[HTML][HTML] Permutation polynomials over finite fields—a survey of recent advances
X Hou - Finite Fields and Their Applications, 2015 - Elsevier
Permutation polynomials over finite fields — A survey of recent advances - ScienceDirect Skip
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On some permutation polynomials over 𝔽_ {𝕢} of the form 𝕩^{𝕣} 𝕙 (𝕩^{(𝕢-1)/𝕕})
M Zieve - Proceedings of the American Mathematical Society, 2009 - ams.org
Several recent papers have given criteria for certain polynomials to permute $\mathbb {F} _q
$, in terms of the periods of certain generalized Lucas sequences. We show that these …
$, in terms of the periods of certain generalized Lucas sequences. We show that these …
[HTML][HTML] New classes of permutation binomials and permutation trinomials over finite fields
K Li, L Qu, X Chen - Finite Fields and Their Applications, 2017 - Elsevier
Permutation polynomials over finite fields play important roles in finite fields theory. They
also have wide applications in many areas of science and engineering such as coding …
also have wide applications in many areas of science and engineering such as coding …
15. polynomials over finite fields: an index approach
Q Wang - Combinatorics and Finite Fields, 2019 - degruyter.com
The degree of a polynomial is an important parameter in the study of numerous problems on
polynomials over finite fields. Recently, a new notion of the index of a polynomial over a …
polynomials over finite fields. Recently, a new notion of the index of a polynomial over a …
[LIBRO][B] Finite geometry and combinatorial applications
S Ball - 2015 - books.google.com
The projective and polar geometries that arise from a vector space over a finite field are
particularly useful in the construction of combinatorial objects, such as latin squares …
particularly useful in the construction of combinatorial objects, such as latin squares …
[HTML][HTML] Determination of a type of permutation trinomials over finite fields, II
X Hou - Finite Fields and Their Applications, 2015 - Elsevier
Determination of a type of permutation trinomials over finite fields, II - ScienceDirect Skip to
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Permutation polynomials over finite fields from a powerful lemma
P Yuan, C Ding - Finite Fields and Their Applications, 2011 - Elsevier
Using a lemma proved by Akbary, Ghioca, and Wang, we derive several theorems on
permutation polynomials over finite fields. These theorems give not only a unified treatment …
permutation polynomials over finite fields. These theorems give not only a unified treatment …
A survey on the applications of Niho exponents
The Niho exponent was introduced by Yoji Niho, who investigated the cross-correlation
function between an m-sequence and its decimation sequence in 1972. Since then, Niho …
function between an m-sequence and its decimation sequence in 1972. Since then, Niho …
Permutation polynomials on F_q induced from bijective Redei functions on subgroups of the multiplicative group of F_q
M Zieve - arxiv preprint arxiv:1310.0776, 2013 - arxiv.org
We construct classes of permutation polynomials over F_ {Q^ 2} by exhibiting classes of low-
degree rational functions over F_ {Q^ 2} which induce bijections on the set of (Q+ 1)-th roots …
degree rational functions over F_ {Q^ 2} which induce bijections on the set of (Q+ 1)-th roots …
Arithmetization-oriented APN permutations
L Budaghyan, M Pal - Designs, Codes and Cryptography, 2024 - Springer
Recently, many cryptographic primitives such as homomorphic encryption (HE), multi-party
computation (MPC) and zero-knowledge (ZK) protocols have been proposed in the literature …
computation (MPC) and zero-knowledge (ZK) protocols have been proposed in the literature …