Sartaj Ul Hasan

collaborators

8 papers

math.NT2026

Permutation polynomials from the trace functions

Sartaj Ul Hasan, Ramandeep Kaur, Hridesh Kumar

We study necessary and sufficient conditions on $γ$ for several classes of polynomials of the form $X + γ Tr_{q}^{q^{n}} (h (X))$ to be permutation polynomials over finite…

math.CO2026

Bivariate local permutation polynomials, their companions, and related enumeration results

Sartaj Ul Hasan, Ramandeep Kaur, Hridesh Kumar

We construct a new family of permutation group polynomials over finite fields of arbitrary characteristic, which are special types of bivariate local permutation polynomials. For t…

math.NT2026

Some new results on permutation trinomials over finite fields with even characteristic

Kirpa Garg, Sartaj Ul Hasan, Chandan Kumar Vishwakarma

The construction of permutation trinomials of the form $X^{r} (X^{I^\pm (2^{m} - 1)} + X^{I^^{2} (2^{m} - 1)} + 1)$ over $\F_{2^{2m}}$, where $m, r and I^\pm > I^^{2}$ are positive integers, is an active…

cs.CR2025

Permutation polynomials over finite fields from low-degree rational functions

Kirpa Garg, Sartaj Ul Hasan, Chunlei Li +2

This paper considers permutation polynomials over the finite field $F_{q^{2}}$ in even characteristic by utilizing low-degree permutation rational functions over $F_{q}$ . As a result,…

math.NT2025

Four new classes of permutation trinomials and their compositional inverses

Sartaj Ul Hasan, Ramandeep Kaur, Hridesh Kumar

We construct four new classes of permutation trinomials over the cubic extension of a finite field with even characteristic. Additionally, we explicitly provide the compositional i…

cs.CR2025

The revised boomerang connectivity tables and their connection to the Difference Distribution Table

Kirpa Garg, Sartaj Ul Hasan, Constanza Riera +1

It is well-known that functions over finite fields play a crucial role in designing substitution boxes (S-boxes) in modern block ciphers. In order to analyze the security of an S-b…