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## An algorithmic construction of finite elliptic curves of order divisible by a large prime

### Authors:

- Maciej Grześkowiak

### Abstract

Given a square-free integer Δ < 0, we present an algorithm constructing a pair of primes p and q such that q|p + 1 - t and 4p - t^{2} = Δf^{2}, where |t| ≤ 2√p for some integers f, t. Together with a CM method presented in the paper, such primes p and q are used for a construction of an elliptic curve E over a finite field F_{p} such that the order of E is divisible by a large prime. It is shown that our algorithm works in polynomial time.

- Record ID
- UAM0bfe4bede79c4e929b8caf8a31bac4f3
- Author
- Journal series
- Fundamenta Informaticae, ISSN 0169-2968
- Issue year
- 2015
- Vol
- 136
- Pages
- 331-343
- ASJC Classification
- ; ; ;
- DOI
- DOI:10.3233/FI-2015-1161 opening in a new tab
- Language
- en English
- Score (nominal)
- 20
- Score source
- journalList
- Score
- Publication indicators
- = 2.000; : 2015 = 0.795; : 2015 = 0.658 (2) - 2015=0.674 (5)

- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAM0bfe4bede79c4e929b8caf8a31bac4f3/

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perishopening in a new tab system.

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