On Types of Elliptic Pseudoprimes
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Published:2021-02-10
Issue:
Volume:Volume 13, issue 1
Page:
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ISSN:
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Container-title:journal of Groups, Complexity, Cryptology
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language:en
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Author:
Babinkostova L.,Hernández-Espiet A.,Kim H.
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
Publisher
Centre pour la Communication Scientifique Directe (CCSD)