On Algebraic Immunity of Tr ( x − 1 ) over F 2 n ?
نویسنده
چکیده
The trace inverse function Tr(x−1) over the finite field F2n is a class of very important Boolean functions in stream ciphers, which possesses many good properties, including high algebraic degree, high nonlinearity, ideal autocorrelation, etc. In this work we discuss properties of Tr(x−1) in resistance to (fast) algebraic attacks. As a result, we prove that the algebraic immunity of Tr(x−1) arrives the upper bound given by Y. Nawaz et al when n ≥ 4, that is, AI(Tr(x−1)) = d2 √ ne − 2, which shows that D.K. Dalai’ conjecture on the algebraic immunity of Tr(x−1) is correct for almost all positive integers n. What is more, we further demonstrate some weak properties of Tr(x−1) in resistance to fast algebraic attacks.
منابع مشابه
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تاریخ انتشار 2013