{"paper":{"title":"On improvements of the $r$-adding walk in a finite field of characteristic 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Ansari Abdullah, Ayan Mahalanobis, Hardik Gajera","submitted_at":"2016-01-16T07:27:08Z","abstract_excerpt":"It is currently known from the work of Shoup and Nechaev that a generic algorithm to solve the discrete logarithm problem in a group of prime order must have complexity at least $k\\sqrt{N}$ where $N$ is the order of the group. In many collision search algorithms this complexity is achieved. So with generic algorithms one can only hope to make the $k$ smaller. This $k$ depends on the complexity of the iterative step in the generic algorithms. The $\\sqrt{N}$ comes from the fact there is about $\\sqrt{N}$ iterations before a collision. So if we can find ways that can reduce the amount of work in o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04134","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"}