TY - JOUR
T1 - ON TYPES OF ELLIPTIC PSEUDOPRIMES
AU - Babinkostova, Liljana
AU - Hernández-Espiet, A.
AU - Kim, H. Y.
N1 - Publisher Copyright:
© L. Babinkostova, A. Hernández-Espiet, and H. Y. Kim.
PY - 2021
Y1 - 2021
N2 - We generalize Silverman’s [31] notions of elliptic pseudoprimes and elliptic Carmichael numbers to analogues of Euler-Jacobi and strong pseudoprimes. We inspect 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 which we introduce and the latter two of which were introduced by Mazur [21] and Silverman [31] respectively. In particular, we expand upon the work of Babinkostova et al. [3] on the density of certain elliptic Korselt numbers of Type I which are products of anomalous primes, proving a conjecture stated in [3].
AB - We generalize Silverman’s [31] notions of elliptic pseudoprimes and elliptic Carmichael numbers to analogues of Euler-Jacobi and strong pseudoprimes. We inspect 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 which we introduce and the latter two of which were introduced by Mazur [21] and Silverman [31] respectively. In particular, we expand upon the work of Babinkostova et al. [3] on the density of certain elliptic Korselt numbers of Type I which are products of anomalous primes, proving a conjecture stated in [3].
KW - Elliptic curves
KW - Euler Elliptic Pseudoprimes
KW - Pseudoprimes
KW - Strong Elliptic Pseudoprimes
UR - http://www.scopus.com/inward/record.url?scp=85177059205&partnerID=8YFLogxK
U2 - 10.46298/jgcc.2021.13.1.6521
DO - 10.46298/jgcc.2021.13.1.6521
M3 - Article
AN - SCOPUS:85177059205
VL - 13
SP - 1:1-1:33
JO - Groups, Complexity, Cryptology
JF - Groups, Complexity, Cryptology
IS - 1
ER -