A Note on 5-bit Quadratic Permutations’ Classification

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.

Keywords

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