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New Classes of 8-bit Permutations Based on a Butterfly Structure
Математические вопросы криптографии. 2019. Vol. 10. No. 2. P. 169-180.
This work introduces new classes of 8-bit permutation based on a butterfly structure. These classes set up a new way for generating 2n-bit permutation from n-bit ones. We introduce some classes that contain permutations with good cryptographic properties and could be efficiently implemented for hardware and software applications.
Коврижных М. А., Fomin D., Прикладная дискретная математика. Приложение 2021 № 14 С. 181-184
Bijective vector Boolean functions (permuta- tions) are used as nonlinear primitives of many symmetric ciphers. In this paper, we study a generalized construction of (2m, 2m)-functions using monomial and arbitrary m-bit per- mutations as constituent elements. A heuristic algorithm for obtaining bijective Boolean functions with given nonlinearity and differential uniformity, based on this construction, is proposed. For ...
Added: September 22, 2021
Fomin D., Обозрение прикладной и промышленной математики 2018 Т. 25 № 4 С. 379-381
Одним из негласных правил создания низкоресурсного блочного шифра стало использование подстановок маленькой размерности. Это обусловлено тем, что такие подстановки хорошо исследованы, требуют небольшого количества ресурсов при аппаратной реализации, и известны эффективные механизмы маскирования, позволяющие защититься от атак по побочным каналам утечки. В то же время, криптографические свойства таких подстановок уступают криптографическим характеристикам подстановок большей размерности.Одним из компромиссов является построение подстановок больших размерностей ...
Added: May 4, 2019
Fomin D., Математические вопросы криптографии 2020 Т. 11 № 4 С. 133-149
We study parameters of some permutations constructed by the «Butterfly» scheme. The influence of these parameters on the algebraic degree of permutation and its differential uniformity is investigated. ...
Added: November 25, 2020
Fomin D., Математические вопросы криптографии 2020 Т. 11 № 3 С. 121-138
We generalize the method of construction of permutations based on the Butterfly structure for the case of arbitrary arithmetic space with even dimension over the field of two elements. An approach to the construction of permutations by means of nonbalanced (2m,m)-functions with high nonlinearity is suggested. ...
Added: November 25, 2020
Ivchenko G., Медведев Ю. И., Математические вопросы криптографии 2012 Т. 3 № 3 С. 21-34
Предлагается общая вероятностная модель для булевых функций от n переменных, задаваемая произвольной вероятностной мерой на множестве всех таких функций. Выводится характеристическая функция спектра Уолша случайной функции и находятся точные и асимптотические (при n→∞) распределения некоторых его характеристик для случая
параметрической меры. ...
Added: November 19, 2012
Lozhkin S. A., Danilov B.R., Computational Mathematics and Modeling 2012 Vol. 23 No. 4 P. 487-506
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements may have different input delays. Asymptotic bounds of the form τ B n±O(1), where τ B is a constant that depends only on the basis B, are obtained for ...
Added: December 2, 2019
Ложкин С. А., Шуплецов М. С., Коноводов В. А. et al., Проблемы разработки перспективных микро- и наноэлектронных систем (МЭС) 2016 Т. 1 С. 40-47
The synthesis of optimal or suboptimal switching circuits is an actual problem of theory of discrete control
systems. Libraries of such circuits could be used in various algorithms of logic synthesis (e.g., see [1]). The structure
analysis of optimal circuits for functions of few variables may be useful in the development of standard cell libraries.
The first catalogs ...
Added: December 2, 2019
Ложкин С. А., Danilov B. R., Прикладная математика и информатика 2011 № 39 С. 107-129
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements may have different input delays. Asymptotic bounds of the form τ_B n ± O(1), where τ_B is a constant that depends only on the basis B, are obtained for ...
Added: December 2, 2019
Fomin D., Трифонов Д. И., Прикладная дискретная математика. Приложение 2019 № 12 С. 134-137
The paper studies the issues of implementation of one class of S-Boxes on FPGA and ASIC and compares them with the implementation of arbitrary mappings V8 → V8. The way of implementation of arbitrary S-Box is studied. It’s shown that any S-Box over V8 can be implemented using 40 LUTs (812 GE). For one class of S-Boxes over V8 with high cryptographic ...
Added: October 6, 2019
Sysoeva L., Вестник Московского университета. Серия 1: Математика. Механика 2019 № 6 С. 51-55
Рассматривается задача о реализации булевых функций инициальными булевыми автоматами с константными состояниями и n входами, т.е. автоматами, такими, что в любом из состояний функция выхода совпадает с одной из булевых констант 0 или 1, зависящих от n переменных, n > 0.
Построен пример инициального булева автомата с минимальным количеством константных состояний и n входами, реализующего максимальное возможное число булевых функций от n фиксированных переменных, при ...
Added: October 14, 2018
D. B. Fomin, M. A. Kovrizhnykh, Математические вопросы криптографии 2022 Vol. 13 No. 2 P. 37-52
The work is dedicated to the theoretical substantiation of a directed search for 8-bit permutations with given cryptographic properties: differential uniformity and nonlinearity. The statements on the partition of the set of vectorial Boolean functions derived using generalized construction into equivalence classes are proved. The statements that allow one to reject functions from equivalence classes ...
Added: August 24, 2022
Fedorov S., Логачёв О. А., Ященко В. В., Discrete Mathematics and Applications 2019 Vol. 29 No. 2 P. 89-101
Added: June 16, 2021
Babash A. V., Романова Е. В., Александров А. А. et al., Системы высокой доступности 2013 Т. 9 № 3 С. 36-45
Приведены методы дешифрования шифра перестановки с оценкой их трудоемкости. Трудоемкости лучше известрых ранее. ...
Added: January 14, 2014
Podolskii V. V., Logical Methods in Computer Science 2013 Vol. 9 No. 2 P. 1-17
An integer polynomial p of n variables is called a threshold gate for a Boolean function f of n variables if for all x∈{0,1}n f(x)=1 if and only if p(x) > 0. The weight of a threshold gate is the sum of its absolute values. In this paper we study how large a weight might be needed if ...
Added: October 20, 2014
Fedorov S., Математические вопросы криптографии 2019 Vol. 10 No. 2 P. 159-168
Рассматривается недавно предложенный подход к исследованию булевых функций, в основе которого лежит понятие класса Δ-эквивалентности: множества булевых функций с одной и той же функцией автокорреляции. Такая классификация представляется полезной, поскольку многие криптографические характеристики булевых функций, принадлежащих одному и тому же классу Δ-эквивалентности, одинаковы. ...
Added: September 4, 2019
Sysoeva L., Ученые записки Казанского университета. Серия: Физико-математические науки 2014 Т. 156 № 3 С. 116-122
In this paper, we consider the problem of implementation of Boolean functions by generalized alpha-formulas. The notion of generalized alpha-formula is introduced. For a given set of Boolean functions, we define the notion of a universal set of generalized alpha-formulas. We also propose the notion of dual generalized alpha-formulas and formulate the principle of duality ...
Added: November 11, 2017
М. А. Коврижных, Д. Б. Фомин, Прикладная дискретная математика 2022 № 57 С. 5-21
In this paper, we study a generalized construction of (2m, 2m)-functions using monomial and arbitrary m-bit permutations as constituent elements. We investigate the possibility of constructing bijective vectorial Boolean functions (permutations) with specified cryptographic properties that ensure the resistance of encryption algorithms to linear and differential methods of cryptographic analysis. We propose a heuristic algorithm ...
Added: October 8, 2022
Fomin D., Прикладная дискретная математика. Приложение 2021 № 14 С. 51-55
The paper studies new ways of con- structing differentially 2δ-uniform bijections over F_{2^{2m}} , m≥3, that are based on TU-construction. Some well known results on the constructing differentially 4-uniform permutations over F_{2^{2m}} are generalized in this work. The core idea is to use TU-construction and differentially δ-uniform bijections to construct 2^t · δ-uniform permutations. A generalized method for constructing 2m-bit differentially 4-uniform permutations ...
Added: September 22, 2021
Sysoeva L., Moscow University Mathematics Bulletin 2013 Vol. 68 No. 4 P. 211-214
The problem of realization of Boolean functions by generalized α-formulas is considered. The notion of a universal set of generalized α-formulas is introduced for a given set of Boolean functions. Universal sets of generalized α-formulas are constructed for the set of constant-preserving Boolean functions. ...
Added: February 28, 2017
Авраамова О. Д., Fomin D., Серов В. А. et al., Математические вопросы криптографии 2021 Vol. 12 No. 2 P. 21-38
In this paper we consider a bit-sliced implementation of the non-linear transformation shared by GOST R 34.12-2015 “Kuznyechik” block cipher and GOST R 34.11-2012 “Streebog” hash function. We combine analytical and computer methods to get a 226 Boolean operations representation. ...
Added: July 26, 2021
Yashunsky A., Вестник Московского университета. Серия 1: Математика. Механика 2019 № 4 С. 3-9
We consider systems of Boolean functions inducing algebras of Bernoulli distributions, whose universal set has a single limit point. We establish a criterion for an algebra generated by a given set of distributions to have a unique limit point. ...
Added: September 9, 2020
Sysoeva L., Вестник Московского университета. Серия 1: Математика. Механика 2017 № 2 С. 19-28
The problem of realization of Boolean functions by initial Boolean automata with constant states and n inputs is considered. Initial Boolean automaton with constant states and n inputs is an initial automaton with output such that in all states output functions are n-ary constant Boolean functions 0 or 1. The exact value of the maximum ...
Added: February 28, 2017
Энатская Н.Ю., Колчин А. В., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2014 № 4 С. 80-86
We consider several procedures to number all outcomes of a permutation scheme, establish a one-to-one correspondence between the outcome and its number generated in the numbering procedure, and give some methods to simulate the outcomes. ...
Added: March 13, 2015
Sysoeva L., Moscow University Mathematics Bulletin 2019 Vol. 74 No. 6 P. 241-245
The problem of realization of Boolean functions by initial Boolean automata with constant states and n inputs is considered. Initial Boolean automaton with constant states and n inputs is an initial automaton with output such that in all states the output functions are n-ary constant Boolean functions 0 or 1. An example of an initial Boolean automaton with the minimum ...
Added: November 22, 2020