{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:2XGAWOANR2NXYGV676AEVMF2YC","short_pith_number":"pith:2XGAWOAN","schema_version":"1.0","canonical_sha256":"d5cc0b380d8e9b7c1abeff804ab0bac0bbf3f23dd741083cd2918265ea3b3c34","source":{"kind":"arxiv","id":"1907.01066","version":1},"attestation_state":"computed","paper":{"title":"On two-to-one mappings over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.IT"],"primary_cat":"cs.IT","authors_text":"Longjiang Qu, Sihem Mesnager","submitted_at":"2019-06-27T16:00:09Z","abstract_excerpt":"Two-to-one ($2$-to-$1$) mappings over finite fields play an important role in symmetric cryptography. In particular they allow to design APN functions, bent functions and semi-bent functions. In this paper we provide a systematic study of two-to-one mappings that are defined over finite fields. We characterize such mappings by means of the Walsh transforms. We also present several constructions, including an AGW-like criterion, constructions with the form of $x^rh(x^{(q-1)/d})$, those from permutation polynomials, from linear translators and from APN functions. Then we present $2$-to-$1$ polyn"},"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":"1907.01066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-06-27T16:00:09Z","cross_cats_sorted":["cs.CR","math.IT"],"title_canon_sha256":"ae627a6721413d7c46b786ba15de5e6ca46ed488d23fa552713c9fa65a6da845","abstract_canon_sha256":"a806b24ce4f660916f33f965782abfd66108ca8ae7464c4f016937793ee5d245"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:41.335153Z","signature_b64":"Yi5c30G5XRnn0oF3kvas7mkYKUccb1mWNcoqsPeET2styFhThlt1/gIdXkt3c65LJy8CMv5rlNOj1pfbyzqwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5cc0b380d8e9b7c1abeff804ab0bac0bbf3f23dd741083cd2918265ea3b3c34","last_reissued_at":"2026-05-17T23:41:41.334351Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:41.334351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On two-to-one mappings over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.IT"],"primary_cat":"cs.IT","authors_text":"Longjiang Qu, Sihem Mesnager","submitted_at":"2019-06-27T16:00:09Z","abstract_excerpt":"Two-to-one ($2$-to-$1$) mappings over finite fields play an important role in symmetric cryptography. In particular they allow to design APN functions, bent functions and semi-bent functions. In this paper we provide a systematic study of two-to-one mappings that are defined over finite fields. We characterize such mappings by means of the Walsh transforms. We also present several constructions, including an AGW-like criterion, constructions with the form of $x^rh(x^{(q-1)/d})$, those from permutation polynomials, from linear translators and from APN functions. Then we present $2$-to-$1$ polyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01066","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.01066","created_at":"2026-05-17T23:41:41.334485+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.01066v1","created_at":"2026-05-17T23:41:41.334485+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01066","created_at":"2026-05-17T23:41:41.334485+00:00"},{"alias_kind":"pith_short_12","alias_value":"2XGAWOANR2NX","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"2XGAWOANR2NXYGV6","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"2XGAWOAN","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC","json":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC.json","graph_json":"https://pith.science/api/pith-number/2XGAWOANR2NXYGV676AEVMF2YC/graph.json","events_json":"https://pith.science/api/pith-number/2XGAWOANR2NXYGV676AEVMF2YC/events.json","paper":"https://pith.science/paper/2XGAWOAN"},"agent_actions":{"view_html":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC","download_json":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC.json","view_paper":"https://pith.science/paper/2XGAWOAN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.01066&json=true","fetch_graph":"https://pith.science/api/pith-number/2XGAWOANR2NXYGV676AEVMF2YC/graph.json","fetch_events":"https://pith.science/api/pith-number/2XGAWOANR2NXYGV676AEVMF2YC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC/action/storage_attestation","attest_author":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC/action/author_attestation","sign_citation":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC/action/citation_signature","submit_replication":"https://pith.science/pith/2XGAWOANR2NXYGV676AEVMF2YC/action/replication_record"}},"created_at":"2026-05-17T23:41:41.334485+00:00","updated_at":"2026-05-17T23:41:41.334485+00:00"}