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Boolean Function Representation of S-Boxes and Boolean Permutations

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Boolean Functions and Their Applications in Cryptography

Part of the book series: Advances in Computer Science and Technology ((ACST))

Abstract

S-boxes are often the core nonlinear component in many encryption algorithms. By using vector Boolean functions to represent S-boxes, cryptographic properties as well as constructions can be made possible. This chapter studies the S-boxes by the view of vector Boolean functions, with focus being on Boolean permutations, which are a special class of vector Boolean functions. Properties and constructions of Boolean permutations are studied; computation of inverses of Boolean functions is also studied. The concept of one-way trapdoor Boolean permutation is proposed. Construction of Boolean permutations using function composition is studied which enables the construction of one-way trapdoor Boolean permutations.

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Authors and Affiliations

  1. Chinese Academy of Sciences, State Key Lab of Information Security Institute of Information Engineering, Beijing, China

    Chuan-Kun Wu

  2. Chinese Academy of Sciences, Institute of Software, Beijing, China

    Dengguo Feng

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  1. Chuan-Kun Wu
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  2. Dengguo Feng
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Wu, CK., Feng, D. (2016). Boolean Function Representation of S-Boxes and Boolean Permutations. In: Boolean Functions and Their Applications in Cryptography. Advances in Computer Science and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48865-2_7

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  • DOI: https://doi.org/10.1007/978-3-662-48865-2_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48863-8

  • Online ISBN: 978-3-662-48865-2

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