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Inspired by the works of Mesnager (IEEE Trans Inf Theory 60(7):4397–4407, 2014) and Tang et al. (IEEE Trans Inf Theory 63(10):6149–6157, 2017), we study a class of bent functions of the form f (x) = g (x) + F (f 1 (x) , f 2 (x) , ... , f τ (x)) , where g(x) is a function from F p n to F p , f i (x) = ∏ j = 1 κ i Tr (u ij x) for 1 ≤ i ≤ τ , κ i ≥ 1 and F (x 1 , ... , x τ) is a reduced polynomial in F p [ x 1 , ... , x τ ] . As a consequence, we obtain a generic result on the Walsh transform of f(x) in terms of g(x) and characterize the bentness of f(x) for the cases F (x 1 , ... , x τ) without and with restrictions respectively, which enables us to generalize some earlier works and derive new bent functions from known ones. In addition, we study the construction of bent functions f(x) when g(x) is not bent for the first time and present a class of bent functions from non-bent Gold functions. [ABSTRACT FROM AUTHOR]

Rotation symmetric bent functions and their generation two-rotation symmetric bent functions are two classes of cryptographically significant Boolean functions. However, few constructions have been presented in the literature, which either have restriction on integer $n$ or have algebraic degree no more than 4. In this paper, for any even integer $n\ge 4$ , three classes of bent functions are presented respectively. Most notably, the proposed $n$ -variable rotation symmetric bent functions and two-rotation symmetric bent functions can have any possible algebraic degree ranging from 2 to $n/2$ . Besides, we obtain bent idempotent functions with the maximal algebraic degree $n/2$ . [ABSTRACT FROM PUBLISHER]

New quadratic bent functions in polynomial form are constructed in this paper. The constructions give new Boolean bent, generalized Boolean bent and \(p\) -ary bent functions. Based on \(\boldsymbol {\mathbb {Z}}_{4}\) -valued quadratic forms, a simple method provides several new constructions of generalized Boolean bent functions. From these generalized Boolean bent functions a method is presented to transform them into Boolean bent and semi-bent functions. Moreover, many new \(p\) -ary bent functions can also be obtained by applying similar methods. [ABSTRACT FROM AUTHOR]

Several new classes of binary and p-ary regular bent functions are obtained in this paper. The bentness of all these functions is determined by some exponential sums over finite fields, most of which have close relations with the well-known Kloosterman sums. [ABSTRACT FROM AUTHOR]