Paper 2016/1131

New construction of single cycle T-function families

Shiyi ZHANG, Yongjuan WANG, and Guangpu GAO


The single cycle T-function is a particular permutation function with complex algebraic structures, maximum period and efficient implementation in software and hardware. In this paper, on the basis of existing methods, by using a class of single cycle T-functions that satisfy some certain conditions, we first present a new construction of single cycle T-function families. Unlike the previous approaches, this method can construct multiple single cycle T-functions at once. Then the mathematical proof of the feasibility is given. Next the numeration for the newly constructed single cycle T-functions is also investigated. Finally, this paper is end up with a discussion of the properties which these newly constructed functions preserve, such as linear complexity and stability (k-error complexity), as well as a comparison with previous construction methods.

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Preprint. MAJOR revision.
cryptographypermutation functionsingle cycle T-functionnumerationlinear complexity
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syzhang1352 @ 163 com
2017-04-21: last of 3 revisions
2016-12-08: received
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      author = {Shiyi ZHANG and Yongjuan WANG and Guangpu GAO},
      title = {New construction of single cycle T-function families},
      howpublished = {Cryptology ePrint Archive, Paper 2016/1131},
      year = {2016},
      note = {\url{}},
      url = {}
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