Descriptor: "Differentially 4 uniform function" - Searchworks@Jio Institute Digital Library Search Results

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Author: Bracken, Carl, Tan, Chik How, and Tan, Yin
Subjects: *BINOMIAL equations, *PERMUTATIONS, *NONLINEAR theories, *CRYPTOGRAPHY, *ALGORITHMS, *INTEGERS
Abstract: Abstract: Differentially 4 uniform permutations with high nonlinearity on fields of even degree are crucial to the design of S-boxes in many symmetric cryptographic algorithms. Until now, there are not many known such functions and all functions known are power functions. In this paper, we construct the first class of binomial differentially 4 uniform permutations with high nonlinearity on , where m is an odd integer. This result gives a positive answer to an open problem proposed in Bracken and Leander (2010) . [Copyright &y& Elsevier]
Published: 2012
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Author: Chik How Tan, Carl Bracken, and Yin Tan
Subjects: Discrete mathematics, APN function, Algebra and Number Theory, Binomial (polynomial), Degree (graph theory), Open problem, Applied Mathematics, General Engineering, Quadratic function, Differentially 4 uniform function, Theoretical Computer Science, Combinatorics, Nonlinear system, Integer, Permutation polynomial, Power function, Engineering(all), Mathematics
Abstract: Differentially 4 uniform permutations with high nonlinearity on fields of even degree are crucial to the design of S-boxes in many symmetric cryptographic algorithms. Until now, there are not many known such functions and all functions known are power functions. In this paper, we construct the first class of binomial differentially 4 uniform permutations with high nonlinearity on F 2 6 m , where m is an odd integer. This result gives a positive answer to an open problem proposed in Bracken and Leander (2010) [7] .
Full Text: View/download PDF

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