In mathematics, the correlation immunity of a Boolean function is a measure of the degree to which its outputs are uncorrelated with some subset of its inputs. Specifically, a Boolean function is said to be correlationimmune of order m if every subset of m or fewer variables in is statistically independent of the value of .
Definition[]
A function is th order correlation immune if for any independent binary random variables , the random variable is independent from any random vector with .
Results in cryptography[]
When used in a stream cipher as a combining function for linear feedback shift registers, a Boolean function with loworder correlationimmunity is more susceptible to a correlation attack than a function with correlation immunity of high order.
Siegenthaler showed that the correlation immunity m of a Boolean function of algebraic degree d of n variables satisfies m + d ≤ n; for a given set of input variables, this means that a high algebraic degree will restrict the maximum possible correlation immunity. Furthermore, if the function is balanced then m + d ≤ n − 1.^{[1]}
References[]
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