State Machines Margus Veanes and Ando Saabas 1 Microsoft Research, Redmond, WA, USA [email protected] 2 Institute of Cybernetics Tallinn University of Technology, Tallinn, Estonia

The characterization and construction of bent functions are challenging problems. The paper generalizes the constructions of Boolean bent functions by Mesnager [33], Xu et al. [40] and p-ary bent functions by Xu et al. [41] to the construction of p-ary weakly regular bent functions and presents new infinite families of p-ary weakly regular bent functions from some known weakly regular bent func...

A difficult task in the theory of bent functions is to determine whether a bent function is equivalent to its dual bent function. In this paper we use certain results on the divisibility of Gauss Sums, mainly Stickelberger’s Theorem, to study monomial bent functions. We find the degree of the dual bent function of the Kasami function, which in general is different from the degree of the Kasami ...

In this paper, for an odd prime p, two positive integers n, m with n = 2m, and pm ≡ 1 (mod 4), we derive an upper bound on the magnitude of the cross-correlation function between two decimated sequences of a p-ary m-sequence. The two decimation factors are 2 and 2(pm + 1), and the upper bound is derived as 3 2 p m + 2 . In fact, those two sequences correspond to the p-ary sequences used for the...

We prove a necessary condition for some polynomials of Kasami degree to be APN over Fqn for large n.

Let q = 2, 0 ≤ k ≤ n− 1 and k 6= n/2. In this paper we determine the value distribution of following exponential sums

This work is motivated by the observation that the function F2m to F2m defined by x + (x + 1) + a for some a ∈ F2m can be used to construct difference sets. A desired condition is, that the functionφd(x) := x+(x+1) is a 2-to-1 mapping. If s = 1, then the function x has to be APN. If s > 1, then there is up to equivalence only one function known: The function φd is a 2-to-1 mapping if d is the G...

Jedlicka, Hernando and McGuire have proved that Gold and Kasami functions are the only power mappings which are APN on infinitely many extensions of F2. For p an odd prime, we prove that the only power mappings x 7→ x such that m ≡ 1 mod p which are PN on infinitely many extensions of of Fp are those such that m = 1 + p , l positive integer. As Jedlicka, Hernando and McGuire, we prove that (x+1...