Permutation Polynomials over Zpn and Their Randomness

Yuyin YU  Lishan KE  Zhiqiang LIN  Qiuyan WANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.3   pp.913-915
Publication Date: 2017/03/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Information Theory
Keyword: 
permutation polynomial,  residue class ring,  single cycle function,  T-function,  

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Summary: 
Permutation polynomials over Zpn are useful in the design of cryptographic algorithms. In this paper, we obtain an equivalent condition for polynomial functions over Zpn to be permutations, and this equivalent condition can help us to analysis the randomness of such functions. Our results provide a method to distinguish permutation polynomials from random functions. We also introduce how to improve the randomness of permutation polynomials over Zpn.