{"paper":{"title":"Fast Bounded-Independence Functions and Their Duals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.CR","authors_text":"Martijn Brehm, Nicolas Resch, Yuval Ishai","submitted_at":"2026-06-05T07:53:04Z","abstract_excerpt":"We continue the study of {\\em fast} functions, computable by linear-size circuits, that share useful properties of random functions. Motivated by cryptographic applications, we generalize and improve on previous results in this area, obtaining the following results:\n  - For any constant $t$, we construct a fast $t$-wise independent hash function with algebraic degree $\\log_2 t$ (over $\\mathbb F_2$), simultaneously optimizing both asymptotic circuit size and degree.\n  - We simplify and improve a recent construction (ITCS 2026) of a family of fast codes with fast duals, both meeting the Gilbert-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07009","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/2606.07009/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"}