Cryptology ePrint Archive: Report 2021/1676

Cryptographic Symmetric Structures Based on Quasigroups

George Teseleanu

Abstract: In our paper we study the effect of changing the commutative group operation used in Feistel and Lai-Massey symmetric structures into a quasigroup operation. We prove that if the quasigroup operation is isotopic with a group $\mathbb G$, the complexity of mounting a differential attack against our generalization of the Feistel structure is the same as attacking the unkeyed version of the general Feistel iteration based on $\mathbb G$. Also, when $\mathbb G$ is non-commutative we show that both versions of the Feistel structure are equivalent from a differential point of view. For the Lai-Massey structure we introduce four non-commutative versions, we argue for the necessity of working over a group and we provide some necessary conditions for the differential equivalency of the four notions.

Category / Keywords: secret-key cryptography / Feistel structure, Lai-Massey structure, quasigroups, block ciphers, differential cryptanalysis

Original Publication (with minor differences): Cryptologia

Date: received 21 Dec 2021

Contact author: george teseleanu at yahoo com

Available format(s): PDF | BibTeX Citation

Version: 20211221:123023 (All versions of this report)

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