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The linear structures and fast points of rotation symmetric Boolean functions

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Abstract

The existence of nonzero fast points and linear structures reflects the properties of Boolean function’s higher order derivatives, which is closely related to many cryptographic differential attacks. Rotation symmetric Boolean functions (RSBFs) is a super-class of symmetric functions, which are used widely in cryptography. We first obtain some existence results of nonzero linear structures of n-variable RSBFs with degree \(n-2\). Moreover, we determine all the possible sets of fast points of n-variable RSBFs with degrees \(n-3\) and \(n-4\) based on integer partition. Finally, we investigate the existence of fast points of p-variable and 2p-variable RSBFs when p is an odd prime.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant No. 61902107), the Natural Science Foundation of Hebei Province (Grant Nos. F2019207112 and A2021205027), the Scientific Research and Development Program of Hebei University of Economics and Business (Grant No. 2021ZD02) and the Science Foundation of Hebei Normal University (Grant No. L2021B04).

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Authors and Affiliations

  1. College of Information Technology, Hebei University of Economics and Business, Shijiazhuang, 050061, China

    Lei Sun

  2. School of Mathematical Sciences & Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang, 050024, China

    Zexia Shi

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  1. Lei Sun
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Correspondence to Zexia Shi.

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Sun, L., Shi, Z. The linear structures and fast points of rotation symmetric Boolean functions. AAECC (2022). https://doi.org/10.1007/s00200-022-00566-3

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  • DOI: https://doi.org/10.1007/s00200-022-00566-3

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