{"title":"用最有效位降低LLL","authors":"Goel Sarushi, I. Morel, D. Stehlé, G. Villard","doi":"10.1145/2608628.2608645","DOIUrl":null,"url":null,"abstract":"Let B be a basis of a Euclidean lattice, and B an approximation thereof. We give a sufficient condition on the closeness between B and B so that an LLL-reducing transformation U for B remains valid for B. Further, we analyse an efficient reduction algorithm when B is itself a small deformation of an LLL-reduced basis. Applications include speeding-up reduction by keeping only the most significant bits of B, reducing a basis that is only approximately known, and efficiently batching LLL reductions for closely related inputs.","PeriodicalId":243282,"journal":{"name":"International Symposium on Symbolic and Algebraic Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"LLL reducing with the most significant bits\",\"authors\":\"Goel Sarushi, I. Morel, D. Stehlé, G. Villard\",\"doi\":\"10.1145/2608628.2608645\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let B be a basis of a Euclidean lattice, and B an approximation thereof. We give a sufficient condition on the closeness between B and B so that an LLL-reducing transformation U for B remains valid for B. Further, we analyse an efficient reduction algorithm when B is itself a small deformation of an LLL-reduced basis. Applications include speeding-up reduction by keeping only the most significant bits of B, reducing a basis that is only approximately known, and efficiently batching LLL reductions for closely related inputs.\",\"PeriodicalId\":243282,\"journal\":{\"name\":\"International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Symbolic and Algebraic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2608628.2608645\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2608628.2608645","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let B be a basis of a Euclidean lattice, and B an approximation thereof. We give a sufficient condition on the closeness between B and B so that an LLL-reducing transformation U for B remains valid for B. Further, we analyse an efficient reduction algorithm when B is itself a small deformation of an LLL-reduced basis. Applications include speeding-up reduction by keeping only the most significant bits of B, reducing a basis that is only approximately known, and efficiently batching LLL reductions for closely related inputs.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
