A Note on 5-bit Quadratic Permutations’ Classification

Authors

  • Dušan Božilov NXP Semiconductors, Leuven, Belgium;imec - Computer Security and Industrial Cryptography (COSIC) research group, Department of Electrical Engineering (ESAT), KU Leuven, Leuven, Belgium
  • Begül Bilgin imec - Computer Security and Industrial Cryptography (COSIC) research group, Department of Electrical Engineering (ESAT), KU Leuven, Leuven, Belgium
  • Hacı Ali Sahin Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

DOI:

https://doi.org/10.13154/tosc.v2017.i1.398-404

Keywords:

Permutation, S-box, classification, affine equivalence, vectorial Boolean function

Abstract

Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold realizations.

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Published

2017-03-08

Issue

Volume 2017, Issue 1

Section

Articles

License

Copyright (c) 2017 Dušan Božilov, Begül Bilgin, Hacı Ali Sahin

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A Note on 5-bit Quadratic Permutations’ Classification. (2017). IACR Transactions on Symmetric Cryptology, 2017(1), 398-404. https://doi.org/10.13154/tosc.v2017.i1.398-404