A Note on 5-bit Quadratic Permutations’ Classification

  • 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
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.
Published
2017-03-08
How to Cite
Božilov, D., Bilgin, B., & Sahin, H. A. (2017). A Note on 5-bit Quadratic Permutations’ Classification. IACR Transactions on Symmetric Cryptology, 2017(1), 398-404. https://doi.org/10.13154/tosc.v2017.i1.398-404
Section
Articles