On Types of Elliptic Pseudoprimes
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Episciences
2021-02-01
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| Series: | Groups, Complexity, Cryptology |
| Subjects: | |
| Online Access: | https://gcc.episciences.org/6521/pdf |
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| author | L. Babinkostova A. Hernández-Espiet H. Kim |
| author_facet | L. Babinkostova A. Hernández-Espiet H. Kim |
| author_sort | L. Babinkostova |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T19:24:56Z |
| format | Article |
| id | doaj.art-06ef802c6d934e8b952ac107e41a44fc |
| institution | Directory Open Access Journal |
| issn | 1869-6104 |
| language | English |
| last_indexed | 2024-04-11T19:24:56Z |
| publishDate | 2021-02-01 |
| publisher | Episciences |
| record_format | Article |
| series | Groups, Complexity, Cryptology |
| spelling | doaj.art-06ef802c6d934e8b952ac107e41a44fc2022-12-22T04:07:11ZengEpisciencesGroups, Complexity, Cryptology1869-61042021-02-01Volume 13, Issue 110.46298/jgcc.2021.13.1.65216521On Types of Elliptic PseudoprimesL. BabinkostovaA. Hernández-EspietH. KimWe 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.https://gcc.episciences.org/6521/pdfmathematics - group theorymathematics - number theory14h52, 14k22, 11y01, 11n25, 11g07, 11g20, 11b99 |
| spellingShingle | L. Babinkostova A. Hernández-Espiet H. Kim On Types of Elliptic Pseudoprimes Groups, Complexity, Cryptology mathematics - group theory mathematics - number theory 14h52, 14k22, 11y01, 11n25, 11g07, 11g20, 11b99 |
| title | On Types of Elliptic Pseudoprimes |
| title_full | On Types of Elliptic Pseudoprimes |
| title_fullStr | On Types of Elliptic Pseudoprimes |
| title_full_unstemmed | On Types of Elliptic Pseudoprimes |
| title_short | On Types of Elliptic Pseudoprimes |
| title_sort | on types of elliptic pseudoprimes |
| topic | mathematics - group theory mathematics - number theory 14h52, 14k22, 11y01, 11n25, 11g07, 11g20, 11b99 |
| url | https://gcc.episciences.org/6521/pdf |
| work_keys_str_mv | AT lbabinkostova ontypesofellipticpseudoprimes AT ahernandezespiet ontypesofellipticpseudoprimes AT hkim ontypesofellipticpseudoprimes |