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Results on Rotation Symmetric Bent and Correlation Immune Boolean Functions [chapter]

Pantelimon Stănică, Subhamoy Maitra, John A. Clark
2004 Lecture Notes in Computer Science  
Here we present new results regarding the Rotation Symmetric (rots) correlation immune (CI) and bent functions.  ...  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  ...  We present enumerative results (based on constructive techniques) on balanced and correlation immune RSBFs.  ... 
doi:10.1007/978-3-540-25937-4_11 fatcat:aru6y4fhuvbnvmdtiietglahlu

Construction of the optimal algebraic immunity Boolean functions with correlation immunity from transformation RSBFs

Jinglian Huang, S.A. Hamouda, M. Mirzaei, Z. Yu
2016 MATEC Web of Conferences  
On construction of rotation symmetric Boolean functions with the optimal algebraic immunity, we construct correlation immunity Boolean functions with the optimal algebraic immunity by translation transformation  ...  In this paper, we discuss the effect of the cryptographic properties of translation transformation rotation symmetric Boolean functions.  ...  The Bent function and the rotational symmetric Boolean functions(RSBFs) are important functions in cryptography.  ... 
doi:10.1051/matecconf/20166103006 fatcat:67a7gisoyrcvhd3vwlthatxbae

Page 1437 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
Summary: “We present a new proof of the Walsh transform char- acterization of correlation immune Boolean functions.  ...  The authors define rotation-symmetric functions as Boolean functions invariant under the cyclic shift of arguments: S (x1, X2,°°+, Xn) = f (Xn, X1,°°*,Xn-1).  ... 

Count of rotational symmetric bent Boolean functions [article]

Shashi Kant Pandey, Prasanna Raghaw Mishra
2019 IACR Cryptology ePrint Archive  
In this paper, we propose an upper bound for the count of rotational symmetric bent Boolean functions and characterize its truth table representation from the necessary condition of a rotational symmetric  ...  bent Boolean function.  ...  In [9] , Shano Jing et al. proposed the enumeration of balanced rotational symmetric Boolean functions and first order correlation immune rotational symmetric Boolean functions for n = p r number of variables  ... 
dblp:journals/iacr/PandeyM19 fatcat:yf7sp3d3cjembc47fjqyamhemm

Searching for Cryptographically Significant Rotation Symmetric Boolean Functions by Designing Heuristic Algorithms

Yongjuan Wang, Guangpu Gao, Qingjun Yuan, Qichun Wang
2022 Security and Communication Networks  
The experimental results show that our methods can generate cryptographically strong Boolean functions with high nonlinearity, 1-resilient functions, and optimal algebraic immunity.  ...  It has been proved that the set of rotation symmetric Boolean functions (RSBFs) is abundant in cryptographically strong functions with multiple criteria.  ...  tables of the rotation symmetric functions (RSTTs).  ... 
doi:10.1155/2022/8188533 fatcat:uvh6qiuw4zedlp7ocbt6o75w3a

On selected issues of Boolean function application in symmetric key cryptography against side channel attacks

Kamaruzzaman Seman, Muhammad Fahim Roslan, Azni Haslizan Ab Halim, M Nor Azizi Syam Mohd Sayuti
2019 Journal of Physics, Conference Series  
Within this work, the nonlinearity and correlation immunity issues of Boolean function is discussed followed by complementary counter measure against side channel attack especially differential power attack  ...  Boolean function plays a prominent role in building strong cryptography algorithm especially in symmetric block cipher.  ...  Correlation Immunity of Boolean function Correlation immunity of degree denoted as is one of the important properties in constructing good linear combiner in stream cipher.  ... 
doi:10.1088/1742-6596/1282/1/012001 fatcat:43gbjqnggvakbno4kmjmxdcviu

A Parallel Approach in Computing Correlation Immunity up to Six Variables

Carole J. Etherington, Matthew W. Anderson, Eric Bach, Jon T. Butler, Pantelimon Stănică
2016 International Journal of Foundations of Computer Science  
Boolean functions with high correlation immunity are desired in cryptographic systems because they are immune to correlation attacks.  ...  We show the use of a reconfigurable computer in computing the correlation immunity of Boolean functions of up to 6 variables.  ...  This is because all functions with these values of correlation immunity are rotation symmetric. Indeed, all of these functions are symmetric, which is a subtype of rotation symmetric functions.  ... 
doi:10.1142/s0129054116500131 fatcat:7v4qkbikubgntiirqwuk3x45ie

Almost Boolean Functions: The Design of Boolean Functions by Spectral Inversion

John A. Clark, Jeremy L. Jacob, Subhamoy Maitra, Pantelimon Stanica
2004 Computational intelligence  
The design of Boolean functions with properties of cryptographic significance is a hard task. In this paper, we adopt an unorthodox approach to the design of such functions.  ...  Our search space is the set of functions that possess the required properties. It is 'Booleanness' that is evolved.  ...  One class of function that has attracted attention recently is that of Rotation Symmetric Boolean Functions (RSBFs) [4, 17, 20] .  ... 
doi:10.1111/j.0824-7935.2004.00245.x fatcat:rdlh433rgbe4nonrwy2ltrmj6m

Generalization of Boolean Functions Properties to Functions Defined over GF(p)

`Hamed
2012 Journal of Computer Science  
Approach: We generalize some of the previous results on cryptographic Boolean functions to functions defined over GF(p); p > 2.  ...  Problem statement: Traditionally, cryptographic applications designed on hardware have always tried to take advantage of the simplicity of implementation functions over GF(p), p = 2, to reduce costs and  ...  The author in (Li, 2008) generalized the counting results of rotation symmetric Boolean functions to the rotation symmetric polynomials over finite fields GF(p).  ... 
doi:10.3844/jcssp.2012.809.814 fatcat:3bduurfp2bgtpjyghyrl5xyy4m

Rotation Symmetric Boolean Functions –; Count and Cryptographic Properties

Pantelimon Stǎnicǎ, Subhamoy Maitra
2003 Electronic Notes in Discrete Mathematics  
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  ...  We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotation symmetric bent function having degree > 2.  ...  Our results show that the search space of rotation symmetric functions is much smaller compared to the complete space of Boolean functions and so we were able to do some experiments on this class of functions  ... 
doi:10.1016/s1571-0653(04)00560-8 fatcat:bvavjsd4zvhnbieffy6cyxzoz4

Idempotents in the neighbourhood of Patterson-Wiedemann functions having Walsh spectra zeros

Sumanta Sarkar, Subhamoy Maitra
2008 Designs, Codes and Cryptography  
We exploit the idempotent structure of the PW functions and interpret them as Rotation Symmetric Boolean Functions (RSBFs).  ...  In the process, we find functions for which the autocorrelation spectra and algebraic immunity parameters are best known till date.  ...  Motivated by these results, we concentrate on PW functions in this paper and exploit the rotation symmetric structure of such functions to get best known nonlinearity results in terms of balanced and 1  ... 
doi:10.1007/s10623-008-9181-y fatcat:4gitpfvkbvayrcufgbzhy2ln5m

Results on Constructions of Rotation Symmetric Bent and Semi-bent Functions [chapter]

Claude Carlet, Guangpu Gao, Wenfen Liu
2014 Lecture Notes in Computer Science  
In this paper, we introduce a class of cubic rotation symmetric (RotS) functions and prove that it can yield bent and semi-bent functions.  ...  Incidentally, the proofs of bentness given here are useful for a paper studying a construction of idempotents from RotS functions, entitled "A secondary construction and a transformation on rotation symmetric  ...  Constructions of Rotation Symmetric Bent and Semi-bent Functions The lemma below is straightforward and well-known. Lemma 1.  ... 
doi:10.1007/978-3-319-12325-7_2 fatcat:x37wh4755ffyzf3jfu4l5mxpaa

A New Construction of odd-variable Rotation symmetric Boolean functions with good cryptographic properties

Bingxin Wang, School of Mathematics and Statistics, Henan University, Kaifeng, 475004, China, Sihong Su
2019 Advances in Mathematics of Communications  
In this paper, based on the theory of ordered integer partitions, we present a new class of odd-variable rotation symmetric Boolean functions with optimal algebraic immunity by modifying the support of  ...  Rotation symmetric Boolean functions constitute a class of cryptographically significant Boolean functions.  ...  Acknowledgments The authors would like to thank the associate editor and the anonymous reviewers for their constructive comments and suggestions which improved the quality of the paper.  ... 
doi:10.3934/amc.2020115 fatcat:7lkrjdpxv5gmtbubj5mbbgsxza

On homogeneous rotation symmetric bent functions

Qiang Meng, Lusheng Chen, Fang-Wei Fu
2010 Discrete Applied Mathematics  
In this paper, we present partial results towards the conjectured nonexistence of homogeneous rotation symmetric bent functions having degree > 2.  ...  Introduction Rotation symmetric (RotS) Boolean functions were first introduced at Eurocrypt 1998 (see [3] ). For RotS functions, one can reuse evaluations from previous iterations.  ...  In another direction, rotation symmetric bent functions have been studied in [3, 10, 11] .  ... 
doi:10.1016/j.dam.2010.02.009 fatcat:6fbtvy6k3rb2zojffa626wpcrm

Symmetric Clusters in Hierarchy with Cryptographic Properties [chapter]

Jeffrey Zheng
2018 Variant Construction from Theoretical Foundation to Applications  
Properties of symmetric clusters and Boolean functions are discussed. Main results are expressed in theorems and tables.  ...  Counting properties on symmetric clusters, vectors in selected clusters and special symmetric Boolean functions are listed. Four sets of symmetric Boolean functions are compared.  ...  Filiol and Fontaine [12] were initially explored on balanced Boolean functions with a good correlation immunity.  ... 
doi:10.1007/978-981-13-2282-2_5 fatcat:lbga5qvvpvbrrhy3vvppxxfmpi
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