Cryptology ePrint Archive: Report 2016/1131

New construction of single cycle T-function families

Shiyi ZHANG and Yongjuan WANG and Guangpu GAO

Abstract: 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.

Category / Keywords: cryptography; permutation function; single cycle T-function; numeration; linear complexity

Date: received 4 Dec 2016, last revised 20 Apr 2017

Contact author: syzhang1352 at 163 com

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Version: 20170421:012221 (All versions of this report)

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