Cryptographically Strong Elliptic Curves of Prime Order

The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields Fp, where p is a Mersenne prime, one of the special primes or a random prime. We search for elliptic curves which orders are also prime numbers. The cryptographically strong elliptic curves are those...

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Bibliographic Details
Published in:	International Journal of Electronics and Telecommunications Vol. 67; no. 2; pp. 207 - 212
Main Authors:	Barański, Marcin, Gliwa, Rafał, Szmidt, Janusz
Format:	Journal Article
Language:	English
Published:	Warsaw Polish Academy of Sciences 01-01-2021
Subjects:	Algorithms Cryptography Curves elliptic curves Magma mersenne primes Prime numbers search algorithm security requirements
Online Access:	Get full text
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Summary:	The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields Fp, where p is a Mersenne prime, one of the special primes or a random prime. We search for elliptic curves which orders are also prime numbers. The cryptographically strong elliptic curves are those for which the discrete logarithm problem is computationally hard. The required mathematical conditions are formulated in terms of parameters characterizing the elliptic curves.We present an algorithm to generate such curves. Examples of elliptic curves of prime order are generated with Magma.
ISSN:	2081-8491 2300-1933
DOI:	10.24425/ijet.2021.135966