On Remarks of Lifting Problems for Elliptic Curves
نویسندگان
چکیده
The Elliptic Curve Discrete Logarithm Problem(ECDLP) is known to be an exponential time problem except the cases of smooth curves, supersingular curves and anomalous curves. Recently, several new methods to solve ECDLP on a prime eld were proposed. All of them try to solve ECDLP on a prime eld by lifting a given elliptic curve to low rank elliptic curves de ned over the rationals. In this extended abstract, we generalize these methods to the cases of elliptic curves over Fpn (possibly, p = 2), where we consider liftings to elliptic curves over function elds. Also we show that liftings to the rationals can be used to factorize a composite number.
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