Algebraic construction of semi bent function via known power function

The study of semi bent functions (2- plateaued Boolean function) has attracted the attention of many researchers due to their cryptographic and combinatorial properties. In this paper, we have given the algebraic construction of semi bent functions defined over the finite field F₂ⁿ (n even) using the notion of trace function and Gold power exponent. Algebraically constructed semi bent functions have some special cryptographical properties such as high nonlinearity, algebraic immunity, and low correlation immunity as expected to use them effectively in cryptosystems. We have illustrated the existence of these properties with suitable examples.Publisher's Versio

Permutation Polynomials modulo n

Based on preliminary numerical computations, we give complete results for linear and quadratic polynomials. Rivest’s result holds in the linear case while there are plenty of counterexamples in the quadratic case

A recent survey of permutation trinomials over finite fields

Constructing permutation polynomials is a hot topic in the area of finite fields, and permutation polynomials have many applications in different areas. Recently, several classes of permutation trinomials were constructed. In 2015, Hou surveyed the achievements of permutation polynomials and novel methods. But, very few were known at that time. Recently, many permutation binomials and trinomials have been constructed. Here we survey the significant contribution made to the construction of permutation trinomials over finite fields in recent years. Emphasis is placed on significant results and novel methods. The covered material is split into three aspects: the existence of permutation trinomials of the respective forms $x^{r}h(x^{s})$, $\lambda_{1}x^{a}+\lambda_{2}x^{b}+\lambda_{3}x^{c}$ and $x+x^{s(q^{m}-1)+1} +x^{t(q^{m}-1)+1}$, with Niho-type exponents $s, t$