Augustine Musukwa, Massimiliano Sala, Irene Villa, Marco Zaninelli
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On cryptographic properties of cubic and splitting Boolean functions
The weight, balancedness and nonlinearity are important properties of Boolean functions, but they can be difficult to determine in general. In this paper, we study how to compute them for two classes of functions where these problems are more tractable. In particular, we study functions of degree three and the so-called “splitting” functions. The latter are functions that can be written as the sum of two functions defined over disjoint sets of variables. We show how, for splitting functions, studying these properties reduces to the study of simpler functions. We provide then a procedure to compute the weight of a cubic Boolean function. We show computationally that, for a cubic Boolean function with limited number of terms, this procedure is on average significantly more efficient than some other methods.
期刊介绍：
Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems.
Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology.
Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal.
On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.
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