{"paper":{"title":"Pseudorandomness Properties of Random Reversible Circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.CR","authors_text":"Nicholas Kocurek, Ryan O'Donnell, William Gay, William He","submitted_at":"2025-02-11T00:54:24Z","abstract_excerpt":"Motivated by practical concerns in cryptography, 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 $\\sqrt{n} \\cdot \\tilde{O}(k^3)$, with each layer consisting of $\\Theta(n)$ random gates in a fixed two-dimensional nearest-neighbor architecture, yields approximate $k$-wise independent permutations.\n  Our result can be seen as a particularly simple/practical block cipher construction that gives provable statistical security against atta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07159","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.07159/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}