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Correlation-immune functions over finite fields

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3 Author(s)
Mulan Liu ; Inst. of Syst. Sci., Acad. Sinica, Beijing, China ; Peizhong Lu ; Mullen, G.L.

We give a series of constructions of correlation-immune function over finite fields. We prove that F2 and F3 are the only finite fields Fq with the property that every (n-1)th correlation-immune function in n>2 variables over Fq is linear. We also show that by choosing larger finite fields one can alleviate the tradeoff between the length of the linear equivalent and the order of correlation immunity. This is useful for the design of various cryptosystems

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 3 )