The Algebraic Normal Form, Linear Complexity and k-Error Linear Complexity of Single-Cycle T-Function

In this paper, we study single-cycle T-functions which have important applications in new cryptographic algorithms. We present the algebraic normal form (ANF) of all single-cycle T-functions and the enumeration of single-cycle functions, which reveal many mysterious aspects of such functions. We also investigate the linear complexity and the k-error complexity of single-cycle T-functions when n=2t, the results also reflect the good stability of single-cycle T-functions.

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