Blar i Faculty of Mathematics and Natural Sciences på forfatter "Budaghyan, Lilya"
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CCZ-equivalence of bent vectorial functions and related constructions
Budaghyan, Lilya; Carlet, Claude (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
Yu, Yuyin; Kaleyski, Nikolay Stoyanov; Budaghyan, Lilya; Li, Yongqiang (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
Budaghyan, Lilya; Calderini, Marco; Carlet, Claude; Coulter, Robert; Villa, Irene (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
Budaghyan, Lilya; Calderini, Marco; Carlet, Claude Michael; Coulter, Robert; Villa, Irene (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
Budaghyan, Lilya; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (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
Budaghyan, Lilya; Calderini, Marco; Villa, Irene (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
Budaghyan, Lilya; Calderini, Marco; Carlet, Claude; Coulter, Robert; Villa, Irene (Chapter; 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
Villa, Irene; Calderini, Marco; Budaghyan, Lilya (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
Budaghyan, Lilya; Kaleyski, Nikolay Stoyanov; Riera, Constanza Susana; Stanica, Pantelimon (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
Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (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 ... -
On Two Fundamental Problems on APN Power Functions
Budaghyan, Lilya; Calderini, Marco; Carlet, Claude Michael; Davidova, Diana; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2022)The six infinite families of power APN functions are among the oldest known instances of APN functions, and it has been conjectured in 2000 that they exhaust all possible power APN functions. Another long-standing open ... -
Partially APN functions with APN-like polynomial representations
Budaghyan, Lilya; Kaleyski, Nikolay Stoyanov; Riera, Constanza Susana; Stănică, Pantelimon (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
Davidova, Diana; Budaghyan, Lilya; Carlet, Claude Michael; Helleseth, Tor; Ihringer, Ferdinand; Penttila, Tim (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
Budaghyan, Lilya; Ivkovic, Ivana; Kaleyski, Nikolay Stoyanov (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 ...