Aleksandr Kutsenko

Novosibirsk State University · Department of Mechanics and Mathematics

The Walsh--Hadamard spectrum of a bent function uniquely determines a dual function. The dual of a bent function is also bent. A bent function that is equal to its dual is called a self-dual function. The Hamming distance between a bent function and its dual is related to its Rayleigh quotient. Carlet, Danielsen, Parker, and Sole studied Rayleigh q...

Non-Stop University CRYPTO is the International Olympiad in Cryptography that was held for the eight time in 2021. Hundreds of university and school students, professionals from 33 countries worked on mathematical problems in cryptography during a week. The aim of the Olympiad is to attract attention to curious and even open scientific problems of...

Bent functions of the form $\mathbb{F}_2^n\rightarrow\mathbb{Z}_q$, where $q\geqslant2$ is a positive integer, are known as generalized bent (gbent) functions. Gbent functions for which it is possible to define a dual gbent function are called regular. A regular gbent function is said to be self-dual if it coincides with its dual. In this paper we...

The International Olympiad in Cryptography NSUCRYPTO is the unique Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. In 2020, it was held for the seventh time. Prizes...

A bent function is a Boolean function in even number of variables which is on the maximal Hamming distance from the set of affine Boolean functions. It is called self-dual if it coincides with its dual. It is called anti-self-dual if it is equal to the negation of its dual. A mapping of the set of all Boolean functions in n variables to itself is s...

NSUCRYPTO is the unique cryptographic Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. From the very beginning, the concept of the Olympiad was not to focus on solvi...

In this work we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We give results for iterative contruction of bent functions in $n+2$ variables based on the concatention of four bent functions and consider related open problem proposed by one of t...

In this paper we study metrical properties of Boolean bent functions which coincide with their dual bent functions. We propose an iterative construction of self-dual bent functions in \(n+2\) variables through concatenation of two self-dual and two anti-self-dual bent functions in n variables. We prove that minimal Hamming distance between self-dua...

Problems and their solutions of the Fifth International Students’ Olympiad in cryptography NSUCRYPTO’2018 are presented. We consider problems related to attacks on ciphers and hash functions, Boolean functions, quantum circuits, Enigma, etc. We discuss several open problems on orthogonal arrays, Sylvester matrices, and disjunct matrices. The proble...

In the paper, we study isometric mappings of the set of all Boolean functions in n variables into itself which preserve self-duality and the Rayleigh quotient of Boolean function and generalize known results. It is proved that isometric mapping preserves self-duality if and only if it preserves anti-self-duality. The complete characterization of th...

Problems and their solutions of the Fifth International Students' Olympiad in cryptography NSUCRYPTO'2018 are presented. We consider problems related to attacks on ciphers and hash functions, Boolean functions, quantum circuits, Enigma, etc. We discuss several open problems on orthogonal arrays, Sylvester matrices and disjunct matrices. The problem...

Mathematical problems and their solutions from the fourth International Students’ Olympiad in cryptography (NSUCRYPTO-2017) are presented. We consider problems related to attacks on ciphers and hash functions, cryptographic Boolean functions, linear branch numbers, addition chains, and error correction codes, among others. We discuss several open p...

We study the properties of self-dual bent functions. It is proved that the minimal Hamming distance between self-dual bent functions is $2^{n/2}$ and the set of self-dual bent functions is a metrically regular set. The necessary and sufficient conditions for the iterative bent functions BI (A. Canteaut, P. Charpin, 2003) to be self-dual bent have b...

Mathematical problems and their solutions of the Fourth International Students' Olympiad in cryptography NSUCRYPTO'2017 are presented. We consider problems related to attacks on ciphers and hash functions, cryptographic Boolean functions, the linear branch number, addition chains, error correction codes, etc. We discuss several open problems on alg...

A bent function is self-dual if it is equal to its dual function. We study the metric properties of the self-dual bent functions constructed on using available constructions. We find the full Hamming distance spectrum between self-dual Maiorana–McFarland bent functions. Basing on this, we find the minimal Hamming distance between the functions unde...

The mathematical problems and their solutions of the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, problems about secrete sharing schemes and pseudorandom binary sequences, biom...

We prove that there doesn't exist an isometry on the set of all Boolean functions in 2k variables which acts on the set of bent functions by assigning the dual bent functions. We state the affine equivalence of a bent function and its dual bent function in the case of small number of variables.