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A large family of Boolean functions

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Liu H., Zhang M.

Acta Arithmetica

2016

tom 172

nr 3

251-262

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.

Solutions for the p-order Feigenbaum's functional equation $h(g(x)) = g^{p}(h(x))$

100%

Zhang M., Si J.

Annales Polonici Mathematici

2014

tom 111

nr 2

183-195

This work deals with Feigenbaum's functional equation ⎧ $h(g(x)) = g^p(h(x))$, ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, $g^p$ is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.

Ograniczanie wyników

1 Acta Arithmetica

1 Annales Polonici Mathematici

2 Zhang M.

1 Liu H.

1 Si J.

1 2016

1 2014

Wyniki wyszukiwania

A large family of Boolean functions

Solutions for the p-order Feigenbaum's functional equation $h(g(x)) = g^{p}(h(x))$