By considering a new metric, we generalize cryptographic properties of Boolean functions such as resiliency and propagation characteristics. These new definitions result in a better understanding of the properties of Boolean functions and provide a better insight in the space defined by this metric. This approach leads to the construction of “hand-made” Boolean functions, i.e., functions for which the security with respect to some specific monotone sets of inputs is considered, instead of the security with respect to all possible monotone sets with the same cardinality, as in the usual definitions. In this way, we are able to relax some trade-offs between important properties of Boolean functions. We show relations between resilient Boolean functions, linear codes, monotone span programs, and orthogonal arrays in this generalized setting.
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