{"paper":{"title":"Predicting the elliptic curve congruential generator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CR","authors_text":"L\\'aszl\\'o M\\'erai","submitted_at":"2016-09-12T08:39:27Z","abstract_excerpt":"Let $p$ be a prime and let $\\mathbf{E}$ be an elliptic curve defined over the finite field $\\mathbb{F}_p$ of $p$ elements. For a point $G\\in\\mathbf{E}(\\mathbb{F}_p)$ the elliptic curve congruential generator (with respect to the first coordinate) is a sequence $(x_n)$ defined by the relation $x_n=x(W_n)=x(W_{n-1}\\oplus G)=x(nG\\oplus W_0)$, $n=1,2,\\dots$, where $\\oplus$ denotes the group operation in $\\mathbf{E}$ and $W_0$ is an initial point. In this paper, we show that if some consecutive elements of the sequence $(x_n)$ are given as integers, then one can compute in polynomial time an ellipt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03305","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"}