{"title":"类rsa系统代数结构的一些性质","authors":"Baodian Wei, Fangguo Zhang, Xiaofeng Chen, Haibo Tian","doi":"10.1109/WCSE.2009.249","DOIUrl":null,"url":null,"abstract":"The algebraic structure Z_n^* , with n being a product of safe primes, is widely used in RSA-like cryptosystems. We have investigated some properties of this kind of structure. Isomorphic structures are presented to represent elements of Z_n^* in a unique way. They also help to determine the form and the number of possible subgroups, to find, in a deterministic rather than probabilistic manner, the elements of any possible orders. The properties of quadratic and high degree residues are analyzed in detail, as well.","PeriodicalId":331155,"journal":{"name":"2009 WRI World Congress on Software Engineering","volume":"56 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some Properties of Algebraic Structures of RSA-like Systems\",\"authors\":\"Baodian Wei, Fangguo Zhang, Xiaofeng Chen, Haibo Tian\",\"doi\":\"10.1109/WCSE.2009.249\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The algebraic structure Z_n^* , with n being a product of safe primes, is widely used in RSA-like cryptosystems. We have investigated some properties of this kind of structure. Isomorphic structures are presented to represent elements of Z_n^* in a unique way. They also help to determine the form and the number of possible subgroups, to find, in a deterministic rather than probabilistic manner, the elements of any possible orders. The properties of quadratic and high degree residues are analyzed in detail, as well.\",\"PeriodicalId\":331155,\"journal\":{\"name\":\"2009 WRI World Congress on Software Engineering\",\"volume\":\"56 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-05-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 WRI World Congress on Software Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/WCSE.2009.249\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 WRI World Congress on Software Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/WCSE.2009.249","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Some Properties of Algebraic Structures of RSA-like Systems
The algebraic structure Z_n^* , with n being a product of safe primes, is widely used in RSA-like cryptosystems. We have investigated some properties of this kind of structure. Isomorphic structures are presented to represent elements of Z_n^* in a unique way. They also help to determine the form and the number of possible subgroups, to find, in a deterministic rather than probabilistic manner, the elements of any possible orders. The properties of quadratic and high degree residues are analyzed in detail, as well.
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