{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OGS5M5Z4E7R3RJRNBGLYPQWS5H","short_pith_number":"pith:OGS5M5Z4","canonical_record":{"source":{"id":"1808.02974","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-08-09T00:25:14Z","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"title_canon_sha256":"b791da9fa27a42310197c0c4bc8878aa2dc1e6390e3eede76cc506650c5d2d91","abstract_canon_sha256":"ac1bfbbd77f94be0f238fdad04745ecabf51a0449738ca604d129bf7d038a714"},"schema_version":"1.0"},"canonical_sha256":"71a5d6773c27e3b8a62d099787c2d2e9e640d6a20995360fb9aa9080fe9f291f","source":{"kind":"arxiv","id":"1808.02974","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02974","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02974v3","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02974","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"OGS5M5Z4E7R3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OGS5M5Z4E7R3RJRN","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OGS5M5Z4","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OGS5M5Z4E7R3RJRNBGLYPQWS5H","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02974","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-08-09T00:25:14Z","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"title_canon_sha256":"b791da9fa27a42310197c0c4bc8878aa2dc1e6390e3eede76cc506650c5d2d91","abstract_canon_sha256":"ac1bfbbd77f94be0f238fdad04745ecabf51a0449738ca604d129bf7d038a714"},"schema_version":"1.0"},"canonical_sha256":"71a5d6773c27e3b8a62d099787c2d2e9e640d6a20995360fb9aa9080fe9f291f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:24.862055Z","signature_b64":"iJSm3ttQ/bsFot93RAWuGkfV0Qn42WgJ1IWwdap5hf0Fshn0MZNfbJavBRgxMtCLD66fvO91tZ2l7U093IpPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71a5d6773c27e3b8a62d099787c2d2e9e640d6a20995360fb9aa9080fe9f291f","last_reissued_at":"2026-05-17T23:58:24.861473Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:24.861473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02974","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1EPYC5qMujAL9TzVocXoynKjjSFD0WYdgiil2wG/MRozDYMwyeTGfZUMZ+9xhxIBoum9/ncWYGHTqDyptLOkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:20:14.414008Z"},"content_sha256":"5ab2f0ffd91f618339e6797ed8fc1c27ee29d7ed8fe7045cd09357416373ddad","schema_version":"1.0","event_id":"sha256:5ab2f0ffd91f618339e6797ed8fc1c27ee29d7ed8fe7045cd09357416373ddad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OGS5M5Z4E7R3RJRNBGLYPQWS5H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secret Sharing with Binary Shares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","math.IT"],"primary_cat":"cs.CR","authors_text":"Fuchun Lin, Huaxiong Wang, Mahdi Cheraghchi, Reihaneh Safavi-Naini, Venkatesan Guruswami","submitted_at":"2018-08-09T00:25:14Z","abstract_excerpt":"Shamir's celebrated secret sharing scheme provides an efficient method for encoding a secret of arbitrary length $\\ell$ among any $N \\leq 2^\\ell$ players such that for a threshold parameter $t$, (i) the knowledge of any $t$ shares does not reveal any information about the secret and, (ii) any choice of $t+1$ shares fully reveals the secret. It is known that any such threshold secret sharing scheme necessarily requires shares of length $\\ell$, and in this sense Shamir's scheme is optimal. The more general notion of ramp schemes requires the reconstruction of secret from any $t+g$ shares, for a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02974","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3qWlx754rgScbEvxZgP6AW1kRdkqmuhaNlIE7pzRT8TZh443cpXv8Sb/wXfXg94QdJP8ORN13GszP5hZqUwMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:20:14.414385Z"},"content_sha256":"2b8cffaa18faf588b3c491a6e7c0a06da9508ce0826c852f9404907139a2504f","schema_version":"1.0","event_id":"sha256:2b8cffaa18faf588b3c491a6e7c0a06da9508ce0826c852f9404907139a2504f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGS5M5Z4E7R3RJRNBGLYPQWS5H/bundle.json","state_url":"https://pith.science/pith/OGS5M5Z4E7R3RJRNBGLYPQWS5H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGS5M5Z4E7R3RJRNBGLYPQWS5H/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T21:20:14Z","links":{"resolver":"https://pith.science/pith/OGS5M5Z4E7R3RJRNBGLYPQWS5H","bundle":"https://pith.science/pith/OGS5M5Z4E7R3RJRNBGLYPQWS5H/bundle.json","state":"https://pith.science/pith/OGS5M5Z4E7R3RJRNBGLYPQWS5H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGS5M5Z4E7R3RJRNBGLYPQWS5H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OGS5M5Z4E7R3RJRNBGLYPQWS5H","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":"ac1bfbbd77f94be0f238fdad04745ecabf51a0449738ca604d129bf7d038a714","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-08-09T00:25:14Z","title_canon_sha256":"b791da9fa27a42310197c0c4bc8878aa2dc1e6390e3eede76cc506650c5d2d91"},"schema_version":"1.0","source":{"id":"1808.02974","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02974","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02974v3","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02974","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"OGS5M5Z4E7R3","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OGS5M5Z4E7R3RJRN","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OGS5M5Z4","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:2b8cffaa18faf588b3c491a6e7c0a06da9508ce0826c852f9404907139a2504f","target":"graph","created_at":"2026-05-17T23:58:24Z","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":"Shamir's celebrated secret sharing scheme provides an efficient method for encoding a secret of arbitrary length $\\ell$ among any $N \\leq 2^\\ell$ players such that for a threshold parameter $t$, (i) the knowledge of any $t$ shares does not reveal any information about the secret and, (ii) any choice of $t+1$ shares fully reveals the secret. It is known that any such threshold secret sharing scheme necessarily requires shares of length $\\ell$, and in this sense Shamir's scheme is optimal. The more general notion of ramp schemes requires the reconstruction of secret from any $t+g$ shares, for a ","authors_text":"Fuchun Lin, Huaxiong Wang, Mahdi Cheraghchi, Reihaneh Safavi-Naini, Venkatesan Guruswami","cross_cats":["cs.CC","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-08-09T00:25:14Z","title":"Secret Sharing with Binary Shares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02974","kind":"arxiv","version":3},"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":"sha256:5ab2f0ffd91f618339e6797ed8fc1c27ee29d7ed8fe7045cd09357416373ddad","target":"record","created_at":"2026-05-17T23:58:24Z","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":"ac1bfbbd77f94be0f238fdad04745ecabf51a0449738ca604d129bf7d038a714","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-08-09T00:25:14Z","title_canon_sha256":"b791da9fa27a42310197c0c4bc8878aa2dc1e6390e3eede76cc506650c5d2d91"},"schema_version":"1.0","source":{"id":"1808.02974","kind":"arxiv","version":3}},"canonical_sha256":"71a5d6773c27e3b8a62d099787c2d2e9e640d6a20995360fb9aa9080fe9f291f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71a5d6773c27e3b8a62d099787c2d2e9e640d6a20995360fb9aa9080fe9f291f","first_computed_at":"2026-05-17T23:58:24.861473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:24.861473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iJSm3ttQ/bsFot93RAWuGkfV0Qn42WgJ1IWwdap5hf0Fshn0MZNfbJavBRgxMtCLD66fvO91tZ2l7U093IpPAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:24.862055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02974","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ab2f0ffd91f618339e6797ed8fc1c27ee29d7ed8fe7045cd09357416373ddad","sha256:2b8cffaa18faf588b3c491a6e7c0a06da9508ce0826c852f9404907139a2504f"],"state_sha256":"c1d406c7e268509b9286605805a13432a69a80bf33630c37e1391f97c1d1f2db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I9LiQMF8lLrFtZapAfqdkeOPAfVpfSOIPqvNxjg8w9MV/Y/LGVfdsGPj5zL6bQJwXojZnOrs70eC6/kkVTD4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:20:14.416457Z","bundle_sha256":"c3c862c22380166272b93b2c58d302aa80ed57051143c50fc4db59a5711cb82d"}}