Open AccessA Note on 5-bit Quadratic Permutations’ Classification
Author(s) -
Dušan Božilov,
Begül Bilgin,
Hacı Ali Sahin
Publication year - 2017
Publication title -
iacr transaction on symmetric cryptology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.715
H-Index - 10
ISSN - 2519-173X
DOI - 10.46586/tosc.v2017.i1.398-404
Subject(s) - boolean function , affine transformation , equivalence (formal languages) , cryptography , mathematics , multiplicative function , quadratic equation , discrete mathematics , symmetric key algorithm , theoretical computer science , combinatorics , computer science , algorithm , pure mathematics , public key cryptography , encryption , mathematical analysis , geometry , operating system
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.