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Pseudorandom Permutations from Random Reversible Circuits
April 24, 2024, 4:11 a.m. | William He, Ryan O'Donnell
cs.CR updates on arXiv.org arxiv.org
Abstract: We study pseudorandomness properties of permutations on $\{0,1\}^n$ computed by random circuits made from reversible $3$-bit gates (permutations on $\{0,1\}^3$). Our main result is that a random circuit of depth $n \cdot \tilde{O}(k^2)$, with each layer consisting of $\approx n/3$ random gates in a fixed nearest-neighbor architecture, yields almost $k$-wise independent permutations. The main technical component is showing that the Markov chain on $k$-tuples of $n$-bit strings induced by a single random $3$-bit nearest-neighbor gate …
architecture arxiv cs.cc cs.cr depth main math.pr random result study
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