{"paper":{"title":"An Indexing for Quadratic Residues Modulo $N$ and a Non-uniform Efficient Decoding Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andr\\'e L. Vignatti, Murilo V. G. da Silva, Nicollas M. Sdroievski","submitted_at":"2018-05-12T14:58:51Z","abstract_excerpt":"An \\emph{indexing} of a finite set $S$ is a bijection $D : \\{1,...,|S|\\} \\rightarrow S$. We present an indexing for the set of quadratic residues modulo $N$ that is decodable in polynomial time on the size of $N$, given the factorization of $N$. One consequence of this result is a procedure for sampling quadratic residues modulo $N$, when the factorization of $N$ is known, that runs in strict polynomial time and requires the theoretical minimum amount of random bits (i.e., $\\log{(\\phi(N)/2^r)}$ bits, where $\\phi(N)$ is Euler's totient function and $r$ is the number of distinct prime factors of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04731","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"}