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Properties of a Family of Cryptographic Boolean Functions

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Sequences and Their Applications - SETA 2014 (SETA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8865))

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Abstract

In 2008, Carlet and Feng studied a class of functions with good cryptographic properties. Based on that function, [18] proposed a family of cryptographically significant Boolean functions which contains the functions proposed by [28, 30]. However, their study is not in-depth. In this paper, we investigate the properties of those functions further, and find that they can be divided into some affine equivalent classes. The bent functions proposed by [18] are in fact in the same class with the function proposed by [30]. We then prove that those functions have optimum algebraic immunity if and only if a combinatorial conjecture is correct, which gives a new direction to prove the conjecture. Furthermore, we improve upon the lower bound on the nonlinearity, and our bound is higher than all other similar bounds. Finally, we extend the construction to a balanced function, and give an example of a 12-variable function which has the best cryptographic properties among all currently known functions.

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Acknowledgment

The first author would like to thank the financial support from the National Natural Science Foundation of China (Grant No. 61202463).

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Authors and Affiliations

  1. Temasek Laboratories, National University of Singapore, Singapore, 117411, Singapore

    Qichun Wang & Chik How Tan

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  1. Qichun Wang
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Correspondence to Qichun Wang .

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Editors and Affiliations

  1. Otto-von-Guericke University, Magdeburg, Germany

    Kai-Uwe Schmidt

  2. Austrian Academy of Sciences, Linz, Austria

    Arne Winterhof

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Wang, Q., Tan, C.H. (2014). Properties of a Family of Cryptographic Boolean Functions. In: Schmidt, KU., Winterhof, A. (eds) Sequences and Their Applications - SETA 2014. SETA 2014. Lecture Notes in Computer Science(), vol 8865. Springer, Cham. https://doi.org/10.1007/978-3-319-12325-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-12325-7_3

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