{"title":"Applications of a new transference theorem to Ajtai's connection factor","authors":"Jin-Yi Cai","doi":"10.1109/CCC.1999.766278","DOIUrl":null,"url":null,"abstract":"We apply a new transference theorem from the geometry of numbers to Ajtai's connection of average-case to worst-case complexity of lattice problems. We also derive stronger bounds for the special class of lattices which possess n/sup /spl epsiv//-unique shortest lattice vectors. This class of lattices plays a significant role in Ajtai's connection of average-case to worst-case complexity of the shortest lattice vector problem, and in the Ajtai-Dwork public-key cryptosystem. Our proofs are non-constructive, based on methods from harmonic analysis. They yield currently the best Ajtai connection factors.","PeriodicalId":432015,"journal":{"name":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","volume":"3 3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.1999.766278","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 16
Abstract
We apply a new transference theorem from the geometry of numbers to Ajtai's connection of average-case to worst-case complexity of lattice problems. We also derive stronger bounds for the special class of lattices which possess n/sup /spl epsiv//-unique shortest lattice vectors. This class of lattices plays a significant role in Ajtai's connection of average-case to worst-case complexity of the shortest lattice vector problem, and in the Ajtai-Dwork public-key cryptosystem. Our proofs are non-constructive, based on methods from harmonic analysis. They yield currently the best Ajtai connection factors.
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