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A large family of Boolean functions

Huaning Liu, Min Zhang (2016)

Acta Arithmetica

In a series of papers many Boolean functions with good cryptographic properties were constructed using number-theoretic methods. We construct a large family of Boolean functions by using polynomials over finite fields, and study their cryptographic properties: maximum Fourier coefficient, nonlinearity, average sensitivity, sparsity, collision and avalanche effect.

A note on evaluations of some exponential sums

Marko J. Moisio (2000)

Acta Arithmetica

1. Introduction. The recent article [1] gives explicit evaluations for exponential sums of the form S ( a , p α + 1 ) : = ∑ x ∈ q χ ( a x p α + 1 ) where χ is a non-trivial additive character of the finite field q , q = p e odd, and a ∈ * q . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of p α + 1 . The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to evaluate certain...

Complete arcs arising from a generalization of the Hermitian curve

Herivelto Borges, Beatriz Motta, Fernando Torres (2014)

Acta Arithmetica

We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin-Schreier curves, which is calculated by using exponential sums via Coulter's approach. We also single out some examples of maximal curves.

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