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Weightwise perfectly balanced functions with high weightwise nonlinearity profile

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Abstract

Boolean functions satisfying good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the recent FLIP stream cipher (Méaux et al.: in Lecture Notes in Computer Science, vol. 9665, pp. 311–343, Springer, Berlin, 2016). In this paper, we propose a large class of weightwise perfectly balanced (WPB) functions, which is 2-rotation symmetric. This new class of WPB functions is not extended affinely equivalent to the known constructions. We also discuss the weightwise nonlinearity profile of these functions, and present general lower bounds on k-weightwise nonlinearity, where k is a power of 2. Moreover, we exhibit a subclass of the family. By a recursive lower bound, we show that these subclass of WPB functions have very high weightwise nonlinearity profile.

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Acknowledgements

The authors thank the anonymous reviewers for their valuable comments which have highly improved the manuscript.

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Authors and Affiliations

  1. School of Computer Software, Tianjin University, Tianjin, 300350, People’s Republic of China

    Jian Liu

  2. CNRS, UMR 7539 LAGA, Paris, France

    Jian Liu

  3. Department of Mathematics, University of Paris VIII, University of Paris XIII, CNRS, UMR 7539 LAGA, Paris, France

    Sihem Mesnager

  4. Telecom ParisTech, Paris, France

    Sihem Mesnager

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  1. Jian Liu
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  2. Sihem Mesnager
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Correspondence to Sihem Mesnager.

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Communicated by A. Pott.

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Liu, J., Mesnager, S. Weightwise perfectly balanced functions with high weightwise nonlinearity profile. Des. Codes Cryptogr. 87, 1797–1813 (2019). https://doi.org/10.1007/s10623-018-0579-x

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  • DOI: https://doi.org/10.1007/s10623-018-0579-x

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