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Classi?cation of Cubic (n ? 4)-springy Boolean Functions An Braeken1 , Yuri Borissov2 , Svetla Nikova1 , and Bart Preneel1 Department Electrical employ science - ESAT/SCD/COSIC, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 Leuven, Belgium an.braeken,svetla.nikova,bart.preneel@esat.kuleuven.ac.be 2 Institute of Mathematics and Informatics, Bulgarian academy of Sciences, 8 G.Bonchev, 1113 So?a, Bulgaria yborisov@moi.math.bas.bg 1 Abstract. Carlet and Charpin classi?ed in [5] the set of blockish (n ? 4)- zippy Boolean functions into four di?erent types with respect to the Walsh spectrum and the mark of the linear space. base on the classi?cation of RM (3, 6)/RM (1, 6), we completed the classi?cation of the three- symmetryal (n?4)-resilient Boolean function by deriving the corresponding ANF and auto coefficient of correlation spectrum for each of the four types. In the very(prenominal) time, we solved an open difficulty of [5] by proving that all platea ued cubelike (n ? 4)-resilient Boolean functions have dimension of the linear space match either to n ? 5 or n ? 6. 1 Introduction The properties of quadratic multinomial Boolean functions (i.e, the second order Reed-Muller code RM (2, n)) are intimately studied, (e.g.

the weight distribution [13], the a?ne equivalence classes [13], the classi?cation of resilient functions [4] and functions compensateing propagation characteristics [16], etc.) However, it is not trivial to extend these results for functions of higher(prenominal) degrees and even for cubic functions. It is important to understand how the properties behave for the di?erent degrees o! f functions. In this paper we charge on the study of cubic functions which satisfy the highest order of resiliency. resiliency is an important property related to (fast) correlation attacks in period ciphers [19, 15], which we de?ne in the next section. In [5], Charpin and Carlet made the ?rst rate in classifying the set of (n ? 4)-resilient cubic Boolean functions by distinguishing four types of functions with respect...If you want to get a bounteous essay, order it on our website: BestEssayCheap.com

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