Constructions of Two Classes of Permutation Polynomials

  • Chenfan Huang China University of Mining and Technology
  • Shixiong Xia
  • Fengrong Zhang
  • Yong Zhou
Keywords: Boolean function, bent function, linear structure, permutation polynomial, linearized polynomial, Trace

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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Published
2019-03-07
How to Cite
Huang, C., Xia, S., Zhang, F., & Zhou, Y. (2019). Constructions of Two Classes of Permutation Polynomials. IJRDO - Journal of Computer Science Engineering (ISSN: 2456-1843), 5(3), 01-13. Retrieved from https://ijrdo.org/index.php/cse/article/view/2729