ÐA nonlinear filter generator is a basic keystream generator for stream cipher applications consisting of a single linear feedback shift register whose output is filtered by a nonlinear combining function. A binary nonlinear filter generator is viewed as a finite input memory automaton with one binary input and one binary output. The generalized inversion attack on a binary nonlinear filter gen...

Firewalls are key security components in computer networks. They filter network traffics based on an ordered list of filtering rules. Firewall configurations must be correct and complete with respect to security policies. Security policy is a set of predicates, which is a high level description of traffic controls. In this paper, we propose an automatic method to verify the correctness of firew...

There is shown that there exists a complete, atomless, σ-centered Boolean algebra, which does not contain any regular countable subalgebra if and only if there exist a nowhere dense ultrafilter. Therefore the existence of such algebras is undecidable in ZFC. A subalgebra B of a Boolean algebra A is called regular whenever for every X ⊆ B, supB X = 1 implies supA X = 1; see e.g. Heindorf and Sha...

Morphological granulometries have been used successfully to discriminate textures in the context of classical featurebased classification, and more recently they have been used as observation variables for estimators in the context of random sets. This paper considers optimal linear parametric estimation of the law of a random set. It is set in a Bayesian framework in that estimation is of the ...

Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...

Stack filters are a special case of non-linear filters. They have a good performance for filtering images with different types of noise while preserving edges and details. A stack filter decomposes an input image into stacks of binary images according to a set of thresholds. Each binary image is then filtered by a Boolean function, which characterizes the filter. Adaptive stack filters can be c...

the square map is one of the functions used in cryptography. for instance, the square map is used in rabin encryption scheme, block cipher rc6 and stream cipher rabbit, in different forms. in this paper, we study statistical properties of the output of the square map as a vectorial boolean function. we obtain the joint probability distribution of arbitrary number of the upper and the lower bits...

This paper introduces a method for optimising digital filter realisations at the gate level. The method is based on a derivative of the primitive operator approach of Bull and Horrocks which is extended using a cany-save decomposition of the primitive operator graph. This facilitates the generation of a set of boolean expressions for the multiply-accumulate section of the filter which can be mi...