{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2HV6TUJFURGNQC7IHT366HVTGS","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":"c174c2e212f8ed2f951b2b4fd6c1b453d1f23891a16736f5502cdda45532c1dd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-29T18:31:39Z","title_canon_sha256":"194f4bdcc2a7c501f545ebcc97ecc44dba2f941aaf7e595c95928f4645c336c3"},"schema_version":"1.0","source":{"id":"1508.00462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00462","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00462v1","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00462","created_at":"2026-05-18T01:35:58Z"},{"alias_kind":"pith_short_12","alias_value":"2HV6TUJFURGN","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2HV6TUJFURGNQC7I","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2HV6TUJF","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:dfda1ad6e81bc8e2e6701cc076b4878bf9ebe9bc063da5ca4c745d5d60cb3af3","target":"graph","created_at":"2026-05-18T01:35:58Z","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":"An oracle chooses a function $f$ from the set of $n$ bits strings to itself, which is either a randomly chosen permutation or a randomly chosen function. When queried by an $n$-bit string $w$, the oracle computes $f(w)$, truncates the $m$ last bits, and returns only the first $n-m$ bits of $f(w)$. How many queries does a querying adversary need to submit in order to distinguish the truncated permutation from a random function?\n  In 1998, Hall et al. showed an algorithm for determining (with high probability) whether or not $f$ is a permutation, using $O(2^{\\frac{m+n}{2}})$ queries. They also s","authors_text":"Shay Gueron, Shoni Gilboa","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-29T18:31:39Z","title":"Distinguishing a truncated random permutation from a random function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00462","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:b5ac3e1497f26815bf17d90ae442d80641f7c6694f5ecb4c4f15ff913ba5df46","target":"record","created_at":"2026-05-18T01:35:58Z","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":"c174c2e212f8ed2f951b2b4fd6c1b453d1f23891a16736f5502cdda45532c1dd","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-29T18:31:39Z","title_canon_sha256":"194f4bdcc2a7c501f545ebcc97ecc44dba2f941aaf7e595c95928f4645c336c3"},"schema_version":"1.0","source":{"id":"1508.00462","kind":"arxiv","version":1}},"canonical_sha256":"d1ebe9d125a44cd80be83cf7ef1eb3349664dddd337ac17ae003d058c9ae583f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1ebe9d125a44cd80be83cf7ef1eb3349664dddd337ac17ae003d058c9ae583f","first_computed_at":"2026-05-18T01:35:58.049281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:58.049281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aQn8uINIa9JZFoD6JSymMmqlT5LpoyizpIqtgQdr0Twipv+zHrjn+M4vdA/EHMtg/PP0jeWOQGvFoCNFE30/Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:58.049961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5ac3e1497f26815bf17d90ae442d80641f7c6694f5ecb4c4f15ff913ba5df46","sha256:dfda1ad6e81bc8e2e6701cc076b4878bf9ebe9bc063da5ca4c745d5d60cb3af3"],"state_sha256":"68b3b7f93ccc409316d747d94092f9b166b0b7a340ab7d359691cb03816b61ad"}