The c-boomerang uniformity and c-boomerang spectrum of two classes of permutation polynomials over the finite field F2n

The boomerang attack developed by Wagner is a cryptanalysis technique against block ciphers. A new theoretical tool, the Boomerang Connectivity Table (BCT) and the corresponding boomerang uniformity were introduced to evaluate the resistance of a block cipher against the boomerang attack. Using a multiplier differential, Stanica (2021) [28] extended the notion of boomerang uniformity to c-boomerang uniformity. In this paper, we focus on two classes of permutation polynomials over F2n. For one of these, we show that the c-boomerang uniformity of this function is equal to 1. For the second type of function, we first consider the c-BCT entries. We then explicitly determine the c-boomerang spectrum of this function by means of characters and some techniques in solving equations over F2n. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.