{"paper":{"title":"Better Sample -- Random Subset Sum in $2^{0.255n}$ and its Impact on Decoding Random Linear Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"cs.DS","authors_text":"Alexander May, Andre Esser","submitted_at":"2019-07-09T17:22:57Z","abstract_excerpt":"We propose a new heuristic algorithm for solving random subset sum instances $a_1, \\ldots, a_n, t \\in \\mathbb{Z}_{2^n}$, which play a crucial role in cryptographic constructions. Our algorithm is search tree-based and solves the instances in a divide-and-conquer method using the representation method. From a high level perspective, our algorithm is similar to the algorithm of Howgrave-Graham-Joux (HGJ) and Becker-Coron-Joux (BCJ), but instead of enumerating the initial lists we sample candidate solutions. So whereas HGJ and BCJ are based on combinatorics, our analysis is stochastic. Our sampli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04295","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/1907.04295/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"}