{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NQBZJVLBZOUES5MOAZCAB6VD6A","short_pith_number":"pith:NQBZJVLB","canonical_record":{"source":{"id":"1102.1053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-05T05:09:28Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"c4cf929dfc05a09a471680b5a73f5b81d52c6a3e0317c0de5dd3d2c632828c06","abstract_canon_sha256":"261f561eaa32e2c4e677491e9477956c25fb3d0efa3911a191ab4ac79ecc3235"},"schema_version":"1.0"},"canonical_sha256":"6c0394d561cba849758e064400faa3f00a21bfcbac73bead41fd55c6a5ab5b05","source":{"kind":"arxiv","id":"1102.1053","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1053","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1053v1","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1053","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"NQBZJVLBZOUE","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NQBZJVLBZOUES5MO","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NQBZJVLB","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NQBZJVLBZOUES5MOAZCAB6VD6A","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-05T05:09:28Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"c4cf929dfc05a09a471680b5a73f5b81d52c6a3e0317c0de5dd3d2c632828c06","abstract_canon_sha256":"261f561eaa32e2c4e677491e9477956c25fb3d0efa3911a191ab4ac79ecc3235"},"schema_version":"1.0"},"canonical_sha256":"6c0394d561cba849758e064400faa3f00a21bfcbac73bead41fd55c6a5ab5b05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:55.116442Z","signature_b64":"hEIGGTmZWeZ2XRU1s5OBQAQ5nqXhN6q5amqqDG4M3NXpTOQ4zq+gE/p/xTIrPnmbno03eRttZ23dlQxjJbbIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c0394d561cba849758e064400faa3f00a21bfcbac73bead41fd55c6a5ab5b05","last_reissued_at":"2026-05-18T04:29:55.115857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:55.115857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1053","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:29:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uspvvEIiKK9HTvLPqfmzrvdQTlOpfWoSy4Yof5LKaPzJc093jBRKNJJ1w/LRehqzD5zSpgaR6C1W/wF5uGiNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:50:04.398846Z"},"content_sha256":"5827ca08b4c7c07fa476067ef8cc9f2cbb9c22d2d5a7feaa775368d8b3e2d139","schema_version":"1.0","event_id":"sha256:5827ca08b4c7c07fa476067ef8cc9f2cbb9c22d2d5a7feaa775368d8b3e2d139"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NQBZJVLBZOUES5MOAZCAB6VD6A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"math.NT","authors_text":"Alina Ostafe, Igor E. Shparlinski, Simon R. Blackburn","submitted_at":"2011-02-05T05:09:28Z","abstract_excerpt":"Given a prime $p$, an elliptic curve $\\E/\\F_p$ over the finite field $\\F_p$ of $p$ elements and a binary \\lrs\\ $\\(u(n)\\)_{n =1}^\\infty$ of order~$r$, we study the distribution of the sequence of points $$ \\sum_{j=0}^{r-1} u(n+j)P_j, \\qquad n =1,..., N, $$ on average over all possible choices of $\\F_p$-rational points $P_1,..., P_r$ on~$\\E$. For a sufficiently large $N$ we improve and generalise a previous result in this direction due to E.~El~Mahassni."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1053","kind":"arxiv","version":1},"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":"2026-05-18T04:29:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/2M3sQTDQCOoJhsvJvqRShfTgf/IIqhNy3B280/oTT7c+e+O5E66jvkjHjStHpnjpOU6G8a0Tyo6WjGCZcrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:50:04.399190Z"},"content_sha256":"ddc8e152e24d8fb73e2c35a3d95a33eae5e82f3cf24a9b8d38215ecba6d05e36","schema_version":"1.0","event_id":"sha256:ddc8e152e24d8fb73e2c35a3d95a33eae5e82f3cf24a9b8d38215ecba6d05e36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQBZJVLBZOUES5MOAZCAB6VD6A/bundle.json","state_url":"https://pith.science/pith/NQBZJVLBZOUES5MOAZCAB6VD6A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQBZJVLBZOUES5MOAZCAB6VD6A/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":"2026-05-27T02:50:04Z","links":{"resolver":"https://pith.science/pith/NQBZJVLBZOUES5MOAZCAB6VD6A","bundle":"https://pith.science/pith/NQBZJVLBZOUES5MOAZCAB6VD6A/bundle.json","state":"https://pith.science/pith/NQBZJVLBZOUES5MOAZCAB6VD6A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQBZJVLBZOUES5MOAZCAB6VD6A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NQBZJVLBZOUES5MOAZCAB6VD6A","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":"261f561eaa32e2c4e677491e9477956c25fb3d0efa3911a191ab4ac79ecc3235","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-05T05:09:28Z","title_canon_sha256":"c4cf929dfc05a09a471680b5a73f5b81d52c6a3e0317c0de5dd3d2c632828c06"},"schema_version":"1.0","source":{"id":"1102.1053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1053","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1053v1","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1053","created_at":"2026-05-18T04:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"NQBZJVLBZOUE","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NQBZJVLBZOUES5MO","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NQBZJVLB","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:ddc8e152e24d8fb73e2c35a3d95a33eae5e82f3cf24a9b8d38215ecba6d05e36","target":"graph","created_at":"2026-05-18T04:29:55Z","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":"Given a prime $p$, an elliptic curve $\\E/\\F_p$ over the finite field $\\F_p$ of $p$ elements and a binary \\lrs\\ $\\(u(n)\\)_{n =1}^\\infty$ of order~$r$, we study the distribution of the sequence of points $$ \\sum_{j=0}^{r-1} u(n+j)P_j, \\qquad n =1,..., N, $$ on average over all possible choices of $\\F_p$-rational points $P_1,..., P_r$ on~$\\E$. For a sufficiently large $N$ we improve and generalise a previous result in this direction due to E.~El~Mahassni.","authors_text":"Alina Ostafe, Igor E. Shparlinski, Simon R. Blackburn","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-05T05:09:28Z","title":"On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1053","kind":"arxiv","version":1},"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":"sha256:5827ca08b4c7c07fa476067ef8cc9f2cbb9c22d2d5a7feaa775368d8b3e2d139","target":"record","created_at":"2026-05-18T04:29:55Z","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":"261f561eaa32e2c4e677491e9477956c25fb3d0efa3911a191ab4ac79ecc3235","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-02-05T05:09:28Z","title_canon_sha256":"c4cf929dfc05a09a471680b5a73f5b81d52c6a3e0317c0de5dd3d2c632828c06"},"schema_version":"1.0","source":{"id":"1102.1053","kind":"arxiv","version":1}},"canonical_sha256":"6c0394d561cba849758e064400faa3f00a21bfcbac73bead41fd55c6a5ab5b05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c0394d561cba849758e064400faa3f00a21bfcbac73bead41fd55c6a5ab5b05","first_computed_at":"2026-05-18T04:29:55.115857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:55.115857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hEIGGTmZWeZ2XRU1s5OBQAQ5nqXhN6q5amqqDG4M3NXpTOQ4zq+gE/p/xTIrPnmbno03eRttZ23dlQxjJbbIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:55.116442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5827ca08b4c7c07fa476067ef8cc9f2cbb9c22d2d5a7feaa775368d8b3e2d139","sha256:ddc8e152e24d8fb73e2c35a3d95a33eae5e82f3cf24a9b8d38215ecba6d05e36"],"state_sha256":"197f691b4a1aeea6072312ee7b708eacfab8844250de6aaaf9a76bd51c4f71e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fmeUkwi9BHMxISXvddWn94dQBRVwjS2WsMyblQMLnpyyhI5eOlHp3pxOPZ+3oZatZBvmwrmL24eM+Akr8BiVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:50:04.401503Z","bundle_sha256":"1b77b85683e9163c6584aaa01f33ed111fc0402748583e436e3127a3e9dead44"}}