Three characterizations of non-binary correlation-immune and resilient functions |
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| Authors: | K Gopalakrishnan D R Stinson |
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| Institution: | (1) Department of Computer Science and Engineering, University of Nebraska-Lincoln, 68588 Lincoln, NE;(2) Department of Computer Science and Engineering and Center for Communication and Information Science, University of Nebraska-Lincoln, 68588 Lincoln, NE |
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| Abstract: | A functionf(X
1,X
2, ...,X
n
) is said to betth-order correlation-immune if the random variableZ=f(X
1,X
2,...,X
n
) is independent of every set oft random variables chosen from the independent equiprobable random variablesX
1,X
2,...,X
n
. Additionally, if all possible outputs are equally likely, thenf is called at-resilient function. In this paper, we provide three different characterizations oft th-order correlation immune functions and resilient functions where the random variable is overGF (q). The first is in terms of the structure of a certain associated matrix. The second characterization involves Fourier transforms. The third characterization establishes the equivalence of resilient functions and large sets of orthogonal arrays. |
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| Keywords: | |
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