On the way of constructing differentially 25-uniform permutations over F22m | Applied Discrete Mathematics. Supplement. 2021. № 14. DOI: 10.17223/2226308X/14/9

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On the way of constructing differentially 25-uniform permutations over F22m

The paper studies new ways of constructing differentially 25-uniform bijections over F22m, m > 3, that are based on TU-con-struction. Some well known results on the constructing differentially 4-uniform permutations over F22m are generalized in this work. The core idea is to use TU-construction and differentially 5-uniform bijections to construct 2t • 5-uniform permutations. A generalized method for constructing 2m-bit differentially 4-uniform permutations is proposed, and new constructions of differentialy 6 and 8-uniform permutations are introduced.

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Keywords

TU-construction, differential uniformity, permutation, S-Box

Authors

NameOrganizationE-mail
Fomin D.B.National Research University Higher School of Economicsdfomin@hse.ru
Всего: 1

References

Carlet C., Tang D., Tang X., and Liao Q. New construction of differentially 4-uniform bijections // LNCS. 2013. V. 8567. P. 22-38.
Фомин Д. Б. Об алгебраической степени и дифференциальной равномерности подстановок пространства V2m, построенных с использованием (2m, т)-функций. // Матем. вопр. криптогр. 2020. Т. 11. №4. С. 133-149.
Fomin D. B. New classes of 8-bit permutations based on a butterfly structure // Матем. вопр. криптогр. 2019. Т. 10. № 2. С. 169-180.
Фомин Д. Б. Построение подстановок пространства V2m с использованием (2m, m)-функций. // Матем. вопр. криптогр. 2020. Т. 11. № 3. С. 121-138.
De la Cruz Jimenez R. A. Generation of 8-bit S-Boxes Having Almost Optimal Cryptographic Properties Using Smaller 4-bit S-Boxes and Finite Field Multiplication. 2017. www.cs.haifa. ac.il/orrd/LC17/paper60.pdf.
Biryukov A., Perrin L., and Udovenko A. Reverse-engineering the S-box of Streebog, Kuznyechik and Stribobr1 // LNCS. 2016. V. 9665. P. 372-402.
Biryukov A., Perrin L., and Udovenko A. Cryptanalysis of a Theorem: Decomposing the Only Known Solution to the Big APN Problem (Full Version). Cryptology ePrint Archive: Report 2016/539.
Canteaut A. and Perrin L. On CCZ-Equivalence, Extended-Affine Equivalence, and Function Twisting. Cryptology ePrint Archive: Report 2018/713.
On the way of constructing differentially 25-uniform permutations over F22m | Applied Discrete Mathematics. Supplement. 2021. № 14. DOI: 10.17223/2226308X/14/9

On the way of constructing differentially 25-uniform permutations over F22m | Applied Discrete Mathematics. Supplement. 2021. № 14. DOI: 10.17223/2226308X/14/9

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