Haode Yan

On $-1$-differential uniformity of ternary APN power functions

2021 · arXiv (Cornell University)

Very recently, a new concept called multiplicative differential and the corresponding $c$-differential uniformity were introduced by Ellingsen et al. A function $F(x)$ over finite field $\mathrm{GF}(p^n)$ to itself is called $c$-differential uniformity $δ$, or equivalent, …

The $c$-differential spectrum of $x\mapsto x^{\frac{p^n+1}{2}}$ in finite fields of odd characteristics

2022 · arXiv (Cornell University)

In the paper, we concentrate on the map $x\mapsto x^{\frac{p^n+1}{2}}$ on $\mathbb{F}_{p^n}$ and using combinatorial and number theory techniques, we compute its detailed $c$-differential spectrum for all values of $c\neq 1$ (the spectrum for $c=1$ …

The Complete Differential Spectrum of a Class of Power Permutations Over Odd Characteristic Finite Fields

2023 · IEEE Transactions on Information Theory

Permutation polynomials over finite fields are fundamental objects as they are used in various theoretical and practical applications in cryptography, coding theory, combinatorial design, and related topics. This family of polynomials constitutes an active research …