The discrete logarithm problem for elliptic curves

Given points $P$ and $Q$ on an elliptic curve, find $k$ such that: $Q = kP$

This is a hard problem if the order of $P$ (number of times we have to add P to itself until reaching the point at infinity) is large and has large factors.

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Given points $P$ and $Q$ on an elliptic curve, find $k$ such that: $Q = kP$

This is a hard problem if the order of $P$ (number of times we have to add P to itself until reaching the point at infinity) is large and has large factors.