Cryptographically Strong Elliptic Curves of Prime Order
IJET International Journal of Electronics and Telecommunications,
(A periodical of Electronics and Telecommunications Committee of Polish Academy of Sciences)
Abstract: 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.
Keywords: Mersenne primes, elliptic curves, security requirements, search algorithm, Magma.