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Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes)

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Information and Communications Security (ICICS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11999))

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Abstract

Boolean functions and their generalization Vectorial Boolean functions or Substitution Boxes (S-Boxes) have attracted much attention in the domain of modern block ciphers that use only these elements to provide the necessary confusion against the cryptanalysis attacks. Thus, a significant number of research has been done to construct cryptographically strong Boolean functions and S-Boxes. Among these researches, several heuristics were applied and therefore the hill climbing heuristic was largely investigated. In this paper, we propose a new variant of Hill Climbing heuristic called Parallel Steepest Ascent Hill Climbing to construct Boolean functions and \(n \times m\) S-Boxes through the progressive construction and incorporation of their m coordinate Boolean functions. The obtained results demonstrate that this new variant provides solutions with high cryptographic properties.

Supported by NSFC program (No. 61872022, 61421003), SKLSDE-2018ZX-16 and partly by the Beijing Advanced Innovation Center for Big Data and Brain Computing.

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Notes

  1. 1.

    Random initial start means that the initial population or individual is not algebraically constructed (base function) like the finite field inversion based S-Box.

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Authors and Affiliations

  1. Beijing Advanced Innovation Center of Big data and Brain Computing, Beihang University, Beijing, China

    Athmane Seghier & Jianxin Li

Authors
  1. Athmane Seghier
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  2. Jianxin Li
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Correspondence to Athmane Seghier .

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Editors and Affiliations

  1. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

  2. The Hong Kong Polytechnic University, Kowloon, Hong Kong

    Xiapu Luo

  3. Peking University, Beijing, China

    Qingni Shen

  4. Institute of Information Engineering, Beijing, China

    Zhen Xu

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Seghier, A., Li, J. (2020). Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes). In: Zhou, J., Luo, X., Shen, Q., Xu, Z. (eds) Information and Communications Security. ICICS 2019. Lecture Notes in Computer Science(), vol 11999. Springer, Cham. https://doi.org/10.1007/978-3-030-41579-2_24

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  • DOI: https://doi.org/10.1007/978-3-030-41579-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41578-5

  • Online ISBN: 978-3-030-41579-2

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