## Cryptology ePrint Archive: Report 2011/547

The Single Cycle T-functions

Zhaopeng Dai and Zhuojun Liu

Abstract: In this paper the single cycle T-functions are studied. Making use of the explicit formulas of sum and product of 2-adic integers, we present the necessary and sufficient conditions on the generalized polynomial \$\widetilde{p(x)} = a_{0} \substack {+ \\ \oplus} a_{1}x \substack {+ \\ \oplus} \cdots \substack {+ \\ \oplus} a_{d}x^{d} (\mbox{mod} \, 2^{n} )\$ being a single cycle T-function. Furthermore, for any given generalized polynomial, we can deduce some expressions about its coefficients by which we can determine whether it is single cycle or not.

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