International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 13 September 2013

Xiutao Feng
ePrint Report ePrint Report
The trace inverse function $\\Tr(x^{-1})$ over the finite field $\\mathbb{F}_{2^n}$ 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 $n\\ge4$, that is, $\\AI(\\Tr(x^{-1}))=\\ceil{2\\sqrt{n}}-2$, 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.

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