# Constructions of Two Classes of Permutation Polynomials

### Abstract

In this paper, we first investigate the constructions of permutation polynomials of the shape over. A mapping function which transforms a Boolean function on *n *variables to a univariate function over * *is provided. On basis of the mapping function, we put forward two methods for constructing two classes of univariate functions over * *. Further, two classes of permutation polynomials of the shape can be obtained using the two classes of univariate functions. At last, based on the one-to-one correspondence between Boolean permutations and Maiorana-McFarland’s (M-M) bent functions, we propose an algorithm to compute the algebraic normal form (ANF) of a *2k*-variable M-M bent function from its truth-table. The complexity of this algorithm is much smaller than that of the Butterfly algorithm which is directly used to compute the ANF of a *2k*-variable M-M bent function from its truth-table.

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