{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G2UQOKJGEBMYEXQUUI2BMQM6BP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3f6a560aca1a859ff70686b70b955efcd9224aba5275c3718b753a2a693980d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2011-03-16T21:02:53Z","title_canon_sha256":"2e4c538725b1747ace4d96c6860f57146c776afe20bcfc78b9d7f989112e2037"},"schema_version":"1.0","source":{"id":"1103.3296","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3296","created_at":"2026-05-18T03:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3296v2","created_at":"2026-05-18T03:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3296","created_at":"2026-05-18T03:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"G2UQOKJGEBMY","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G2UQOKJGEBMYEXQU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G2UQOKJG","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:016b489cda9875f9826db6334a053832d0c3d6e2c648d43517b4868c4aa03681","target":"graph","created_at":"2026-05-18T03:38:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a new, efficient non-deterministic decoding algorithm for square-free Goppa codes over $\\F_p$ for any prime $p$. If the code in question has degree $t$ and the average distance to the closest codeword is at least $(4/p)t + 1$, the proposed decoder can uniquely correct up to $(2/p)t$ errors with high probability. The correction capability is higher if the distribution of error magnitudes is not uniform, approaching or reaching $t$ errors when any particular error value occurs much more often than others or exclusively. This makes the method interesting for (semantically secure) crypt","authors_text":"Paulo S. L. M. Barreto, Rafael Misoczki, Richard Lindner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2011-03-16T21:02:53Z","title":"Decoding square-free Goppa codes over $\\F_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3296","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c638badd930ad3cf8168e5ad69695270c9ae9e45b4ae17385a49a4976cd4cbac","target":"record","created_at":"2026-05-18T03:38:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3f6a560aca1a859ff70686b70b955efcd9224aba5275c3718b753a2a693980d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2011-03-16T21:02:53Z","title_canon_sha256":"2e4c538725b1747ace4d96c6860f57146c776afe20bcfc78b9d7f989112e2037"},"schema_version":"1.0","source":{"id":"1103.3296","kind":"arxiv","version":2}},"canonical_sha256":"36a90729262059825e14a23416419e0bfc663c60f5c216c8f04bd543af690702","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36a90729262059825e14a23416419e0bfc663c60f5c216c8f04bd543af690702","first_computed_at":"2026-05-18T03:38:14.538280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:14.538280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f5kJA9OZeBhQ2FPImGSATzVYLxMQrrGGFKCQ8rSEBt4yOarHq6TK6kLd2avS9FKf1FBaXUgRGWzUENRt4S1WBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:14.538775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3296","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c638badd930ad3cf8168e5ad69695270c9ae9e45b4ae17385a49a4976cd4cbac","sha256:016b489cda9875f9826db6334a053832d0c3d6e2c648d43517b4868c4aa03681"],"state_sha256":"ebef37a02fc2b9d64660763b3b2217a30af8d9508aa96798f6c223f1f8451ad5"}