Pseudoprime reductions of elliptic curves

Alina Carmen Cojocaru; Florian Luca; Igor E. Shparlinski

doi:10.1017/S0305004108001758

Pseudoprime reductions of elliptic curves

Alina Carmen Cojocaru^*, Florian Luca, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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Abstract

Let b ≥ 2 be an integer and let E/ q 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).

Original language	English
Pages (from-to)	513-522
Number of pages	10
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	146
Issue number	3
DOIs	https://doi.org/10.1017/S0305004108001758 https://doi.org/10.1017/S0305004111000399
Publication status	Published - May 2009

Bibliographical note

Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Corrigendum can be found in Mathematical Proceedings of the Cambridge Philosophical Society, Volume 152(3), 571, http://dx.doi.org/10.1017/S0305004111000399.

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N2 - Let b ≥ 2 be an integer and let E/ q 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).

AB - Let b ≥ 2 be an integer and let E/ q 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).

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Pseudoprime reductions of elliptic curves

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