A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes Fields of Even Degree

Bracken, Carl and Leander, Gregor (2010) A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes Fields of Even Degree. Finite Fields and Their Applications, 16 (4). pp. 231-242. ISSN ISSN: 1071-5797

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Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially- 4 uniform function called the inverse function. Any function used in a symmetric cryptosystem should be a permutation. Also, it is required that the function is highly nonlinear so that it is resistant to Matsui’s linear attack. In this article we demonstrate that the highly nonlinear permutation f(x) = x22k+2k+1, discovered by Hans Dobbertin [7], has differential uniformity of four and hence, with respect to differential and linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem as the inverse function.

Item Type: Article
Additional Information: Preprint version of published article. © 2010 Elsevier Inc. All rights reserved.
Keywords: Boolean functions; Power functions; Fourier transform; Block cipher; s-Box;
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 2635
Identification Number: 10.1016/j.ffa.2010.03.001
Depositing User: Library Editor
Date Deposited: 12 Aug 2011 15:55
Journal or Publication Title: Finite Fields and Their Applications
Publisher: Elsevier
Refereed: No

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