Abstract
Suzaki and Minematsu (LNCS, 2010) present a comprehensive study of the diffusion property of the improved generalized Feistel structure (\(GFS_{\pi }\)) which is a generalization of the classical Feistel cipher. They study the case when one and the same permutation is applied at each round and finally remark that the usage of different permutations at the different rounds might lead to better diffusion in return for a larger implementation cost, but that it is an open question whether multiple permutations can really improve the diffusion property.
We give a positive answer to this question. For cyphers with 10, 12, 14 and 16 subblocks we present examples of permutations (different at each round) leading to \(GFS_{\pi }\) with better diffusion than the one which can be obtained if the same permutation is applied at all rounds. The examples were found by a computer-aided search which is described in the present paper.
The research of the first author was partially supported by the Bulgarian National Science Fund under Contract 12/8, 15.12.2017 and of the second author by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICTinSES)”, financed by the Ministry of Education and Science.
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Baicheva, T., Topalova, S. (2019). On the Diffusion Property of the Improved Generalized Feistel with Different Permutations for Each Round. In: Ćirić, M., Droste, M., Pin, JÉ. (eds) Algebraic Informatics. CAI 2019. Lecture Notes in Computer Science(), vol 11545. Springer, Cham. https://doi.org/10.1007/978-3-030-21363-3_4
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