The binary Gold function and its c-boomerang connectivity table

TL;DR

This paper provides a comprehensive analysis of the c-Boomerang Connectivity Table for the Gold function over finite fields of even characteristic, utilizing double Weil sums to extend previous results on boomerang uniformity.

Contribution

It introduces a complete description of the c-Boomerang Connectivity Table for the Gold function and generalizes existing results on boomerang uniformity using advanced mathematical tools.

Findings

Complete description of c-Boomerang Connectivity Table for Gold functions

Generalization of boomerang uniformity results

Application of double Weil sums in cryptographic analysis

Abstract

Here, we give a complete description of the c-Boomerang Connectivity Table for the Gold function over finite fields of even characteristic, by using double Weil sums. In the process we generalize a result of Boura and Canteaut (IACR Trans. Symmetric Cryptol. 2018(3) : 290-310, 2018) for the classical boomerang uniformity.