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Instead of the shortest vector we apply an approximation given by the LLL algorithm for lattice basis reduction. We empirically demonstrate the speed-up and the quality loss obtained by the LLL reduction, and we present important applications for parameter selections.<\/p>","DOI":"10.1090\/s0025-5718-01-01415-6","type":"journal-article","created":{"date-parts":[[2002,9,20]],"date-time":"2002-09-20T15:46:54Z","timestamp":1032536814000},"page":"1231-1242","source":"Crossref","is-referenced-by-count":7,"title":["Efficient lattice assessment for LCG and GLP parameter searches"],"prefix":"10.1090","volume":"71","author":[{"given":"Karl","family":"Entacher","sequence":"first","affiliation":[]},{"given":"Thomas","family":"Schell","sequence":"additional","affiliation":[]},{"given":"Andreas","family":"Uhl","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,12,21]]},"reference":[{"issue":"3-4","key":"1","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1007\/BF01186658","article-title":"The sub-lattice structure of linear congruential random number generators","volume":"55","author":"Afflerbach, Lothar","year":"1986","journal-title":"Manuscripta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-2611","issn-type":"print"},{"key":"2","unstructured":"J Ajtai, Generating Hard Instances of Lattice Problems, Report TR96-007, Electronic Colloquium on Computational Complexity ECCC, 1996, Web-page: [ECCC, Electronic Colloquium on Computational Complexity ECCC, \\url{http:\/\/www.eccc.uni-trier.de\/eccc\/}]."},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492900002804","article-title":"Monte Carlo and quasi-Monte Carlo methods","author":"Caflisch, Russel E.","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/0521643163"},{"key":"4","unstructured":"J Cai, Some Recent Progress on the Complexity of Lattice Problems, Report TR99-006, Electronic Colloquium on Computational Complexity ECCC, 1999, Web-page: [ECCC, Electronic Colloquium on Computational Complexity ECCC, \\url{http:\/\/www.eccc.uni-trier.de\/eccc\/}]."},{"key":"5","unstructured":"P. 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