A new class of S-boxes with optimal Feistel boomerang uniformity

2024/08/21 by Yu‐Jing Lu, Sihem Mesnager, Lu, Yuxuan +7 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2408.11291

openalex publication_date 2024/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Feistel Boomerang Connectivity Table (\rmFBCT), which is the Feistel version of the Boomerang Connectivity Table (\rmBCT), plays a vital role in analyzing block ciphers' ability to withstand strong attacks, such as boomerang attacks. However, as of now, only four classes of power functions are known to have explicit values for all entries in their \rmFBCT. In this paper, we focus on studying the FBCT of the power function F(x)=x^2^n-2-1 over \mathbbF_2ⁿ, where n is a positive integer. Through certain refined manipulations to solve specific equations over \mathbbF_2ⁿ and employing binary Kloosterman sums, we determine explicit values for all entries in the \rmFBCT of F(x) and further analyze its Feistel boomerang spectrum. Finally, we demonstrate that this power function exhibits the lowest Feistel boomerang uniformity.

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