{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:OOQHR7X5ORFUSWW5DZWTV2KZGG","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":"01ad519a0912adbf84de2eed8d0a52d33cff599f9536eb440676131c25834778","cross_cats_sorted":["cs.CC","math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2002-07-08T16:30:10Z","title_canon_sha256":"986521aa7f17f5c0b966b09629c1eafa98136fc7fada677a00a181289420a588"},"schema_version":"1.0","source":{"id":"cs/0207027","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0207027","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0207027v6","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0207027","created_at":"2026-05-18T04:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"OOQHR7X5ORFU","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"OOQHR7X5ORFUSWW5","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"OOQHR7X5","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:00220a7ee28dafe46f59d024de73bcc442ed051d1dbfab5f21e19bcb1828e014","target":"graph","created_at":"2026-05-18T04:37:23Z","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":"A permutation P on {1,..,N} is a_fast_forward_permutation_ if for each m the computational complexity of evaluating P^m(x)$ is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation on {1,..,N} is Theta(N) if one does not use queries of the form P^m(x), but is only Theta(1) if one is allowed to make such queries.\n  We construct fast forward permutations which are indistinguishable from ran","authors_text":"Boaz Tsaban","cross_cats":["cs.CC","math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2002-07-08T16:30:10Z","title":"Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0207027","kind":"arxiv","version":6},"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":"sha256:2d07ba231f03cd288aeab155df37c70156625e7e373a86f02f516cb8896d909e","target":"record","created_at":"2026-05-18T04:37:23Z","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":"01ad519a0912adbf84de2eed8d0a52d33cff599f9536eb440676131c25834778","cross_cats_sorted":["cs.CC","math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2002-07-08T16:30:10Z","title_canon_sha256":"986521aa7f17f5c0b966b09629c1eafa98136fc7fada677a00a181289420a588"},"schema_version":"1.0","source":{"id":"cs/0207027","kind":"arxiv","version":6}},"canonical_sha256":"73a078fefd744b495add1e6d3ae95931ad2d4fe10aee93f722080b2c20c48eb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73a078fefd744b495add1e6d3ae95931ad2d4fe10aee93f722080b2c20c48eb2","first_computed_at":"2026-05-18T04:37:23.244275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:23.244275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rj80bpZZTXWReE3Ef2abOzmPdJQAVmlJ433RDRQJ/EjTqdRqUmKzzgM5cYy+1ReHB/v+QMWJt6+KRcI7FrEIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:23.244712Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0207027","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d07ba231f03cd288aeab155df37c70156625e7e373a86f02f516cb8896d909e","sha256:00220a7ee28dafe46f59d024de73bcc442ed051d1dbfab5f21e19bcb1828e014"],"state_sha256":"cbe52a167250b974e3e27d2a4823b95739e51198a2199c7d0b7afc9c537cf9d3"}