论文标题
在有限字段的单一功能中查找$ C $ -Boomerang连接表
Using double Weil sums in finding the $c$-Boomerang Connectivity Table for monomial functions on finite fields
论文作者
论文摘要
在本文中，我们表征了$ c $ -Boomerang连接表（BCT），$ C \ neq 0 $（因此，包括经典$ c = 1 $ case），对于所有单体函数$ x^d $的字符和有限字段上的weil总和〜$ \ $ \ f_ f_ {p^n} $。我们进一步简化了金函数的这些表达式$ x^{p^k+1} $，用于所有$ 1 \ leq k <n $，$ p $奇数。对于所有涉及的所有参数，这是对经典BCT及其相对$ C $ -BCT进行完整描述的第一次尝试。
In this paper we characterize the $c$-Boomerang Connectivity Table (BCT), $c\neq 0$ (thus, including the classical $c=1$ case), for all monomial function $x^d$ in terms of characters and Weil sums on the finite field~$\F_{p^n}$. We further simplify these expressions for the Gold functions $x^{p^k+1}$ for all $1\leq k<n$, 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.
