Results 1 - 10 of 1,185

Rotation Symmetric Boolean Functions – Count and Cryptographic Properties

by Pantelimon Stănica ̆ A, Subhamoy Maitra B
"... Rotation symmetric (RotS) Boolean functions have been used as components of dif-ferent cryptosystems. This class of Boolean functions 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 2gn, ..."
Abstract - Add to MetaCart
the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by ex-ecuting computer programs. We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotation symmetric bent function having

Rotation Symmetric Boolean Functions – Count and Cryptographic Properties

by Pantelimon Stănică, Subhamoy Maitra - In R. C. Bose Centenary Symposium on Discrete Mathematics and Applications, December 2002. Electronic Notes in Discrete Mathematics, Elsevier, Vol 15 , 2002
"... In 1999, Pieprzyk and Qu presented rotation symmetric (RotS) functions as components in the rounds of hashing algorithm. Later, in 2002, Cusick and Stănică presented further advancement in this area. This class of Boolean functions are invariant under circular translation of indices. In this paper, ..."
Abstract - Cited by 20 (6 self) - Add to MetaCart
, and 15104, RotS bent functions on 4, 6, and 8 variables respectively. Experimental results up to 10 variables show that there is no homogeneous rotation symmetric bent function with degree> 2. Further, we studied the RotS functions on 5, 6, 7 variables for correlation immunity and propagation

Results on Rotation Symmetric Bent and Correlation Immune Boolean Functions

by Pantelimon Stănică, Subhamoy Maitra, John A. Clark - Fast Software Encryption Workshop (FSE 2004 , 2004
"... Abstract. Recent research shows that the class of Rotation Symmetric Boolean Functions (RSBFs), i.e., the class of Boolean functions that are invariant under circular translation of indices, is potentially rich in functions of cryptographic significance. Here we present new results regarding the Rot ..."
Abstract - Cited by 14 (6 self) - Add to MetaCart
the Rotation Symmetric (rots) correlation immune (CI) and bent functions. We present important data structures for efficient search strategy of rots bent and CI functions. Further, we prove the nonexistence of homogeneous rots bent functions of degree ≥ 3 on a single cycle.

On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees

by Sihong Su, Xiaohu Tang
"... In the literature, few constructions of n-variable rotation symmetric bent functions have been pre-sented, which either have restriction on n or have algebraic degree no more than 4. In this paper, for any even integer n = 2m ≥ 2, a first systemic construction of n-variable rotation symmetric bent f ..."
Abstract - Add to MetaCart
In the literature, few constructions of n-variable rotation symmetric bent functions have been pre-sented, which either have restriction on n or have algebraic degree no more than 4. In this paper, for any even integer n = 2m ≥ 2, a first systemic construction of n-variable rotation symmetric bent

Rotation Symmetric Boolean Functions – Count and Cryptographic Properties

by Stanica Pantelimon, Pantelimon Stănica ̆ A, Subhamoy Maitra B , 2008
"... Rotation symmetric (RotS) Boolean functions have been used as components of dif-ferent cryptosystems. This class of Boolean functions 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 2gn, ..."
Abstract - Add to MetaCart
the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by ex-ecuting computer programs. We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotation symmetric bent

Homogeneous bent functions

by Chengxin Qu, Jennifer Seberry, Josef Pieprzyk - Discrete Applied Math , 2000
"... This paper discusses homogeneous bent functions. The space of homogeneous func-tions of degree three in six boolean variables was exhaustively searched and thirty bent functions were found. These are found to occur in a single orbit under the action of relabeling of the variables. The homogeneous be ..."
Abstract - Cited by 7 (1 self) - Add to MetaCart
This paper discusses homogeneous bent functions. The space of homogeneous func-tions of degree three in six boolean variables was exhaustively searched and thirty bent functions were found. These are found to occur in a single orbit under the action of relabeling of the variables. The homogeneous

On the Degree of Homogeneous Bent Functions

by Qing-shu Meng, Huan-guo Zhang, Min Yang, Jing-song Cui , 2004
"... It is well known that the degree of a 2m-variable bent function is at most m. However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree m in 2m variables when m > 3; there is no homogenous bent function of d ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
It is well known that the degree of a 2m-variable bent function is at most m. However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree m in 2m variables when m > 3; there is no homogenous bent function

Fast Evaluation, Weights and Nonlinearity of Rotation-Symmetric Functions

by Thomas Cusick, Pantelimon Stanica - Discrete Mathematics , 2000
"... We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu [6]. We give exact results for the nonlinearity and weight of 2-degree RotS functions with the help of the semi-bent functions [2] and we give the generating function for the weight of the ..."
Abstract - Cited by 25 (4 self) - Add to MetaCart
We study the nonlinearity and the weight of the rotation-symmetric (RotS) functions defined by Pieprzyk and Qu [6]. We give exact results for the nonlinearity and weight of 2-degree RotS functions with the help of the semi-bent functions [2] and we give the generating function for the weight

On the symmetric property of homogeneous boolean functions, Information Security and

by Chengxin Qu, Jennifer Seberry, Josef Pieprzyk - Privacy, ACISP ' 99, Lecture Notes in Computer Science , 1999
"... Abstract. We use combinatorial methods and permutation groups to classify homogeneous boolean functions. The property of symmetry of a boolean function limits the size of the function’s class. We exhaustively searched for all boolean functions on V6. We found two interesting classes of degree 3 homo ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
homogeneous boolean functions: the first class is degree 3 homogeneous bent boolean functions; and the second is degree 3 homogeneous balanced boolean functions. Both the bent and balanced functions discovered have nice algebraic and combinatorial structures. We note that some structures can be extended to a

On the Bent Boolean Functions Which Are Symmetric

by Petr Savicky
"... Bent functions are the boolean functions having the maximal possible Hamming distance from the linear boolean functions. Bent functions were introduced and studied rst by Rothaus (1976). We prove that there are exactly four symmetric bent functions on every even number of variables. These functions ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
Bent functions are the boolean functions having the maximal possible Hamming distance from the linear boolean functions. Bent functions were introduced and studied rst by Rothaus (1976). We prove that there are exactly four symmetric bent functions on every even number of variables. These functions
Results 1 - 10 of 1,185