The revised boomerang connectivity tables and their connection to the Difference Distribution Table

Fuente: arXiv
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Main Authors: Garg, Kirpa, Hasan, Sartaj Ul, Riera, Constanza, Stanica, Pantelimon
Format: Preprint
Published: 2024
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_version_ 1866913666220163072
author Garg, Kirpa
Hasan, Sartaj Ul
Riera, Constanza
Stanica, Pantelimon
author_facet Garg, Kirpa
Hasan, Sartaj Ul
Riera, Constanza
Stanica, Pantelimon
contents It is well-known that functions over finite fields play a crucial role in designing substitution boxes (S-boxes) in modern block ciphers. In order to analyze the security of an S-box, recently, three new tables have been introduced: the Extended Boomerang Connectivity Table (EBCT), the Lower Boomerang Connectivity Table (LBCT), and the Upper Boomerang Connectivity Table (UBCT). In fact, these tables offer improved methods over the usual Boomerang Connectivity Table (BCT) for analyzing the security of S-boxes against boomerang-style attacks. Here, we put in context these new EBCT, LBCT, and UBCT concepts by connecting them to the DDT for a differentially $δ$-uniform function and also determine the EBCT, LBCT, and UBCT entries of three classes of differentially $4$-uniform power permutations, namely, Gold, Kasami and Bracken-Leander. We also determine the Double Boomerang Connectivity Table (DBCT) entries of the Gold function. As byproducts of our approach, we obtain some previously published results quite easily.
format Preprint
id arxiv_https___arxiv_org_abs_2407_12617
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The revised boomerang connectivity tables and their connection to the Difference Distribution Table
Garg, Kirpa
Hasan, Sartaj Ul
Riera, Constanza
Stanica, Pantelimon
Cryptography and Security
Information Theory
12E20, 11T06, 94A60
It is well-known that functions over finite fields play a crucial role in designing substitution boxes (S-boxes) in modern block ciphers. In order to analyze the security of an S-box, recently, three new tables have been introduced: the Extended Boomerang Connectivity Table (EBCT), the Lower Boomerang Connectivity Table (LBCT), and the Upper Boomerang Connectivity Table (UBCT). In fact, these tables offer improved methods over the usual Boomerang Connectivity Table (BCT) for analyzing the security of S-boxes against boomerang-style attacks. Here, we put in context these new EBCT, LBCT, and UBCT concepts by connecting them to the DDT for a differentially $δ$-uniform function and also determine the EBCT, LBCT, and UBCT entries of three classes of differentially $4$-uniform power permutations, namely, Gold, Kasami and Bracken-Leander. We also determine the Double Boomerang Connectivity Table (DBCT) entries of the Gold function. As byproducts of our approach, we obtain some previously published results quite easily.
title The revised boomerang connectivity tables and their connection to the Difference Distribution Table
topic Cryptography and Security
Information Theory
12E20, 11T06, 94A60
url https://arxiv.org/abs/2407.12617