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This article is cited in 3 scientific papers (total in 3 papers)
Constructing $8$-bit permutations, $8$-bit involutions and $8$-bit orthomorphisms with almost optimal cryptographic parameters
R. A. de la Cruz Jiménez Institute of Cryptography, Havana University, Cuba
Abstract:
Nonlinear bijective transformations are crucial components in the design of many symmetric ciphers. To construct permutations having cryptographic properties close to the optimal ones is not a trivial problem. We propose a new construction based on the well-known Lai – Massey structure for generating binary permutations of dimension $n=2k$, $k\geq2$. The main cores of our constructions are: the inversion in $\mathbb{F}_{2^k}$, an arbitrary $k$-bit non-bijective function (which has no preimage for $0$) and any $k$-bit permutation. Combining these components with the finite field multiplication, we provide new $8$-bit permutations with high values of its basic cryptographic parameters. Also, we show that our approach may be used for constructing $8$-bit involutions and $8$-bit orthomorphisms that have strong cryptographic properties.
Key words:
S-Box, permutation, involution, orthomorphism.
Received 22.XI.2020
Citation:
R. A. de la Cruz Jiménez, “Constructing $8$-bit permutations, $8$-bit involutions and $8$-bit orthomorphisms with almost optimal cryptographic parameters”, Mat. Vopr. Kriptogr., 12:3 (2021), 89–124
Linking options:
https://www.mathnet.ru/eng/mvk377https://doi.org/10.4213/mvk377 https://www.mathnet.ru/eng/mvk/v12/i3/p89
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Abstract page: | 294 | Full-text PDF : | 131 | References: | 31 | First page: | 12 |
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