We present an algorithm that, on input of an integer N ≥ 1 together with its prime factorization, constructs a finite field F and an elliptic curve E over F for which E(F) has order N . Although it is unproved that this can be done for all N , a heuristic analysis shows that the algorithm has an expected run time that is polynomial in 2ω(N) logN , where ω(N… (More)

@article{Brker2007EfficientCO,
title={Efficient CM-constructions of elliptic curves over finite fields},
author={Reinier Br{\"o}ker and Peter Stevenhagen},
journal={Math. Comput.},
year={2007},
volume={76},
pages={2161-2179}
}