Correlation-immune functions over finite fields
Mulan Liu, Peizhong Lu, Gary L. Mullen · IEEE Transactions on Information Theory · 1998
We give a series of constructions of correlation-immune function over finite fields. We prove that F/sub 2/ and F/sub 3/ are the only finite fields F/sub q/ with the property that every (n-1)th correlation-immune function in n>2 variables over F/sub q/ 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.