{"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"}