On the number of unsuitable boolean functions in constructions of filter and combining models of stream ciphers

It is well known that every stream cipher is based on a good pseudorandom generator. For cryptographic purposes, we are interested in generation of pseudorandom sequences of the maximal possible period. A feedback register is one of the most known cryptographic primitives that is used in construction of stream generators. We analyze periodic properties of pseudorandom sequences produced by filter and combiner generators equipped with nonlinear Boolean functions. We determine which nonlinear functions in these schemes lead to pseudorandom sequences of not maximal possible period. We call such functions unsuitable and count the exact number of them for an arbitrary n

О числе ℓ-подходящих булевых функций в конструкциях фильтрующей и комбинирующей моделей поточных шифров

It is well known that every stream cipher is based on a good pseudorandom generator. For cryptographic purposes, we are interested in generating pseudorandom sequences with the maximum possible period. A feedback register is one of the most known cryptographic primitives that is used to construct stream ciphers. We consider periodic properties of pseudorandom sequences produced by filter and combiner generators (two known schemes of stream generators based on feedback registers). We analyze functions in these schemes that lead to output sequences of period at least a given number I. We call such functions l-suitable and count the exact number of them for an arbitrary n

Mathematical problems and solutions of the Ninth International Olympiad in Cryptography NSUCRYPTO

Every year the International Olympiad in Cryptography Non-Stop University CRYPTO (NSUCRYPTO) offers mathematical problems for university and school students and, moreover, for professionals in the area of cryptography and computer science. The mail goal of NSUCRYPTO is to draw attention of students and young researchers to modern cryptography and raise awareness about open problems in the field. We present problems of NSUCRYPTO'22 and their solutions. There are 16 problems on the following topics: ciphers, cryptosystems, protocols, e-money and cryptocurrencies, hash functions, matrices, quantum computing, S-boxes, etc. They vary from easy mathematical tasks that could be solved by school students to open problems that deserve separate discussion and study. So, in this paper, we consider several open problems on three-pass protocols, public and private keys pairs, modifications of discrete logarithm problem, cryptographic permutations and quantum circuits

Математические проблемы и решения Девятой международной олимпиады по криптографии NSUCRYPTO

Every year the International Olympiad in Cryptography Non-Stop University CRYPTO (NSUCRYPTO) offers mathematical problems for university and school students and, moreover, for professionals in the area of cryptography and computer science. The main goal of NSUCRYPTO is to draw attention of students and young researchers to modern cryptography and raise awareness about open problems in the field. We present problems of NSUCRYPTO'22 and their solutions. There are 16 problems on the following topics: ciphers, cryptosystems, protocols, e-money and cryptocurrencies, hash functions, matrices, quantum computing, S-boxes, etc. They vary from easy mathematical tasks that could be solved by school students to open problems that deserve separate discussion and study. So, in this paper, we consider several open problems on three-pass protocols, public and private keys pairs, modifications of discrete logarithm problem, cryptographic permutations, and quantum circuits