I would expect a complicated answer for what seems like a simple question about Elliptic curve cryptography. I've read several entries here such as "Elliptic curve cryptography related key attacks" and afterwards I am still left wondering what the primary attack vector would be and also what can be done by an implementer to shore-up a weakness.
Is hashing of keys the main weakness or is it in the PRNG? At the end of the day I want to do what I can to prevent "anyone" from reading what Alice or Bob have communicated.
To summarize, what is the weak point in the algorithm and what can be done to minimize the effectiveness of an attack?