Geodesic
Method for constructing elliptic curves using complex multiplication and its optimizations
Prikladnaâ diskretnaâ matematika, no. 3 (2011), pp. 17-54

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Elliptic curves over finite fields with predefined conditions on the order are practically constructed using the theory of complex multiplication. A stage with the longest calculations in this method reconstructs some polynomial with integer coefficients. We prove some theoretical results and give a detailed account of the method itself and show how one can use a divisor of the mentioned polynomial with coefficients in an extension of the rational number field.
Keywords: elliptic curves, finite fields, simultaneous approximations.
Mots-clés : complex multiplication 
@article{PDM_2011_3_a2,
     author = {E. A. Grechnikov},
     title = {Method for constructing elliptic curves using complex multiplication and its optimizations},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {17--54},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_3_a2/}
}
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E. A. Grechnikov. Method for constructing elliptic curves using complex multiplication and its optimizations. Prikladnaâ diskretnaâ matematika, no. 3 (2011), pp. 17-54. http://geodesic.mathdoc.fr/item/PDM_2011_3_a2/