Constructions of Two Classes of Permutation Polynomials - Huang, Chenfan; Xia, Shixiong; Zhang, Fengrong; Zhou, Yong (IJRDO -Journal of Computer Science Engineering, 2019)
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.