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Improved cryptographic properties of Boolean functions obtained from the neighbourhood of Patterson-Wiedemann functions

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Abstract

More than a decade ago, the balanced and 1-resilient Boolean functions on 15 variables with the best known nonlinearities 16272 and 16264, respectively, were identified by interpreting the Patterson-Wiedemann (PW) functions as rotation-symmetric Boolean functions (RSBFs) and performing a deterministic search in their neighbourhood. We here perform an efficient exhaustive search for all the RSBFs belonging to that neighbourhood and enumerate those with the best cryptographic properties, which yields some improvements in terms of algebraic degree, algebraic immunity, and absolute indicator. In the process, by considering the PW functions as 3-RSBFs, we attain balanced Boolean functions with nonlinearity 16268 and absolute indicator 192, which improve the previously best known result in terms of nonlinearity.

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Data availability

The programming code supporting the results presented in this manuscript is available in the GitHub repository, https://github.com/Selcuk-kripto/PWneighborhood.

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Acknowledgements

We would like to thank the Editor and the anonymous reviewers for their insightful comments, which improved the presentation of the paper.

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This research has received no funds or grants.

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Authors and Affiliations

  1. Computer Engineering Department, Faculty of Engineering, Balıkesir University, Balıkesir, 10145, Turkey

    Selçuk Kavut

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  1. Selçuk Kavut
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Selçuk Kavut implemented the search algorithm, found all the results presented in this manuscript, and wrote this manuscript.

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Correspondence to Selçuk Kavut.

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Kavut, S. Improved cryptographic properties of Boolean functions obtained from the neighbourhood of Patterson-Wiedemann functions. Cryptogr. Commun. 15, 433–442 (2023). https://doi.org/10.1007/s12095-022-00610-6

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  • DOI: https://doi.org/10.1007/s12095-022-00610-6

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