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A Note on the Construction of Differentially Uniform Permutations Using Extension Fields
Qichun WANG Haibin KAN
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E95A
No.11
pp.20802083 Publication Date: 2012/11/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E95.A.2080
Print ISSN: 09168508 Type of Manuscript: LETTER Category: Cryptography and Information Security Keyword: block ciphers, vectorial Boolean functions, extension fields,
Full Text: PDF(81.9KB)>>
Summary:
Constructing APN or 4differentially uniform permutations achieving all the necessary criteria is an open problem, and the research on it progresses slowly. In ACISP 2011, Carlet put forth an idea for constructing differentially uniform permutations using extension fields, which was illustrated with a construction of a 4differentially uniform (n,n)permutation. The permutation has optimum algebraic degree and very good nonlinearity. However, it was proved to be a permutation only for n odd. In this note, we investigate further the construction of differentially uniform permutations using extension fields, and construct a 4differentially uniform (n,n)permutation for any n. These permutations also have optimum algebraic degree and very good nonlinearity. Moreover, we consider a more general type of construction, and illustrate it with an example of a 4differentially uniform (n,n)permutation with good cryptographic properties.

