In this paper we characterize the c-Boomerang Connectivity Table (BCT), \(c\ne 0\) (thus, including the classical \(c=1\) case), for all monomial function \(x^d\) in terms of characters and Weil sums on the finite field \({\mathbb F}_{p^n}\), for an odd prime p. We further simplify these expressions for the Gold functions \(x^{p^k+1}\) for all \(1\le k<n\), and p odd. It is the first such attempt for a complete description for the classical BCT and its relative c-BCT, for all parameters involved, albeit in terms of characters.

中文翻译：

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使用双 Weil 和找到有限域上单项式函数的 c-boomerang 连通表

在本文中，我们描述了c -Boomerang Connectivity Table (BCT), \(c\ne 0\)（因此，包括经典的\(c=1\)情况），对于所有单项式函数\(x^d\)就有限域\({\mathbb F}_{p^n}\)上的字符和 Weil 和而言 ，对于奇素数 p。对于所有\(1\le k<n\)和p奇数，我们进一步简化了 Gold 函数\(x^{p^k+1}\) 的这些表达式。这是对经典 BCT 及其相关c -BCT的完整描述的第一次此类尝试，包括所有涉及的参数，尽管是字符方面的。