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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"cs/0207027","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2002-07-08T16:30:10Z","cross_cats_sorted":["cs.CC","math.CO","math.PR"],"title_canon_sha256":"986521aa7f17f5c0b966b09629c1eafa98136fc7fada677a00a181289420a588","abstract_canon_sha256":"01ad519a0912adbf84de2eed8d0a52d33cff599f9536eb440676131c25834778"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:23.244712Z","signature_b64":"Rj80bpZZTXWReE3Ef2abOzmPdJQAVmlJ433RDRQJ/EjTqdRqUmKzzgM5cYy+1ReHB/v+QMWJt6+KRcI7FrEIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73a078fefd744b495add1e6d3ae95931ad2d4fe10aee93f722080b2c20c48eb2","last_reissued_at":"2026-05-18T04:37:23.244275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:23.244275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO","math.PR"],"primary_cat":"cs.CR","authors_text":"Boaz Tsaban","submitted_at":"2002-07-08T16:30:10Z","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. 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