{"title":"一个新的转移定理在Ajtai连接因子中的应用","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":"{\"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}","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}
Applications of a new transference theorem to Ajtai's connection factor
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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