A Note on 5-bit Quadratic Permutations’ Classification

  • Dušan Božilov NXP Semiconductors, Leuven; imec-COSIC, ESAT, KU Leuven, Leuven
  • Begül Bilgin imec-COSIC, ESAT, KU Leuven, Leuven
  • Hacı Ali Sahin Institute of Applied Mathematics, Middle East Technical University, Ankara
Keywords: Permutation, S-box, classification, affine equivalence, vectorial Boolean function


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.
How to Cite
Božilov, D., Bilgin, B., & Sahin, H. (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