Using double Weil sums in finding the Boomerang and the c-Boomerang Connectivity Table for monomial functions on finite fields.
Pantelimon Stănică · arXiv (Cornell University) · 2020
In this paper we characterize the $c$-Boomerang Connectivity Table ($c eq 0$), 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 $1\leq k<n$, $p$ odd. It is the first such complete description for the classical BCT and its relative $c$-BCT, for all parameters involved.