A function$F: \mathbb {F}_{2}^{n}\rightarrow \mathbb {F} _{2}^{n}$,$n=2m$, can have at most$2^{n}-2^{m}$bent component functions. Trivial examples are vectorial bent functions from$\mathbb {F}_{2}^{n}$to$\mathbb {F}_{2}^{m}$, seen as functions on$\mathbb {F}_{2}^{n}$. The first nontrivial example is given in univariate form as$x^{2^{r}} {\rm Tr^{n}_{m}}(x), 1\le r < m$(Pott et al. 2018), a few more examples of similar shape are given by Mesnager et al. 2019, and finally it has been shown that the quadratic function$F(x) = x^{2^{r}} {\rm Tr^{n}_{m}}(\Lambda (x))$, has$2^{n}-2^{m}$bent components if and only if$\Lambda $is a linearized permutation polynomial of$\mathbb {F}_{2^{m}}[x]$(Anbar et al. 2021). In the first part of this article, an upper bound for the nonlinearity of plateaued functions with$2^{n}-2^{m}$bent components is shown, which is attained by the example$x^{2^{r}} {\rm Tr^{n}_{m}}(x)$. We then analyse in detail nonlinearity and differential spectrum of the class of functions$F(x) = x^{2^{r}} {\rm Tr^{n}_{m}}(\Lambda (x))$, which, as will be seen, requires the study of the functions$x^{2^{r}}\Lambda (x)$. In the last part we demonstrate that this class belongs to a larger class of functions with$2^{n}-2^{m}$Maiorana-McFarland bent components, which also contains nonquadratic and non-plateaued functions.

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. In this paper, we slightly modify this notion to obtain the so-called irreducible-expansion complexity which is more suitable for certain applications. We analyze both, the classical and the modified expansion complexity. Moreover, we also study the expansion complexity of the explicit inversive congruential generator.

In the paper the pseudorandomness of binary sequences defined over elliptic curves is studied and both the well-distribution and correlation measures are estimated. The paper is based on the Kohel-Shparlinski bound and the Erdös-Turán-Koksma inequali