The Experts below are selected from a list of 105 Experts worldwide ranked by ideXlab platform
Wenying Zhang - One of the best experts on this subject based on the ideXlab platform.
-
the Algebraic Normal Form linear complexity and k error linear complexity of single cycle t function
Lecture Notes in Computer Science, 2006Co-Authors: Wenying ZhangAbstract:In this paper, we study single-cycle T-functions which have important applications in new cryptographic algorithms. We present the Algebraic Normal Form (ANF) of all single-cycle T-functions and the enumeration of single-cycle functions, which reveal many mysterious aspects of such functions. We also investigate the linear complexity and the k-error complexity of single-cycle T-functions when n = 2 t , the results also reflect the good stability of single-cycle T-functions.
Palash Sarkar - One of the best experts on this subject based on the ideXlab platform.
-
computing partial walsh transForm from the Algebraic Normal Form of a boolean function
IEEE Transactions on Information Theory, 2009Co-Authors: Chand K Gupta, Palash SarkarAbstract:We study the relationship between the Walsh transForm and the Algebraic Normal Form (ANF) of a Boolean function. In the first part of the paper, we obtain a Formula for the Walsh transForm at a certain point in terms of parameters derived from the Algebraic Normal Form. We use previous results by Carlet and Guillot to obtain an explicit expression for the Walsh transForm at a point in terms of parameters derived from the ANF. The second part of the paper is devoted to simplify this Formula and develop an algorithm to evaluate it. This algorithm can be applied in situations where it is practically impossible to use the fast Walsh transForm algorithm. Experimental results show that under certain conditions it is possible to execute our algorithm to evaluate the Walsh transForm (at a small set of points) of functions on a few scores of variables having a few hundred terms in the Algebraic Normal Form.
-
computing walsh transForm from the Algebraic Normal Form of a boolean function
Electronic Notes in Discrete Mathematics, 2003Co-Authors: Kishan Chand Gupta, Palash SarkarAbstract:Abstract We study the relationship between the Walsh transForm and the Algebraic Normal Form of a Boolean function. In the first part of the paper, we carry out a combinatorial analysis to obtain a Formula for the Walsh transForm at a certain point in terms of parameters derived from the Algebraic Normal Form. The second part of the paper is devoted to simplify this Formula and develop an algorithm to evaluate it. Our algorithm can be applied in situations where it is practically impossible to use the fast Walsh transForm algorithm. Experimental results show that under certain conditions it is possible to execute our algorithm to evaluate the Walsh transForm (at a small set of points) of functions on a few scores of variables having a few hundred terms in the Algebraic Normal Form.
-
Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions
Finite Fields and Their Applications, 2002Co-Authors: Claude Carlet, Palash SarkarAbstract:We use a general property of Fourier transForm to obtain direct proofs of recent divisibility results on the Walsh transForm of correlation immune and resilient functions. Improved upper bounds on the nonlinearity of these functions are obtained from the divisibility results. We deduce further inFormation on correlation immune and resilient functions. In particular, we obtain a necessary condition on the Algebraic Normal Form of correlation immune functions attaining the maximum possible nonlinearity.
Dong Xinfen - One of the best experts on this subject based on the ideXlab platform.
-
optimal Algebraic immune boolean function based on Algebraic Normal Form construction
Computer Engineering, 2013Co-Authors: Dong XinfenAbstract:The present methods of constructing optimal Algebraic immune Boolean functions are mostly based on the support set.The methods by Algebraic Normal Form are few.This paper gives a method of constructing optimal Algebraic immune Boolean functions by Algebraic Normal Form,and studies the primarily cryptographic properties of these functions.Such as Algebraic degree,the Algebraic immunity,the hamming weight,the nonlinearity etc.The number of the constructed optimal Algebraic immune functions is given.By using the construction method,a large class of Boolean functions can be obtained with optimal Algebraic immunity,which contains some special known results,and shows this method is more general,contains more functions with maximum Algebraic immunity order.
Xuexuan Hao - One of the best experts on this subject based on the ideXlab platform.
-
quantum algorithms for learning the Algebraic Normal Form of quadratic boolean functions
Quantum Information Processing, 2020Co-Authors: Xuexuan Hao, Fengrong Zhang, Shixiong Xia, Yong ZhouAbstract:Quantum algorithms for the analysis of Boolean functions have received a lot of attention over the last few years. The Algebraic Normal Form (ANF) of a linear Boolean function can be recovered by using the Bernstein–Vazirani (BV) algorithm. No research has been carried out on quantum algorithms for learning the ANF of general Boolean functions. In this paper, quantum algorithms for learning the ANF of quadratic Boolean functions are studied. We draw a conclusion about the influences of variables on quadratic functions, so that the BV algorithm can be run on them. We study the functions obtained by inversion and zero-setting of some variables in the quadratic function and show the construction of their quantum oracle. We introduce the concept of “club” to group variables that appear in quadratic terms and study the properties of clubs. Furthermore, we propose a bunch of algorithms for learning the full ANF of quadratic Boolean functions. The most efficient algorithm, among those we propose, provides an O(n) speedup over the classical one, and the number of queries is independent of the degenerate variables.
Yong Zhou - One of the best experts on this subject based on the ideXlab platform.
-
quantum algorithms for learning the Algebraic Normal Form of quadratic boolean functions
Quantum Information Processing, 2020Co-Authors: Xuexuan Hao, Fengrong Zhang, Shixiong Xia, Yong ZhouAbstract:Quantum algorithms for the analysis of Boolean functions have received a lot of attention over the last few years. The Algebraic Normal Form (ANF) of a linear Boolean function can be recovered by using the Bernstein–Vazirani (BV) algorithm. No research has been carried out on quantum algorithms for learning the ANF of general Boolean functions. In this paper, quantum algorithms for learning the ANF of quadratic Boolean functions are studied. We draw a conclusion about the influences of variables on quadratic functions, so that the BV algorithm can be run on them. We study the functions obtained by inversion and zero-setting of some variables in the quadratic function and show the construction of their quantum oracle. We introduce the concept of “club” to group variables that appear in quadratic terms and study the properties of clubs. Furthermore, we propose a bunch of algorithms for learning the full ANF of quadratic Boolean functions. The most efficient algorithm, among those we propose, provides an O(n) speedup over the classical one, and the number of queries is independent of the degenerate variables.