{"paper":{"title":"Speeding Up Elliptic Curve Multiplication with Mixed-base Representation for Applications to SIDH Ciphers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CR","authors_text":"Marius C. Silaghi, Wesam Eid","submitted_at":"2019-05-16T01:49:32Z","abstract_excerpt":"Elliptic curve multiplications can be improved by replacing the standard ladder algorithm's base 2 representation of the scalar multiplicand, with mixed-base representations with power-of-2 bases, processing the n bits of the current digit in one optimized step. For this purpose, we also present a new methodology to compute, for Weierstrass form elliptic curves in the affine plane, operations of the type mP+nQ where m and n are small integers. This provides implementations with the lower cost than previous algorithms, using only one inversion. In particular, the proposed techniques enable more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06492","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"}