Permutation polynomials (PPs) of the form (x^ q-x+ c)^ q^ 2-1 3+ 1+ x (xq-x+ c) q 2-1 3+ 1+ x
over F _ q^ 2 F q 2 were presented by Li et al.(Finite Fields Appl 22: 16–23, 2013). More …

In this paper we propose an efficient multivariate encryption scheme based on permutation
polynomials over finite fields. We single out a commutative group L (q, m) of permutation …

In this paper, we investigate some classes of complete permutation polynomials (CPPs) with
the form (L 1 (x)) t+ L 2 (x) for some specific linearized polynomials L 1 (x) and L 2 (x) over …

The use of traditional cryptography based on symmetric keys has been replaced with the
revolutionary idea discovered by Diffie and Hellman in 1976 that fundamentally changed …

Permutation is a natural phenomenon useful for understanding and explaining the structural
and functional behavior of objects or concepts. The mathematical formulation of permutation …

Abstract At present,'mixed-type'multivariate schemes are relatively rare except the Dragon
scheme and its variants (Little Dragon Two scheme and Poly-Dragon scheme). However …

In this paper, we respond to the proposal of the Permutation Polynomial Encryption Scheme,
introduced by Singh, Sarma, and Saikia in 2020. We simplify the private key and prove the …

Constructing permutation polynomials is a hot topic in the area of finite fields, and
permutation polynomials have many applications in different areas. Recently, several …

Polynomials of the form∑ aijxpi+ pj+ L (x) are called quadratic polynomials over a finite field
𝔽 pn and the quadratic polynomials of the form∑ aijxpi+ pj are called Dembowski–Ostrom …

A function f: Fq→ Fq is perfect nonlinear or planar if, for every nonzero b∈ Fq, the discrete
derivative f (x+ b)− f (x)− f (b) of f (x) is a bijection of Fq. Perfect nonlinear functions have a …