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...
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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.
rotationsymmetric (RotS) booleanfunctions have been used as components of different cryptosystems. This class of booleanfunctions are invariant under circular translation of indices. Using Burnside's lemma it c...
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rotationsymmetric (RotS) booleanfunctions have been used as components of different cryptosystems. This class of booleanfunctions are invariant under circular translation of indices. Using Burnside's lemma it can be seen that the number of n-variable rotation symmetric boolean functions is 2(gn), where g(n) = (t/n)Sigma(t\n) phi(t)2(n/t), and phi(.) is the Euler phi-function, In this paper, we find the number of short and long cycles of elements in F-2(n) having fixed weight, under the RotS action. As a consequence we obtain the number of homogeneous RotS functions having algebraic degree w. Our results make the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by executing computer programs. We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotationsymmetric bent function having degree > 2. Further, we studied the RotS functions on 5, 6, 7 variables by computer search for correlation immunity and propagation characteristics and found some functions with very good cryptographic properties which were not known earlier. (C) 2007 Elsevier B.V. All rights reserved.
In 1999, Pieprzyk and Qu presented rotationsymmetric (RotS) functions as components in the rounds of hashing algorithm. Later, in 2002, Cusick and Stǎnicǎ presented further advancement in this area. This class of B...
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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...
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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 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...
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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.
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...
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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.
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,...
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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...
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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.
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...
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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...
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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.
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