Paper 2021/1676

Cryptographic Symmetric Structures Based on Quasigroups

George Teseleanu


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.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. MINOR revision.Cryptologia
Feistel structureLai-Massey structurequasigroupsblock ciphersdifferential cryptanalysis
Contact author(s)
george teseleanu @ yahoo com
2022-03-15: revised
2021-12-21: received
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Creative Commons Attribution


      author = {George Teseleanu},
      title = {Cryptographic Symmetric Structures Based on Quasigroups},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1676},
      year = {2021},
      note = {\url{}},
      url = {}
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