{"paper":{"title":"A Continued Fraction-Hyperbola based Attack on RSA cryptosystem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CR","authors_text":"Basile Guy R. Bossoto, Gilda Rech Bansimba, Regis Freguin Babindamana","submitted_at":"2023-04-08T08:46:19Z","abstract_excerpt":"In this paper we present new arithmetical and algebraic results following the work of Babindamana and al. on hyperbolas and describe in the new results an approach to attacking a RSA-type modulus based on continued fractions, independent and not bounded by the size of the private key $d$ nor the public exponent $e$ compared to Wiener's attack. When successful, this attack is bounded by $\\displaystyle\\mathcal{O}\\left( b\\log{\\alpha_{j4}}\\log{(\\alpha_{i3}+\\alpha_{j3})}\\right)$ with $b=10^{y}$, $\\alpha_{i3}+\\alpha_{j3}$ a non trivial factor of $n$ and $\\alpha_{j4}$ such that $(n+1)/(n-1)=\\alpha_{i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.03957","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/2304.03957/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"}