The revised boomerang connectivity tables and their connection to the Difference Distribution Table
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913666220163072 |
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| 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 |