Revisiting Correlation-Immunity in Filter Generators

Correlation-immunity is a cryptographic criterion on Boolean functions arising from correlation attacks on combining functions. When it comes to filtering functions, the status of correlation-immunity lacks study in itself and, if it is commonly accepted as a requirement for nonlinear filter generators, this is for other concerns. We revisit the concept of correlation-immunity and clear up its meaning for filtering functions. We summarize existing criteria similar to correlation-immunity and attacks in two different models, showing that such criteria are not relevant in both models. We also derive a precise property to avoid correlations due to the filter function only, which appears to be a bit looser than correlation-immunity. We then propose new attacks based on whether this property is verified.