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Pseudoprime reductions of elliptic curves

Published online by Cambridge University Press:  01 May 2009

ALINA CARMEN COJOCARU ,
FLORIAN LUCA  and
IGOR E. SHPARLINSKI
ALINA CARMEN COJOCARU
Affiliation:
Dept. of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607-7045, U.S.A. and The Institute of Mathematics of the Romanian Academy, Bucharest, Romania. e-mail: [email protected]
FLORIAN LUCA
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México. e-mail: [email protected]
IGOR E. SHPARLINSKI
Affiliation:
Dept. of Computing, Macquarie University, Sydney, NSW 2109, Australia. e-mail: [email protected]
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Abstract

Let b ≥ 2 be an integer and let E/ be a fixed elliptic curve. In this paper, we estimate the number of primes p ≤ x such that the number of points nE(p) on the reduction of E modulo p is a base b prime or pseudoprime. In particular, we improve previously known bounds which applied only to prime values of nE(p).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 3 , May 2009 , pp. 513 - 522
Copyright
Copyright © Cambridge Philosophical Society 2008

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