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Classi?cation of Cubic (n ? 4)-springy Boolean Functions
An Braeken1 , Yuri Borissov2 , Svetla Nikova1 , and Bart Preneel1
Department Electrical applied 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
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Abstract. Carlet and Charpin classi?ed in [5] the set of blockish (n ? 4)-resilient Boolean functions into four di?erent types with respect to the Walsh spectrum and the dimension of the linear space. base on the classi?cation of RM (3, 6)/RM (1, 6), we completed the classi?cation of the three-dimensional (n?4)-resilient Boolean function by deriving the corresponding ANF and auto correlativity spectrum for each of the four types. In the very(prenominal) time, we solved an open problem of [5] by proving that all plateaued cubic (n ? 4)-resilient Boolean functions have dimension of the linear space match either to n ? 5 or n ? 6.

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Introduction

The properties of quadratic polynomial Boolean functions (i.e, the second order Reed-Muller code RM (2, n)) are substantially 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 focus on the study of cubic functions which satisfy the highest order of resiliency. Resiliency is an important property related to (fast) correlation attacks in stream ciphers [19, 15], which we de?ne in the next section. In [5], Charpin and Carlet made the ?rst step 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: Ordercustompaper.com



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