Recovering or testing extended-affine equivalence
Extended Affine (EA) equivalence is the equivalence relation between two vectorial Boolean
functions and such that there exist two affine permutations,, and an affine function satisfying …
functions and such that there exist two affine permutations,, and an affine function satisfying …
Deciding EA-equivalence via invariants
N Kaleyski - Cryptography and communications, 2022 - Springer
We define a family of efficiently computable invariants for (n, m)-functions under EA-
equivalence, and observe that, unlike the known invariants such as the differential spectrum …
equivalence, and observe that, unlike the known invariants such as the differential spectrum …
On apn functions whose graphs are maximal sidon sets
C Carlet - Latin American Symposium on Theoretical Informatics, 2022 - Springer
Abstract The graphs GF={(x, F (x)); x∈ F 2 n} of those (n, n)-functions F: F 2 n↦ F 2 n that are
almost perfect nonlinear (in brief, APN; an important notion in symmetric cryptography) are …
almost perfect nonlinear (in brief, APN; an important notion in symmetric cryptography) are …
The classification of quadratic APN functions in 7 variables and combinatorial approaches to search for APN functions
K Kalgin, V Idrisova - Cryptography and Communications, 2023 - Springer
Almost perfect nonlinear functions possess optimal resistance to differential cryptanalysis
and are widely studied. Most known APN functions are defined using their representation as …
and are widely studied. Most known APN functions are defined using their representation as …
On CCZ-inequivalence of some families of almost perfect nonlinear functions to permutations
F Göloğlu, J Pavlu̇ - Cryptography and Communications, 2021 - Springer
Abstract Browning et al.(2010) exhibited almost perfect nonlinear (APN) permutations on F 2
6 F_2^6. This was the first example of an APN permutation on an even degree extension of …
6 F_2^6. This was the first example of an APN permutation on an even degree extension of …
Invariants for EA-and CCZ-equivalence of APN and AB functions
NS Kaleyski - Cryptography and Communications, 2021 - Springer
Abstract An (n, m)-function is a mapping from F 2 n F_2^n to F 2 m F_2^m. Such functions
have numerous applications across mathematics and computer science, and in particular …
have numerous applications across mathematics and computer science, and in particular …
The classification of quadratic APN functions in 7 variables
K Kalgin, V Idrisova - Cryptology ePrint Archive, 2020 - eprint.iacr.org
Almost perfect nonlinear functions possess the optimal resistance to the differential
cryptanalysis and are widely studied. Most known APN functions are obtained as functions …
cryptanalysis and are widely studied. Most known APN functions are obtained as functions …
Triplicate functions
L Budaghyan, I Ivkovic, N Kaleyski - Cryptography and Communications, 2023 - Springer
We define the class of triplicate functions as a generalization of 3-to-1 functions over F 2 n
for even values of n. We investigate the properties and behavior of triplicate functions, and of …
for even values of n. We investigate the properties and behavior of triplicate functions, and of …
Two generalizations of almost perfect nonlinearity
C Carlet - Cryptology ePrint Archive, 2024 - eprint.iacr.org
Almost perfect nonlinear (in brief, APN) functions are (so-called vectorial) functions $ F: F_2^
n\to F_2^ n $ playing roles in several domains of information protection, at the intersection of …
n\to F_2^ n $ playing roles in several domains of information protection, at the intersection of …
On functions of low differential uniformity in characteristic 2: A close look (I)
N Anbar, T Kalaycı, A Topuzoğlu - arXiv preprint arXiv:2406.07468, 2024 - arxiv.org
We introduce a new concept, the APN-defect, which can be thought of as measuring the
distance of a given function $ G:\mathbb {F} _ {2^ n}\rightarrow\mathbb {F} _ {2^ n} $ to the …
distance of a given function $ G:\mathbb {F} _ {2^ n}\rightarrow\mathbb {F} _ {2^ n} $ to the …