{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4U3PFKSVY5GAKL43RFRXNEZMF3","short_pith_number":"pith:4U3PFKSV","schema_version":"1.0","canonical_sha256":"e536f2aa55c74c052f9b896376932c2ef9cd8a3fc6eddb6b5c7ba871ae26ec05","source":{"kind":"arxiv","id":"1209.0618","version":2},"attestation_state":"computed","paper":{"title":"Analysis of the Width-w Non-Adjacent Form in Conjunction with Hyperelliptic Curve Cryptography and with Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Krenn","submitted_at":"2012-09-04T11:56:48Z","abstract_excerpt":"We analyse the number of occurrences of a fixed non-zero digit in the width-w non-adjacent forms of all elements of a lattice in some region (e.g. a ball). Our result is an asymptotic formula, where its main term coincides with the full block length analysis. In its second order term a periodic fluctuation is exhibited. The proof follows Delange's method. This result in a general lattice set-up is then used for numeral systems with an algebraic integer as base. Those come from efficient scalar multiplication methods (Frobenius-and-add methods) in hyperelliptic curves cryptography, and our resu"},"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":"1209.0618","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-04T11:56:48Z","cross_cats_sorted":[],"title_canon_sha256":"8ea5981d2cf570fd8b11f7fee7b7e48af122d6bbf8ddcf31cc2e792494e57978","abstract_canon_sha256":"62d28c9116926b36b3240d6a58aff51b31f0c06aaf8d53e9b570a8e867b4a72a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:55.371510Z","signature_b64":"twDq4AQGVUyWN3AdffwOAc0CdgWuz6mEZEWVQhzMbL2Kj/x0vw73ndUzJOO+lseh/NfXBLDRhGrj/VyW/cYPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e536f2aa55c74c052f9b896376932c2ef9cd8a3fc6eddb6b5c7ba871ae26ec05","last_reissued_at":"2026-05-18T03:30:55.370364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:55.370364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of the Width-w Non-Adjacent Form in Conjunction with Hyperelliptic Curve Cryptography and with Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Krenn","submitted_at":"2012-09-04T11:56:48Z","abstract_excerpt":"We analyse the number of occurrences of a fixed non-zero digit in the width-w non-adjacent forms of all elements of a lattice in some region (e.g. a ball). Our result is an asymptotic formula, where its main term coincides with the full block length analysis. In its second order term a periodic fluctuation is exhibited. The proof follows Delange's method. This result in a general lattice set-up is then used for numeral systems with an algebraic integer as base. Those come from efficient scalar multiplication methods (Frobenius-and-add methods) in hyperelliptic curves cryptography, and our resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0618","kind":"arxiv","version":2},"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":"1209.0618","created_at":"2026-05-18T03:30:55.370546+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.0618v2","created_at":"2026-05-18T03:30:55.370546+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0618","created_at":"2026-05-18T03:30:55.370546+00:00"},{"alias_kind":"pith_short_12","alias_value":"4U3PFKSVY5GA","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4U3PFKSVY5GAKL43","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4U3PFKSV","created_at":"2026-05-18T12:26:53.410803+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/4U3PFKSVY5GAKL43RFRXNEZMF3","json":"https://pith.science/pith/4U3PFKSVY5GAKL43RFRXNEZMF3.json","graph_json":"https://pith.science/api/pith-number/4U3PFKSVY5GAKL43RFRXNEZMF3/graph.json","events_json":"https://pith.science/api/pith-number/4U3PFKSVY5GAKL43RFRXNEZMF3/events.json","paper":"https://pith.science/paper/4U3PFKSV"},"agent_actions":{"view_html":"https://pith.science/pith/4U3PFKSVY5GAKL43RFRXNEZMF3","download_json":"https://pith.science/pith/4U3PFKSVY5GAKL43RFRXNEZMF3.json","view_paper":"https://pith.science/paper/4U3PFKSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.0618&json=true","fetch_graph":"https://pith.science/api/pith-number/4U3PFKSVY5GAKL43RFRXNEZMF3/graph.json","fetch_events":"https://pith.science/api/pith-number/4U3PFKSVY5GAKL43RFRXNEZMF3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4U3PFKSVY5GAKL43RFRXNEZMF3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4U3PFKSVY5GAKL43RFRXNEZMF3/action/storage_attestation","attest_author":"https://pith.science/pith/4U3PFKSVY5GAKL43RFRXNEZMF3/action/author_attestation","sign_citation":"https://pith.science/pith/4U3PFKSVY5GAKL43RFRXNEZMF3/action/citation_signature","submit_replication":"https://pith.science/pith/4U3PFKSVY5GAKL43RFRXNEZMF3/action/replication_record"}},"created_at":"2026-05-18T03:30:55.370546+00:00","updated_at":"2026-05-18T03:30:55.370546+00:00"}