Now showing items 1-13 of 13

• #### CCZ-equivalence of bent vectorial functions and related constructions ﻿

(Peer reviewed; Journal article, 2011-01-06)
We observe that the CCZ-equivalence of bent vectorial functions over F2nFn2 (n even) reduces to their EA-equivalence. Then we show that in spite of this fact, CCZ-equivalence can be used for constructing bent functions ...
• #### Classification of quadratic APN functions with coefficients in F2 for dimensions up to 9 ﻿

(Journal article; Peer reviewed, 2020)
Almost perfect nonlinear (APN) and almost bent (AB) functions are integral components of modern block ciphers and play a fundamental role in symmetric cryptography. In this paper, we describe a procedure for searching for ...
• #### Constructing APN functions through isotopic shifts ﻿

(Journal article; Peer reviewed, 2020)
Almost perfect nonlinear (APN) functions over fields of characteristic 2 play an important role in cryptography, coding theory and, more generally, mathematics and information theory. In this paper we deduce a new method ...
• #### Generalized isotopic shift construction for APN functions ﻿

(Journal article; Peer reviewed, 2021)
In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (IEEE Trans Inform Theory 66:5299–5309, 2020), when the initial function is a Gold function. In ...
• #### A New Family of APN Quadrinomials ﻿

(Journal article; Peer reviewed, 2020)
The binomial B(x) = x 3 +βx 36 (where β is primitive in F 2 2) over F 2 10 is the first known example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a power function, and has remained unclassified ...
• #### On equivalence between known families of quadratic APN functions ﻿

(Journal article; Peer reviewed, 2020)
This paper is dedicated to a question whether the currently known families of quadratic APN polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these families to those CCZ-inequivalent to each ...
• #### On Isotopic Shift Construction for Planar Functions ﻿

(Chapter; Conference object; Peer reviewed, 2019)
CCZ-equivalence is the most general currently known equivalence relation for functions over finite fields preserving planarity and APN properties. However, for the particular case of quadratic planar functions isotopic ...
• #### On relations between CCZ- and EA-equivalences ﻿

(Peer reviewed; Journal article, 2020)
In the present paper we introduce some sufficient conditions and a procedure for checking whether, for a given function, CCZ-equivalence is more general than EA-equivalence together with taking inverses of permutations. ...
• #### On the behavior of some APN permutations under swapping points ﻿

(Journal article; Peer reviewed, 2022)
We define the pAPN-spectrum (which is a measure of how close a function is to being APN) of an (n, n)-function F and investigate how its size changes when two of the outputs of a given function F are swapped. We completely ...
• #### On the Distance Between APN Functions ﻿

(Journal article; Peer reviewed, 2020)
We investigate the differential properties of a vectorial Boolean function G obtained by modifying an APN function F . This generalizes previous constructions where a function is modified at a few points. We characterize ...
• #### Partially APN functions with APN-like polynomial representations ﻿

(Journal article; Peer reviewed, 2020)
In this paper we investigate several families of monomial functions with APN-like exponents that are not APN, but are partially 0-APN for infinitely many extensions of the binary field F2. We also investigate the differential ...
• #### Relation between o-equivalence and EA-equivalence for Niho bent functions ﻿

(Journal article; Peer reviewed, 2021)
Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for a special type of bent ...
• #### Triplicate functions ﻿

(Journal article; Peer reviewed, 2022)
We define the class of triplicate functions as a generalization of 3-to-1 functions over $\mathbb {F}_{2^{n}}$ for even values of n. We investigate the properties and behavior of triplicate functions, and of 3-to-1 among ...