At Eurocrypt'18, Cid et al. introduced a new tool, called the Boomerang Connectivity Table (BCT) that permits to simplify this analysis. Next, Boura and Canteaut introduced an important parameter for cryptographic S-boxes called boomerang uniformity, that is the maximum value in the BCT. Very recently, the boomerang uniformity of some classes of permutations (in particular quadratic functions) have been studied by Li, Qu, Sun and Li, and by Mesnager, Chunming and Maosheng.
In this paper we further study the boomerang uniformity of some non-quadratic differentially 4-uniform functions. In particular, we consider the case of the Bracken-Leander cubic function and three classes of 4-uniform functions constructed by Li, Wang and Yu, obtained from modifying the inverse functions.
Category / Keywords: secret-key cryptography / Vectorial Boolean functions, Boomerang uniformity, Boomerang connectivity table, Boomerang attack Date: received 31 Jul 2019, last revised 2 Mar 2020 Contact author: irene villa at uib no Available format(s): PDF | BibTeX Citation Version: 20200302:140016 (All versions of this report) Short URL: ia.cr/2019/881