{"title":"将fpLLL库扩展到厄米格","authors":"P. Elbaz-Vincent, Etienne Marcatel","doi":"10.1145/3493492.3493498","DOIUrl":null,"url":null,"abstract":"We present an Hermitian version of the classical floating-point LLL reduction algorithm of Nguyen and Stehlé[16]. This new variant works on imaginary quadratic fields which are norm-Euclidean and also for some adequate cyclotomic fields. An optimized C++ implementation has been performed, based on the fpLLL code and results show a significant improvement for Hermitian lattices reduction of dimension N when compared to fpLLL reduction on the corresponding Euclidean lattice of dimension 2N. We demonstrate our implementation in the special case of the Gaussian integers.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"55 1","pages":"54 - 58"},"PeriodicalIF":0.4000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"An extension of the fpLLL library to Hermitian lattices\",\"authors\":\"P. Elbaz-Vincent, Etienne Marcatel\",\"doi\":\"10.1145/3493492.3493498\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an Hermitian version of the classical floating-point LLL reduction algorithm of Nguyen and Stehlé[16]. This new variant works on imaginary quadratic fields which are norm-Euclidean and also for some adequate cyclotomic fields. An optimized C++ implementation has been performed, based on the fpLLL code and results show a significant improvement for Hermitian lattices reduction of dimension N when compared to fpLLL reduction on the corresponding Euclidean lattice of dimension 2N. We demonstrate our implementation in the special case of the Gaussian integers.\",\"PeriodicalId\":41965,\"journal\":{\"name\":\"ACM Communications in Computer Algebra\",\"volume\":\"55 1\",\"pages\":\"54 - 58\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Communications in Computer Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3493492.3493498\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Communications in Computer Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3493492.3493498","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
An extension of the fpLLL library to Hermitian lattices
We present an Hermitian version of the classical floating-point LLL reduction algorithm of Nguyen and Stehlé[16]. This new variant works on imaginary quadratic fields which are norm-Euclidean and also for some adequate cyclotomic fields. An optimized C++ implementation has been performed, based on the fpLLL code and results show a significant improvement for Hermitian lattices reduction of dimension N when compared to fpLLL reduction on the corresponding Euclidean lattice of dimension 2N. We demonstrate our implementation in the special case of the Gaussian integers.
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