Efficient CM-constructions of elliptic curves over finite fields


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)
DOI: 10.1090/S0025-5718-07-01980-1


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@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} }