{"paper":{"title":"Cryptography from Lossy Reductions: Towards OWFs from ETH, and Beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CR","authors_text":"Alex B. Grilo, Garazi Muguruza, Mahshid Riahinia, Pouria Fallahpour","submitted_at":"2025-05-27T17:15:30Z","abstract_excerpt":"One-way functions (OWFs) form the foundation of modern cryptography, yet their unconditional existence remains a major open question. In this work, we study this question by exploring its relation to lossy reductions, i.e., reductions $R$ for which it holds that $I(X;R(X)) \\ll n$ for all distributions $X$ over inputs of size $n$. Our main result is that either OWFs exist or any lossy reduction for any promise problem $\\Pi$ runs in time $2^{\\Omega(\\log\\tau_\\Pi / \\log\\log n)}$, where $\\tau_\\Pi(n)$ is the infimum of the runtime of all (worst-case) solvers of $\\Pi$ on instances of size $n$. In fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21442","kind":"arxiv","version":2},"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/2505.21442/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"}