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Classi?cation of Cubic (n ? 4)-springy Boolean Functions An Braeken1 , Yuri Borissov2 , Svetla Nikova1 , and Bart Preneel1 Department Electrical utilize 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)- racy Boolean functions into quaternary 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- proportionalityal (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 worry of [5] by proving that al l plateaued 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 polynomial Boolean functions (i.e, the second order Reed-Muller code RM (2, n)) are considerably 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 of functions. In this paper we centralise on the study of cubic functions which satisfy the highest order of resiliency. resiliency is an important property related to (fast) correlation attacks in flow ciphers [19, 15], which we de?ne in the next section. In [5], Charpin and Carlet made the ?rst measuring 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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