linear complexity. Moreover, we obtain certain results concerning the jump multiple-recursive matrix generator and establish that sequences generated by them have better period and componentwise linear complexity as compared to usual multiple-recursive matrix generator sequences. We also include analogous results for transformation shift registers for generating pseudorandom vectors.

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Acknowledgements

Daniel Panario and Qiang Wang are partially supported by NSERC of Canada.

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Authors and Affiliations

  1. Scientific Analysis Group, Defence Research and Development Organisation, Metcalfe House, Delhi, 110054, India

    Sartaj Ul Hasan

  2. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada

    Daniel Panario & Qiang Wang

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  1. Sartaj Ul Hasan
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  2. Daniel Panario
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  3. Qiang Wang
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Correspondence to Sartaj Ul Hasan.

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This article is part of the Topical Collection on Special Issue on Sequences and Their Applications

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Hasan, S.U., Panario, D. & Wang, Q. Nonlinear vectorial primitive recursive sequences. Cryptogr. Commun. 10, 1075–1090 (2018). https://doi.org/10.1007/s12095-017-0265-2

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