The Feistel Boomerang Connectivity Table ($\rm{FBCT}$), which is the Feistel version of the Boomerang Connectivity Table ($\rm{BCT}$), plays a vital role in analyzing block ciphers' ability to withstand strong attacks, such as boomerang attacks. However, as of now, only four classes of power functions are known to have explicit values for all entries in their $\rm{FBCT}$. In this paper, we focus on studying the FBCT of the power function $F(x)=x^{2^{n-2}-1}$ over $\mathbb{F}_{2^n}$, where $n$ is a positive integer. Through certain refined manipulations to solve specific equations over $\mathbb{F}_{2^n}$ and employing binary Kloosterman sums, we determine explicit values for all entries in the $\rm{FBCT}$ of $F(x)$ and further analyze its Feistel boomerang spectrum. Finally, we demonstrate that this power function exhibits the lowest Feistel boomerang uniformity.
Locally-APN Binomials with Low Boomerang Uniformity in Odd Characteristic
Institute of Basic Science, Sungkyunkwan University（成均馆大学基础科学研究院）；Department of Mathematics, Sungkyunkwan University（成均馆大学数学系）；Applied Algebra and Optimization Research Center, Sungkyunkwan University（成均馆大学应用代数与优化研究中心）
On APN Exponents and the Differential and Boomerang Properties of Binomials in Characteristic 3
Institute of Basic Science, Sungkyunkwan University（基础科学研究所，成均馆大学）；Department of Mathematics, Sungkyunkwan University（数学系，成均馆大学）；Applied Algebra and Optimization Research Center, Sungkyunkwan University（应用代数与优化研究中心，成均馆大学）
On Differential and Boomerang Properties of a Class of Binomials over Finite Fields of Odd Characteristic
Institute of Basic Science, Sungkyunkwan University（基础科学研究院，成均馆大学）；Department of Mathematics, Sungkyunkwan University（数学系，成均馆大学）；Applied Algebra and Optimization Research Center, Sungkyunkwan University（应用代数与优化研究中心，成均馆大学）
An in-depth study of the power function $x^{q+2}$ over the finite field $\mathbb{F}_{q^2}$: the differential, boomerang, and Walsh spectra, with an application to coding theory
