More Efficient $k$-wise Independent Permutations from Random Reversible Circuits via log-Sobolev Inequalities

Lucas Gretta, William He, Angelos Pelecanos

We prove that the permutation computed by a reversible circuit with $\tilde{O}(nk\cdot \log (1/\epsilon ))$ random $3$-bit gates is $\epsilon$-approximately $k$-wise independen…