Permutation Polynomials over Zpn and Their Randomness

Yuyin YU; Lishan KE; Zhiqiang LIN; Qiuyan WANG

doi:10.1587/transfun.E100.A.913

Permutation Polynomials over Z_pⁿ and Their Randomness

Yuyin YU, Lishan KE, Zhiqiang LIN, Qiuyan WANG

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Permutation polynomials over Z_pⁿ are useful in the design of cryptographic algorithms. In this paper, we obtain an equivalent condition for polynomial functions over Z_pⁿ 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 Z_pⁿ.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.3 pp.913-915

Publication Date: 2017/03/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.913

Type of Manuscript: LETTER

Category: Information Theory

Authors

Yuyin YU
  Guangzhou University
Lishan KE
  Guangzhou University
Zhiqiang LIN
  Guangzhou University
Qiuyan WANG
  Tianjin Polytechnic University

Keyword

permutation polynomial, residue class ring, single cycle function, T-function

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Yuyin YU, Lishan KE, Zhiqiang LIN, Qiuyan WANG, "Permutation Polynomials over Zpn and Their Randomness" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 3, pp. 913-915, March 2017, doi: 10.1587/transfun.E100.A.913.
Abstract: Permutation polynomials over Z_pⁿ are useful in the design of cryptographic algorithms. In this paper, we obtain an equivalent condition for polynomial functions over Z_pⁿ 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 Z_pⁿ.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.913/_p

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@ARTICLE{e100-a_3_913,
author={Yuyin YU, Lishan KE, Zhiqiang LIN, Qiuyan WANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Permutation Polynomials over Zpn and Their Randomness},
year={2017},
volume={E100-A},
number={3},
pages={913-915},
abstract={Permutation polynomials over Z_pⁿ are useful in the design of cryptographic algorithms. In this paper, we obtain an equivalent condition for polynomial functions over Z_pⁿ 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 Z_pⁿ.},
keywords={},
doi={10.1587/transfun.E100.A.913},
ISSN={1745-1337},
month={March},}

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TY - JOUR
TI - Permutation Polynomials over Zpn and Their Randomness
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 913
EP - 915
AU - Yuyin YU
AU - Lishan KE
AU - Zhiqiang LIN
AU - Qiuyan WANG
PY - 2017
DO - 10.1587/transfun.E100.A.913
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2017
AB - Permutation polynomials over Z_pⁿ are useful in the design of cryptographic algorithms. In this paper, we obtain an equivalent condition for polynomial functions over Z_pⁿ 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 Z_pⁿ.
ER -