Non-adaptive preprocessing for discrete log and similar problems cannot beat O(sqrt(N)) online time without Omega(sqrt(N)) advice bits, proven via a Shearer-like inequality for permutations.
Three tutorial lectures on entropy and counting
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abstract
We explain the notion of the {\em entropy} of a discrete random variable, and derive some of its basic properties. We then show through examples how entropy can be useful as a combinatorial enumeration tool. We end with a few open questions.
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Non-Adaptive Cryptanalytic Time-Space Lower Bounds via a Shearer-like Inequality for Permutations
Non-adaptive preprocessing for discrete log and similar problems cannot beat O(sqrt(N)) online time without Omega(sqrt(N)) advice bits, proven via a Shearer-like inequality for permutations.