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Permutation Polynomials over Zpn and Their Randomness
Yuyin YU Lishan KE Zhiqiang LIN Qiuyan WANG
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2017/03/01
Online ISSN: 1745-1337
Type of Manuscript: LETTER
Category: Information Theory
permutation polynomial, residue class ring, single cycle function, T-function,
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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.