{"title":"On Types of Elliptic Pseudoprimes","authors":"L. Babinkostova, A. Hern'andez-Espiet, H. Kim","doi":"10.46298/jgcc.2021.13.1.6521","DOIUrl":null,"url":null,"abstract":"We generalize the notions of elliptic pseudoprimes and elliptic Carmichael\nnumbers introduced by Silverman to analogues of Euler-Jacobi and strong\npseudoprimes. We investigate the relationships among Euler Elliptic Carmichael\nnumbers , strong elliptic Carmichael numbers, products of anomalous primes and\nelliptic Korselt numbers of Type I: The former two of these are introduced in\nthis paper, and the latter two of these were introduced by Mazur (1973) and\nSilverman (2012) respectively. In particular, we expand upon a previous work of\nBabinkostova et al. by proving a conjecture about the density of certain\nelliptic Korselt numbers of Type I that are products of anomalous primes.\nComment: Revised for publication. 33 pages","PeriodicalId":41862,"journal":{"name":"Groups Complexity Cryptology","volume":"21 1","pages":""},"PeriodicalIF":0.1000,"publicationDate":"2017-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complexity Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/jgcc.2021.13.1.6521","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: 2
Abstract
We generalize the notions of elliptic pseudoprimes and elliptic Carmichael
numbers introduced by Silverman to analogues of Euler-Jacobi and strong
pseudoprimes. We investigate the relationships among Euler Elliptic Carmichael
numbers , strong elliptic Carmichael numbers, products of anomalous primes and
elliptic Korselt numbers of Type I: The former two of these are introduced in
this paper, and the latter two of these were introduced by Mazur (1973) and
Silverman (2012) respectively. In particular, we expand upon a previous work of
Babinkostova et al. by proving a conjecture about the density of certain
elliptic Korselt numbers of Type I that are products of anomalous primes.
Comment: Revised for publication. 33 pages
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