Constructions of booleanfunctions with various cryptographic properties have always been an important challenge in cryptography. This paper proposes systematic constructions of even- variable rotationsymmetric Boole...
详细信息
Constructions of booleanfunctions with various cryptographic properties have always been an important challenge in cryptography. This paper proposes systematic constructions of even- variable rotation symmetric boolean functions satisfying almost all cryptographic criteria, that is, resiliency, optimal algebraic degree, strict avalanche criterion, high nonlinearity, nonexistence of nonzero linear structures, good global avalanche characteristics. Moreover, some of the constructions also have high algebraic immunity. This is the first time that booleanfunctions having such cryptographic properties are obtained, which can be considered as good candidates for the design of real-life encryption schemes.
How to design cryptographic booleanfunctions is a challenge work in the design of stream and block ciphers. Cryptographic criteria of booleanfunctions are connected with some known cryptanalytic attacks. To resist t...
详细信息
How to design cryptographic booleanfunctions is a challenge work in the design of stream and block ciphers. Cryptographic criteria of booleanfunctions are connected with some known cryptanalytic attacks. To resist these known attacks, it is important to search booleanfunctions with some properties, including balancedness, optimal algebraic immunity, high algebraic degree, good nonlinearity, high correlation immunity, etc. rotation symmetric boolean functions (RSBFs) can have these properties simultaneously. In this paper, we propose a new class of balanced 2p-variable RSBFs based on the compositions of an integer, where pis an odd prime. It is found that the functions of this class have optimal algebraic immunity, and their nonlinearity reaches 22p-1 - (2p-1 ) + 2 p-2 i=3 (i - 1) (i - 2) ( p-2 ) + N eta + 1 (where N eta = p-2-(p mod 4) and p is an odd prime), which is higher than the previously constructed balanced even-variable RSBFs with optimal algebraic immunity. At the same time, the algebraic degree of the constructed functions are studied, and the results show that they can be optimal under certain conditions. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
rotation symmetric boolean functions are potentially rich in functions of cryptographic significance. In this paper, a new construction of odd-variable rotation symmetric boolean functions with optimal algebraic immun...
详细信息
rotation symmetric boolean functions are potentially rich in functions of cryptographic significance. In this paper, a new construction of odd-variable rotation symmetric boolean functions with optimal algebraic immunity is presented. By a direct calculation, the nonlinearity of the newly constructed functions is higher than the nonlinearities of all the known odd-variable rotation symmetric boolean functions with optimal algebraic immunity. The algebraic degree and the fast algebraic immunity of our functions are also considered. (C) 2021 Elsevier B.V. All rights reserved.
rotation symmetric boolean functions (RSBFs) are used widely in symmetric cryptography. In this paper, a systematic construction of balanced odd-variable RSBFs satisfying strict avalanche criterion is proposed. Hence,...
详细信息
rotation symmetric boolean functions (RSBFs) are used widely in symmetric cryptography. In this paper, a systematic construction of balanced odd-variable RSBFs satisfying strict avalanche criterion is proposed. Hence, a class of (6k + 3)-variable resilient RSBFs satisfying strict avalanche criterion is also presented for any k >= 2. Some of the obtained RSBFs have many other good cryptographic properties at the same time, that is, optimal algebraic degree, good global avalanche characteristics, high nonlinearity and nonexistence of nonzero linear structures. Moreover, we obtain some count results of RSBFs satisfying strict avalanche criterion. This is the first time that the autocorrelation properties of RSBFs are investigated systemically.
Exponential sums of symmetricbooleanfunctions are linear recurrent with integer coefficients. This was first established by Cai, Green and Thierauf in the mid nineties. Consequences of this result has been used to s...
详细信息
Exponential sums of symmetricbooleanfunctions are linear recurrent with integer coefficients. This was first established by Cai, Green and Thierauf in the mid nineties. Consequences of this result has been used to study the asymptotic behavior of symmetricbooleanfunctions. Recently, Cusick extended it to rotation symmetric boolean functions, which are functions with good cryptographic properties. In this article, we put all these results in the general context of Walsh transforms and some of its generalizations (nega-Hadamard transform, for example). Precisely, we show that Walsh transforms, for which exponential sums are just an instance, of symmetric and rotation symmetric boolean functions satisfy linear recurrences with integer coefficients. We also provide a closed formula for the Walsh transform and nega-Hadamard transform of any symmetricbooleanfunctions. Moreover, using the techniques presented in this work, we show that some families of rotation symmetric boolean functions are not bent when the number of variables is sufficiently large and provide asymptotic evidence to a conjecture of Stnic and Maitra.
This paper studies the properties of orbit matrix and gives a formula to compute the number of these orbit matrices on 4p variables, where p is an odd prime. It has been demonstrated that the construction of 1-resilie...
详细信息
This paper studies the properties of orbit matrix and gives a formula to compute the number of these orbit matrices on 4p variables, where p is an odd prime. It has been demonstrated that the construction of 1-resilient rotation symmetric boolean functions(RSBFs) on 4p variables is equivalent to solving an equation system. By the proposed method, all 1-resilient RSBFs on 12 variables can be constructed. We present a counting formula for the total number of all 1-resilient RSBFs on 4p variables. As application of our method, some 1-resilient RSBFs on 12 variables are presented.
rotation symmetric boolean functions (RSBFs) that are invariant under circular translation of indices have been used as components of different cryptosystems. In this paper, odd-variable balanced RSBFs with maximum al...
详细信息
rotation symmetric boolean functions (RSBFs) that are invariant under circular translation of indices have been used as components of different cryptosystems. In this paper, odd-variable balanced RSBFs with maximum algebraic immunity (AI) are investigated. We provide a construction of n-variable (n = 2k + 1 odd and n >= 13) RSBFs with maximum AI and nonlinearity >= 2(n-1) - ((n-1)(k)) + 2(k) + 2(k-2) - k, which have nonlinearities significantly higher than the previous nonlinearity of RSBFs with maximum AI.
The rotation symmetric boolean functions which are invariant under the action of cyclic group have been used as components of different cryptosystems. In order to resist algebraic attacks, booleanfunctions should hav...
详细信息
The rotation symmetric boolean functions which are invariant under the action of cyclic group have been used as components of different cryptosystems. In order to resist algebraic attacks, booleanfunctions should have high algebraic immunity. This paper studies the construction of even-variable rotation symmetric boolean functions with optimum algebraic immunity. We construct ([ n/4] - 3) different rotation symmetric boolean functions which achieve both optimum algebraic immunity and high nonlinearity when an even n (n >= 16) . is given.
Plateaued functions play a significant role in cryptography as they have nice cryptographic properties. How to construct plateaued functions with high algebraic degree is always a challenge in cryptography. A boolean ...
详细信息
Plateaued functions play a significant role in cryptography as they have nice cryptographic properties. How to construct plateaued functions with high algebraic degree is always a challenge in cryptography. A boolean function over F2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{2<^>n}$$\end{document} is an idempotent if f(x2)=f(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(x<^>2)=f(x)$$\end{document} for all x is an element of F2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\in \mathbb {F}_{2<^>n}$$\end{document}. This paper presents some generic constructions of plateaued idempotents over F2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{2<^>n}$$\end{document} from known plateaued functions. Some classes of plateaued idempotents with high algebraic degree are obtained, including semi-bent idempotents with any possible algebraic degree. rotation symmetric boolean functions are invariant under the action of cyclic group. As there is a bijective correspondence between idempotents and rotation symmetric boolean functions, a large class of rotationsymmetric plateaued functions with high algebraic degree can be obtained.
We show that, under certain conditions, restricted and biased exponential sums and Walsh transforms of symmetric and rotation symmetric boolean functions are, as in the case of nonbiased domain, C-finite sequences. We...
详细信息
We show that, under certain conditions, restricted and biased exponential sums and Walsh transforms of symmetric and rotation symmetric boolean functions are, as in the case of nonbiased domain, C-finite sequences. We also prove that under other conditions, these sequences are P-finite, which is a somewhat different behavior than their nonbiased counterparts. We further show that exponential sums and Walsh transforms of a family of rotationsymmetric monomials over the restricted domain E-n,E-j = {x is an element of F-2(n) : wt ( x) = j} (wt (x) is the weight of the vector x) are given by polynomials of degree at most j, and so, they are also C-finite sequences. Finally, we also present a study of the behavior of symmetricbooleanfunctions under these biased transforms.
暂无评论