{"paper":{"title":"Sidon sets and statistics of the ElGamal function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ana Zumalac\\'arregui, Joachim von zur Gathen, Lucas Boppr\\'e Niehues, Lucas Pandolfo Perin","submitted_at":"2017-08-15T05:04:18Z","abstract_excerpt":"In the ElGamal signature and encryption schemes, an element $x$ of the underlying group $G = \\mathbb{Z}_p^\\times = \\{1, \\ldots, p-1 \\}$ for a prime $p$ is also considered as an exponent, for example in $g^x$, where $g$ is a generator of G. This ElGamal map $x \\mapsto g^x$ is poorly understood, and one may wonder whether it has some randomness properties. The underlying map from $G$ to $\\mathbb{Z}_{p-1}$ with $x \\mapsto x$ is trivial from a computer science point of view, but does not seem to have any mathematical structure.\n  This work presents two pieces of evidence for randomness. Firstly, e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04395","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"}