{"title":"基于三次方程的多质点 RSA 密码系统攻击研究","authors":"Aleksėjus Michalkovič, Jokūbas Žitkevičius","doi":"10.15388/lmr.2023.33590","DOIUrl":null,"url":null,"abstract":"In this paper we consider a modification of the attack on the classic RSA cryptosystem aimed at factoring the public modulus n, which is a product of three primes. To improve the performance of the modified attack we introduce additional parameters. We present the theoretical upper bound on the search range parameter and define a shifting parameter based on the empirical results. Since these changes make our attack probabilistic, we investigate the dependence of the success on the values of the newly defined parameters.","PeriodicalId":33611,"journal":{"name":"Lietuvos Matematikos Rinkinys","volume":"5 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Investigation of an attack on the multi-prime RSA cryptosystem based on cubic equations\",\"authors\":\"Aleksėjus Michalkovič, Jokūbas Žitkevičius\",\"doi\":\"10.15388/lmr.2023.33590\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider a modification of the attack on the classic RSA cryptosystem aimed at factoring the public modulus n, which is a product of three primes. To improve the performance of the modified attack we introduce additional parameters. We present the theoretical upper bound on the search range parameter and define a shifting parameter based on the empirical results. Since these changes make our attack probabilistic, we investigate the dependence of the success on the values of the newly defined parameters.\",\"PeriodicalId\":33611,\"journal\":{\"name\":\"Lietuvos Matematikos Rinkinys\",\"volume\":\"5 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lietuvos Matematikos Rinkinys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15388/lmr.2023.33590\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lietuvos Matematikos Rinkinys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15388/lmr.2023.33590","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在本文中,我们考虑对经典 RSA 密码系统的攻击进行修改,目的是对公共模 n 进行因式分解,而公共模 n 是三个素数的乘积。为了提高修改后攻击的性能,我们引入了额外的参数。我们提出了搜索范围参数的理论上限,并根据经验结果定义了移动参数。由于这些变化使得我们的攻击具有概率性,因此我们研究了成功与否取决于新定义的参数值。
Investigation of an attack on the multi-prime RSA cryptosystem based on cubic equations
In this paper we consider a modification of the attack on the classic RSA cryptosystem aimed at factoring the public modulus n, which is a product of three primes. To improve the performance of the modified attack we introduce additional parameters. We present the theoretical upper bound on the search range parameter and define a shifting parameter based on the empirical results. Since these changes make our attack probabilistic, we investigate the dependence of the success on the values of the newly defined parameters.