The efficiency of optimal sampling in the random S-box model

In this paper we show a closed caption formula for the efficiency of the optimal sampling technique in the random S-box model. This formula is derived by analyzing the given model and sampling technique using statistical techniques. We further generalize the original random S-box model in two ways; allowing multiple-bit entries, xor of several random S-box outputs. For all cases we show the corresponding closed caption efficiency formula. Using these new formulas, it is now possible to instantaneously give accurate analytical estimates of the output quality of random S-boxes. This can be of great practical importance in, for example, analysis and design of cryptographic primitives based on such building blocks.