Corrigendum: The Distribution of Lucas and Elliptic Pseudoprimes

1993 ◽  
Vol 60 (202) ◽  
pp. 877
Author(s):  
D. M. Gordon ◽  
C. Pomerance
Keyword(s):  
Elliptic Pseudoprimes

scholarly journals Strongly nonzero points and elliptic pseudoprimes

2021 ◽  
Vol 14 (1) ◽  
pp. 65-88
Author(s):  
Liljana Babinkostova ◽  
Dylan Fillmore ◽  
Philip Lamkin ◽  
Alice Lin ◽  
Calvin L. Yost-Wolff
Keyword(s):  
Elliptic Pseudoprimes

scholarly journals On the number of elliptic pseudoprimes

1989 ◽  
Vol 52 (185) ◽  
pp. 231-231 ◽  
Author(s):  
Daniel M. Gordon
Keyword(s):  
Elliptic Pseudoprimes

scholarly journals The distribution of Lucas and elliptic pseudoprimes

1991 ◽  
Vol 57 (196) ◽  
pp. 825-825 ◽  
Author(s):  
Daniel M. Gordon ◽  
Carl Pomerance
Keyword(s):  
Elliptic Pseudoprimes

scholarly journals Elliptic pseudoprimes

1989 ◽  
Vol 53 (187) ◽  
pp. 415-415 ◽  
Author(s):  
I. Miyamoto ◽  
M. Ram Murty
Keyword(s):  
Elliptic Pseudoprimes

scholarly journals Pseudoprime Reductions of Elliptic Curves

2012 ◽  
Vol 64 (1) ◽  
pp. 81-101 ◽  
Author(s):  
C. David ◽  
J. Wu
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Complex Multiplication ◽  
Upper Bounds ◽  
Good Reduction ◽  
Elliptic Pseudoprimes

Abstract Let E be an elliptic curve over ℚ without complex multiplication, and for each prime p of good reduction, let nE(p) = |E(𝔽p)|. For any integer b, we consider elliptic pseudoprimes to the base b. More precisely, let QE,b(x) be the number of primes p ⩽ x such that bnE(p) ≡ b (mod nE(p)), and let πpseuE,b (x) be the number of compositive nE(p) such that bnE(p) ≡ b (mod nE(p)) (also called elliptic curve pseudoprimes). Motivated by cryptography applications, we address the problem of finding upper bounds for QE,b(x) and πpseuE,b (x), generalising some of the literature for the classical pseudoprimes to this new setting.

scholarly journals On Types of Elliptic Pseudoprimes

2021 ◽  
Vol Volume 13, issue 1 ◽  
Author(s):  
L. Babinkostova ◽  
A. Hernández-Espiet ◽  
H. Kim
Keyword(s):  
Type I ◽  
Carmichael Numbers ◽  
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 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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