I've wondered about this, but I don't trust myself to figure out the answer. Even though I have a background in math and I've done some cryptography related work, I know enough about the crypto space to know that I don't know enough to make my own decisions. The featured article by Filippo Valsorda makes a lot of sense.

On the other hand, if the NSA really could find backdoors into elliptic curves (perhaps with a great deal of work) they would be motivated to gaslight the rest of us about elliptic curves by creating article like TFA.