Document detail
ID
oai:arXiv.org:2311.00982
Topic
Computer Science - Information The...Author
Zhou, Huan Du, Xiaoni Yuan, Wenping Qiao, XingbinCategory
Computer Science
Year
2023
listing date
11/8/2023
Keywords
power uniformity $ -1 $f$ $c$-differentialAbstract
Power functions with low $c$-differential uniformity have been widely studied not only because of their strong resistance to multiplicative differential attacks, but also low implementation cost in hardware.
Furthermore, the $c$-differential spectrum of a function gives a more precise characterization of its $c$-differential properties.
Let $f(x)=x^{\frac{p^n+3}{2}}$ be a power function over the finite field $\mathbb{F}_{p^{n}}$, where $p\neq3$ is an odd prime and $n$ is a positive integer.
In this paper, for all primes $p\neq3$, by investigating certain character sums with regard to elliptic curves and computing the number of solutions of a system of equations over $\mathbb{F}_{p^{n}}$, we determine explicitly the $(-1)$-differential spectrum of $f$ with a unified approach.
We show that if $p^n \equiv 3 \pmod 4$, then $f$ is a differentially $(-1,3)$-uniform function except for $p^n\in\{7,19,23\}$ where $f$ is an APcN function, and if $p^n \equiv 1 \pmod 4$, the $(-1)$-differential uniformity of $f$ is equal to $4$.
In addition, an upper bound of the $c$-differential uniformity of $f$ is also given.
Zhou, Huan,Du, Xiaoni,Yuan, Wenping,Qiao, Xingbin, 2023, The c-differential properties of a class of power functions
