{"paper":{"title":"On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"math.NT","authors_text":"Alina Ostafe, Igor E. Shparlinski, Simon R. Blackburn","submitted_at":"2011-02-05T05:09:28Z","abstract_excerpt":"Given a prime $p$, an elliptic curve $\\E/\\F_p$ over the finite field $\\F_p$ of $p$ elements and a binary \\lrs\\ $\\(u(n)\\)_{n =1}^\\infty$ of order~$r$, we study the distribution of the sequence of points $$ \\sum_{j=0}^{r-1} u(n+j)P_j, \\qquad n =1,..., N, $$ on average over all possible choices of $\\F_p$-rational points $P_1,..., P_r$ on~$\\E$. For a sufficiently large $N$ we improve and generalise a previous result in this direction due to E.~El~Mahassni."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1053","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"}