Class Of Permutation Polynomials Research Articles

A class of permutation polynomials over the group ring F_pC_p^n

Let p be a prime number and F_pC_p^n denote the group ring of a cyclic group of order pn over Fp. We study the permutation property of the polynomial a_0 + a_1x + a_px^p + · · · + a_p^n x^(p^n) with coefficients a_i ∈ F_pC_p^n where i = 0, 1, p, . . . , p^n. Necessary and sufficient conditions on the coefficients have been obtained so that it becomes a permutation polynomial.

On a conjecture about a class of permutation quadrinomials

Very recently, Tu et al. presented a sufficient condition on (a1,a2,a3), see Theorem 1.1, such that f(x)=x3⋅2m+a1x2m+1+1+a2x2m+2+a3x3 is a class of permutation polynomials over F2n with n=2m and m odd. In this present paper, we prove that the sufficient condition is also necessary.

Further results on permutation polynomials via linear translators

In this paper, by using linear translators, we characterize a new class of permutation polynomials of the form [Formula: see text], which has a more general form than [Formula: see text]. Then, we present the compositional inverses of such permutation polynomials. Furthermore, by specifying the functions [Formula: see text] and [Formula: see text], we can get some new permutation polynomials of the forms [Formula: see text] and [Formula: see text] where [Formula: see text] is the trace function.

One Class of Permutation Polynomials over Finite Fields of even Characteristic

One Class of Permutation Polynomials over Finite Fields of even Characteristic

Further results on a class of permutation polynomials over finite fields

A class of permutation polynomials with given form over finite fields is investigated in this paper, which is a further study on a recent work of Zha and Hu. Based on some particular techniques over finite fields, two results obtained by Zha and Hu are improved and new permutation polynomials are also obtained.

Almost Perfect Nonlinear Power Functions on GF(2n): The Niho Case

Almost perfect nonlinear (APN) mappings are of interest for applications in cryptography We prove for odd n and the exponent d =2 2 r +2 r −1, where 4 r +1≡0 mod n , that the power functions x d on GF(2 n ) is APN. The given proof is based on a new class of permutation polynomials which might be of independent interest. Our result supports a conjecture of Niho stating that the power function x d is even maximally nonlinear or, in other terms, that the crosscorrelation function between a binary maximum-length linear shift register sequences of degree n and a decimation of that sequence by d takes on precisely the three values −1, −1±2 ( n +1)/2 .

Permutation Properties of Chebyshev Polynomials of the Second Kind over a Finite Field

A class of permutation polynomials amongst the Chebyshev polynomials of the second kind has been described by the second author. Cohen has shown that in prime fields of odd order or their degree 2 extensions these are the only examples of such polynomials. In this paper, the authors present new classes of such permutation polynomials in fields of characteristic ≤ 5. The results are extended to fields of characceristic 2, a case not considered previously.