Samir Hodžić

University of Primorska | UP · Department of Mathematics (UP IAM)

Quadratic almost bent (AB) functions are characterized by the property that the duals of their component functions are bent functions. We prove that these duals are also quadratic and illustrate that these bent duals may give rise to vectorial bent functions (in certain cases having a maximal output dimension). A necessary and sufficient condition...

Some recent research articles (Zhang et al. in Lecture Notes in Computer Science, 10194, 298-313. (2017), Zhang et al. in Discret. Appl. Math. 285(1), 458-472. (2020)) addressed an explicit specification of indicators that specify bent functions in the so-called C and D classes, derived from the Maiorana-McFarland (M) class by C. Carlet in 1994 (Ca...

Farfalle is a permutation-based pseudo-random function which has been proposed by G. Bertoni et al. in 2017. In this work, we show that by observing suitable inputs to Farfalle, one can derive various constructions of a periodic function with a period that involves a secret key. As this admits the application of Simon's algorithm in the so-called Q...

Integral cryptanalysis based on division property is a powerful cryptanalytic method whose range of successful applications was recently extended through the use of Mixed-Integer Linear Programming (MILP). Although this technique was demonstrated to be efficient in specifying distinguishers of reduced round versions of several families of lightweig...

The first and the third authors recently introduced a spectral construction of plateaued and of 5-value spectrum functions. In particular, the design of the latter class requires a specification of integers $\{W(u):u\in \mathbb {F}^{n}_{2}\}$ , where $W(u)\in \left\{{0, \pm 2^{\frac {n+s_{1}}{2}}, \pm 2^{\frac {n+s_{2}}{2}}}\right\}$ , so that...

Constructions of quantum distinguishers (extended to key recovery attacks) for generalized Feistel networks have been recently proposed in several works, where the main focus has been on Type 1 and 2 schemes. In this work, we derive a quantum distinguisher for 7 and 8 rounds of the SMS4 block cipher, which belongs to the class of unbalanced (contra...

In this work, we employ the concept of composite representation of Boolean functions, which represents an arbitrary Boolean function as a composition of one Boolean function and one vectorial function, for the purpose of specifying new secondary constructions of bent/plateaued functions. This representation gives a better understanding of the exist...

In this work, we derive a method for constructing quantum distinguishers for GFNs (Generalized Feistel-like schemes with invertible inner functions and XORs), where for simplicity 4 branches are considered. The construction technique is demonstrated on Type-3 GFN, where some other cyclically inequivalent GFNs are considered as examples. Introducing...

\(\mathbb {Z}\)-bent functions, mappings from \(\mathbb {F}_2^n\) to a subset of \(\mathbb {Z}\), were introduced by Dobbertin and Leander (Des Codes Cryptogr 49:3–22, 2008) as an attempt to capture the origin of standard bent functions and in particular to understand better a recursive construction framework of bent functions. Nevertheless, many q...

Non‐linear filtering generators, as a well‐known family of stream ciphers, employ a filtering function F:GF(2)n→GF(2)m to process the secret state bits and thus outputs binary keystream blocks of length m. In this study, the authors extend the framework of a generic cryptanalytic method applicable to non‐linear filtering generators called generalis...

Various methods for reducing hardware implementation cost of incompletely specified index generating functions have been proposed lately. Considering the methods based on linear decomposition, for the first time in this work, we provide necessary and sufficient conditions which describe the linear decomposition of these functions in general. These...

The design of plateaued functions over GF(2) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> , also known as 3-valued Walsh spectra functions (taking the values from the set {0, ±2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Γ(n+s/2)1</sup> }),...

Whereas the design and properties of bent and plateaued functions have been frequently addressed during the past few decades, there are only a few design methods of the so-called five-valued spectra Boolean functions whose Walsh spectra take the values in {0, ±2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999...

This work extends the idea introduced by Hou and Langevin (J. Combin. Theory, Ser. A, 80:232–246, 1997) of applying nonlinear permutations to (a portion of) the input variable space of a given Boolean function so that the resulting function is bent. Applying such a permutation to a bent function that can be represented in a suitable form then gives...

Whereas the design and properties of bent and plateaued functions have been frequently addressed during the past few decades, there are only a few design methods of so-called 5-valued spectra Boolean functions whose Walsh spectra takes the values in $\{0, \pm 2^{\lambda_1}, \pm 2^{\lambda_2}\}$. Moreover, these design methods mainly regards the spe...

Whereas the design and properties of bent and plateaued functions have been frequently addressed during the past few decades, there are only a few design methods of so-called 5-valued spectra Boolean functions whose Walsh spectra takes the values in $\{0, \pm 2^{\lambda_1}, \pm 2^{\lambda_2}\}$. Moreover, these design methods mainly regards the spe...

The design of plateaued functions over $GF(2)^n$, also known as 3-valued Walsh spectra functions (taking the values from the set $\{0, \pm 2^{\lceil \frac{n+s}{2} \rceil}\}$), has been commonly approached by specifying a suitable algebraic normal form which then induces this particular Walsh spectral characterization. In this article, we consider t...

In this work, we employ the concept of {\em composite representation} of Boolean functions, which represents an arbitrary Boolean function as a composition of one Boolean function and one vectorial function, for the purpose of specifying new secondary constructions of bent/plateaued functions. This representation gives a better understanding of the...

Generalized bent (gbent) functions is a class of functions f:Z2n→Zq, where q≥2 is a positive integer, that generalizes a concept of classical bent functions through their co-domain extension. A lot of research has recently been devoted towards derivation of the necessary and sufficient conditions when f is represented as a collection of Boolean fun...

In this article, using rather elementary technique and the derived formula that relates the coefficients of a polynomial over a finite field and its derivative, we deduce many interesting results related to derivatives of Boolean functions and derivatives of mappings over finite fields. For instance, we easily identify several infinite classes of p...

In this article an optimal selection of tap positions for certain LFSR-based encryption schemes is investigated from both design and cryptanalytic perspective. Two novel algorithms towards an optimal selection of tap positions are given which can be satisfactorily used to provide (sub)optimal resistance to some generic cryptanalytic techniques appl...

Although several methods for estimating the resistance of a random Boolean function against (fast) algebraic attacks were proposed, these methods are usually infeasible in practice for relative large input variables n (for instance n ≥ 30) due to increased computational complexity. An efficient estimation the resistance of Boolean function (with re...

In difference to many recent articles that deal with generalized bent (gbent) functions $f:\mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$ for certain small valued $q\in \{4,8,16 \}$, we give a complete description of these functions for both $n$ even and odd and for any $q=2^k$ in terms of both the necessary and sufficient conditions their component func...

Generalized bent (gbent) functions is a class of functions $f: \mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$, where $q \geq 2$ is a positive integer, that generalizes a concept of classical bent functions through their co-domain extension. A lot of research has recently been devoted towards derivation of the necessary and sufficient conditions when $f$...

The necessary and sufficient conditions for a class of functions $f:\mathbb{Z}_2^n \rightarrow \mathbb{Z}_q$, where $q \geq 2$ is an even positive integer, have been recently identified for $q=4$ and $q=8$. In this article we give an alternative characterization of the generalized Walsh-Hadamard transform in terms of the Walsh spectra of the compon...

In this article we present a broader theoretical framework useful in studying the properties of so-called generalized bent functions. We give the sufficient conditions (and in many cases also necessary) for generalized bent functions when these functions are represented as a linear combination of: generalized bent; Boolean bent; and a mixture of ge...

Although there are many different approaches used in cryptanalysis of nonlinear filter generators, the selection of tap positions in connection to guess and determine cryptanalysis has not received enough attention yet. In a recent article [18], it was shown that the so-called filter state guessing attack (FSGA) introduced in [15], which applies to...