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.
Homogeneous rotationsymmetric (invariant under cyclic permutation of the variables) booleanfunctions have been extensively studied in recent years due to their applications in cryptography. In this paper we give an ...
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Homogeneous rotationsymmetric (invariant under cyclic permutation of the variables) booleanfunctions have been extensively studied in recent years due to their applications in cryptography. In this paper we give an explicit formula for the number of homogeneous rotationsymmetricfunctions over the finite field GF (p(m)) using Polya's enumeration theorem, which completely solves the open problem proposed by Yuan Li in 2008. This result simplifies the proof and the nonexplicit counting formula given by Shaojing Fu et al. over the field GF(p). This paper also gives an explicit count for n-variable balanced rotation symmetric boolean functions with n = pq, where p and q are distinct primes. Previous work only gave an explicit count for the case where n is prime and lower bounds for the case where n is a prime power. (C) 2013 Elsevier B.V. All rights reserved.
It is known that the set of rotation symmetric boolean functions has many functions with various useful properties for cryptography. This study shows how to construct some families of rotationsymmetricfunctions whic...
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It is known that the set of rotation symmetric boolean functions has many functions with various useful properties for cryptography. This study shows how to construct some families of rotationsymmetricfunctions which are balanced or plateaued. The authors also consider vectorial booleanfunctions [that is, maps from GF(2)(n) to GF(2)(m)] which are k-rotationsymmetric and they give two infinite families of such functions which are permutations with the maximum possible algebraic degree. The families of functions that they give provide a source, which can be searched for functions with other useful cryptographic properties.
Due to its richness in terms Of cryptographically properties along with its small search space 2(2n/n) comparable to the whole space 2(2n), the class of rotation symmetric boolean functions (RSBFs) has become the main...
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ISBN:
(纸本)9781424441983
Due to its richness in terms Of cryptographically properties along with its small search space 2(2n/n) comparable to the whole space 2(2n), the class of rotation symmetric boolean functions (RSBFs) has become the main focus on searching for a boolean function with good properties. Additionally, there are some other characteristics these functions might have which considered failure and should be avoided. For instance, the linear structure in boolean function other than all-zero is regarded as a weakness and the function posses this characteristic is considered fragile and should be excluded from using in the cryptographic algorithms. Therefore, in this paper we examine the existence of linear structures in RSBFs, and then we categorize them based on the number of input variables and their algebraic degree.
In this paper, we present partial results towards the conjectured nonexistence of homogeneous rotationsymmetric bent functions having degree > 2. (C) 2010 Elsevier B.V. All rights reserved.
In this paper, we present partial results towards the conjectured nonexistence of homogeneous rotationsymmetric bent functions having degree > 2. (C) 2010 Elsevier B.V. All rights reserved.
Recently, 9-variable booleanfunctions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of rotation symmetric boolean functions (RSBFs) by ...
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ISBN:
(纸本)9783540772231
Recently, 9-variable booleanfunctions having nonlinearity 241, which is strictly greater than the bent concatenation bound of 240, have been discovered in the class of rotation symmetric boolean functions (RSBFs) by Kavut, Maitra and Yucel. In this paper, we present several 9-variable booleanfunctions having nonlinearity of 242, which we obtain by suitably generalizing the classes of RSBFs and Dihedral symmetricbooleanfunctions (DSBFs). These functions do not have any zero in the Walsh spectrum values, hence they cannot be made balanced easily. This result also shows that the covering radius of the first order Reed-Muller code R(1, 9) is at least 242.
In this paper we study the neighbourhood of 15-variable Patterson-Wiedemann (PW) functions, i.e., the functions that differ by a small Hamming distance from the PW functions in terms of truth table representation. We ...
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In this paper we study the neighbourhood of 15-variable Patterson-Wiedemann (PW) functions, i.e., the functions that differ by a small Hamming distance from the PW functions in terms of truth table representation. We exploit the idempotent structure of the PW functions and interpret them as rotation symmetric boolean functions (RSBFs). We present techniques to modify these RSBFs to introduce zeros in the Walsh spectra of the modified functions with minimum reduction in nonlinearity. Our technique demonstrates 15-variable balanced and 1-resilient functions with currently best known nonlinearities 16272 and 16264 respectively. In the process, we find functions for which the autocorrelation spectra and algebraic immunity parameters are best known till date.
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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In this paper we present a constructive detection of minimal monomials in the algebraic normal form of rotation symmetric boolean functions (immune to circular translation of indices). This helps in constructing rotat...
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In this paper we present a constructive detection of minimal monomials in the algebraic normal form of rotation symmetric boolean functions (immune to circular translation of indices). This helps in constructing rotation symmetric boolean functions by respecting the rules we present here. (C) 2003 Elsevier B.V. All rights reserved.
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