Elliptic curves play an important r\^ole in many areas of modern
cryptology such as integer factorization and primality proving.
Moreover, they can be used in cryptosystems based on discrete
logarithms for building one-way permutations. For the latter
purpose, it is required to have cyclic elliptic curves over finite
fields. The aim of this note
is to explain how to construct such curves over a
finite field of large prime cardinality, using the ECPP primality
proving test of Atkin and Morain.