Parametrizations for Families of ECM-Friendly Curves
نویسندگان
چکیده
We provide a new family of elliptic curves that results in a one to two percent performance improvement of the elliptic curve integer factorization method. The speedup is confirmed by extensive tests for factors ranging from 15 to 63 bits.
منابع مشابه
Finding Suitable Curves for the Elliptic Curve Method of Factorization
Using the parametrizations of Kubert, we show how to produce in nite families of elliptic curves which have prescribed nontrivial torsion over Q and rank at least one. These curves can be used to speed up the ECM factorization algorithm of Lenstra. We also brie y discuss curves with complex multiplication in this context.
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