Diffusion properties of generalized quasi-hadamard transformations on finite abelian groups | Applied Discrete Mathematics. Supplement. 2022. № 15. DOI: 10.17223/2226308X/15/4

Diffusion properties of generalized quasi-hadamard transformations on finite abelian groups

In this paper, we introduce a generalization of quasi-Hadamard transformations on a nite abelian group X. For X = Z2m, it includes the pseudo-Hadamard transformation employed in block ciphers Safer and Two sh, and the quasi-Hadamard transformations proposed by H. Lipmaa. For bijective generalized quasi-Hadamard transformations, we describe di usion properties of imprimitivity systems of regular permutation representations of additive groups Z22 m and Z22m. We describe a set of generalized quasi-Hadamard transformations having the best di usion properties of the imprimitivity systems. We also give conditions such that some generalized quasi-Hadamard transformations have bad di usion properties.

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Keywords

Safer block cipher family, Twofish block cipher, pseudo-Hadamard transformation, quasi-Hadamard transformation, imprimitivity system, regular permutation representation, primitive group

Authors

Name	Organization	E-mail
Pogorelov Boris A.	Academy of Cryptography of the Russian Federation
Pudovkina Marina A.	NRNU MEPhI	maricap@rambler.ru

Всего: 2

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