{"title":"Some applications of arithmetic groups in cryptography","authors":"Delaram Kahrobaei, Keivan Mallahi-Karai","doi":"10.1515/gcc-2019-2002","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we will offer a new symmetric-key cryptographic scheme which is based on the existence of exponentially distorted subgroups in arithmetic groups. Aside from this, we will also provide new examples of distorted subgroups in SL n ( ℤ [ x ] ) {\\mathrm{SL}_{n}(\\mathbb{Z}[x])} which can be utilized for the same purpose.","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"15 1","pages":"25 - 33"},"PeriodicalIF":0.1000,"publicationDate":"2018-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc-2019-2002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract In this paper, we will offer a new symmetric-key cryptographic scheme which is based on the existence of exponentially distorted subgroups in arithmetic groups. Aside from this, we will also provide new examples of distorted subgroups in SL n ( ℤ [ x ] ) {\mathrm{SL}_{n}(\mathbb{Z}[x])} which can be utilized for the same purpose.
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