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 …

In this paper, we investigate the power function over the finite field, where is a positive
integer and. We prove that this power function is AP with respect to all satisfying, and we …

In this paper, we characterize the coefficients of f (x)= x+ a 1 xs 1 (2 m− 1)+ 1+ a 2 xs 2 (2 m−
1)+ 1+ a 3 xs 3 (2 m− 1)+ 1 over F 2 2 m that lead f (x) to be a permutation of F 2 2 m for the …

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 …

We prove a conjecture by Tu, Zeng, Li, and Helleseth concerning trinomials f α, β (x)= x+ α
xq (q− 1)+ 1+ β x 2 (q− 1)+ 1∈ F q 2 [x], α β≠ 0, q even, characterizing all the pairs (α, β)∈ F …

Let p> 3 and consider a prime power q= p h. We completely characterize permutation
polynomials of F q 2 of the type fa, b (X)= X (1+ a X q (q− 1)+ b X 2 (q− 1))∈ F q 2 [X]. In …

In this paper, we propose three new classes of permutation trinomials over F q 3. The first
two classes are of the form x+ L (xq 2+ q− 1), where L (x)∈{x+ A xq, x+ A xq 2}, q even, and …

Several types of functions over finite fields have relevant applications in applied areas of
mathematics, such as cryptography and coding theory. Among them, planar functions, APN …

We classify all permutation polynomials of the form x 3 g (xq-1) of F q 2 where g (x)= x 3+
bx+ c and b, c∈ F q∗. Moreover we find new examples of permutation polynomials and we …

In Eurocrypt'18, Cid et al. proposed a new cryptanalysis tool called Boomerang Connectivity
Table (BCT), to evaluate S-boxes of block ciphers. Later, Boura and Canteaut further …