We initiate the study of Boolean function analysis on high-dimensional expanders. We give a random-walk based definition of high-dimensional expansion, which coincides with the earlier definition in terms of two-sided link expanders. Using this definition, we describe an analog of the Fourier ...
Instructions on web page. Blog: http://boolean-analysis.blogspot Evaluation: ² About 5 problem sets. ² 2 or 2.5 scribe notes, graded (worth equal to that of a problem set) The Boolean function The boolean function All things to all people x f (x) 0000 0 0001 1 0010 1 0011 1...
Algebraic Immunity of Boolean Functions - Analysis and Construction. In this paper, we first analyse the method of finding algebraic immunity of a Boolean function. Given a Boolean function f on n-variables, we identify a re... DALAI,D Kumar,MAITRA,... - 《Computación Y Sistemas》 被引量...
摘要: The notion of transparency order, proposed by Prouff (DPA attacks and S-boxes, FSE 2005, LNCS 3557, Springer, Berlin, 2005) and then redefined by Chakraborty et al. (Des Codes Cryptogr 82:95–115,...关键词: Transparency order Boolean function Nonlinearity ...
It has been observed that a Boolean function f, interpreted as a mul... DK Dalai,KC Gupta,S Maitra - International Conference on Cryptology in India 被引量: 436发表: 2004年 Cryptographically significant boolean functions: construction and analysis in terms of algebraic immunity In a different ...
A Boolean function is called (co-)connected if the subgraph of the Boolean hypercube induced by its (false) true points is connected; it is called strongly... O Ekin,PL Hammer,A Kogan - 《Discrete Applied Mathematics》 被引量: 52发表: 1999年 Electronic Colloquium on Computational Complexity...
Through studying the linear space of the partially Bent function, this paper quantrficationally described the correlation immune order, pervasion order and algebra degree affected by the linear dimension. And then, it constructed a kind of balanced and correlation immune functions with highly nonlineari...
Recent advances in the theory and practice of Logical Analysis of Data Miguel Lejeune, ... Soumaya Yacout, in European Journal of Operational Research, 2019 2.1 Boolean function terminology Let us denote B={0,1}. The set Bn consists of all binary words (i.e. ordered sequences of 0’s ...
A key idea of the reduction method is that a Boolean function is represented as a disjunction of Boolean functions with fewer zeros. In a number of practically important cases, this technique makes it possible to considerably reduce the complexity of DNF implementations of Boolean functions. 展开 ...
Recall that a Boolean functionfis balanced if#{x | f(x) = 0} = #{x | f(x) = 1}. 5. It can be shown from the definition of the Kronecker product that (A⊗B)(C⊗D)=AC⊗BD, assuming that these products are defined. ...