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 correlation-immune of order m if every subset of m is statistically independent.

Definition

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Results in cryptography

When used in a stream cipher as a combining function for linear feedback shift registers, a Boolean function with low-order correlation-immunity 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≤n1.

References

Further reading

1. Cusick, Thomas W. & Stanica, Pantelimon (2009). "Cryptographic Boolean functions and applications". Academic Press. .