Browsing Department of Informatics by Author "Kaleyski, Nikolay Stoyanov"
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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 ... 
Deciding EAequivalence via invariants
Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2022)We define a family of efficiently computable invariants for (n,m)functions under EAequivalence, and observe that, unlike the known invariants such as the differential spectrum, algebraic degree, and extended Walsh spectrum, ... 
Generalization of a class of APN binomials to Goldlike functions
Davidova, Diana; Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2021)In 2008 Budaghyan, Carlet and Leander generalized a known instance of an APN function over the finite field F212 and constructed two new infinite families of APN binomials over the finite field F2n , one for n divisible ... 
An infinite family of 0APN monomials with two parameters
Kaleyski, Nikolay Stoyanov; Nesheim, Kjetil Amundsen; Stănică, Pantelimon (Journal article; Peer reviewed, 2023)We consider an infinite family of exponents e(l, k) with two parameters, l and k, and derive sufficient conditions for e(l, k) to be 0APN over F2n . These conditions allow us to generate, for each choice of l and k, an ... 
Invariants for EA and CCZequivalence of APN and AB functions
Kaleyski, Nikolay Stoyanov (Journal article; Peer reviewed, 2021)An (n,m)function is a mapping from \({\mathbb {F}_{2}^{n}}\) to \({\mathbb {F}_{2}^{m}}\). Such functions have numerous applications across mathematics and computer science, and in particular are used as building blocks ... 
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 CCZequivalent to a power function, and has remained unclassified ... 
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 pAPNspectrum (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 longstanding open ... 
Partially APN functions with APNlike 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 APNlike exponents that are not APN, but are partially 0APN for infinitely many extensions of the binary field F2. We also investigate the differential ... 
Towards a deeper understanding of APN functions and related longstanding problems
Kaleyski, Nikolay Stoyanov (Doctoral thesis, 20210824)This dissertation is dedicated to the properties, construction and analysis of APN and AB functions. Being cryptographically optimal, these functions lack any general structure or patterns, which makes their study very ... 
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 3to1 functions over \(\mathbb {F}_{2^{n}}\) for even values of n. We investigate the properties and behavior of triplicate functions, and of 3to1 among ...