To answer that you will have to define "trustworthy". I'm personally leaning toward trusting the curves proposed by Dan Bernstein [1], since he clearly explains

To answer that you will have to define "trustworthy". I'm personally leaning toward trusting the curves proposed by Dan Bernstein [1], since he clearly explains the reasons for choosing the specific parameters and they're demonstrably valid. [1]: http://cr.yp.to/ecdh.html http://cr.yp.to/ecdh.html