Welcome to the resource topic for 2024/847
Title:
More Efficient k-wise Independent Permutations from Random Reversible Circuits via log-Sobolev Inequalities
Authors: Lucas Gretta, William He, Angelos Pelecanos
Abstract:We prove that the permutation computed by a reversible circuit with \widetilde{O}(nk\cdot \log(1/\epsilon)) random 3-bit gates is \epsilon-approximately k-wise independent. Our bound improves on currently known bounds in the regime when the approximation error \epsilon is not too small. We obtain our results by analyzing the log-Sobolev constants of appropriate Markov chains rather than their spectral gaps.
ePrint: https://eprint.iacr.org/2024/847
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