The Dual_EC exploit was possible not because the NSA were cleverer than everyone else but because they wrote the standard and chose the parameters. The paramete

The Dual_EC exploit was possible not because the NSA were cleverer than everyone else but because they wrote the standard and chose the parameters. The parameters involved two points, P and Q, on an elliptic curve group with rank 1 and prime order. Because of these properties there must be some number e such that P = Q^e (written P = e * Q in the common elliptic curve group notation) but it is hard to find e from only P and Q (this is the discrete log problem for this EC group and it, or its close relative the Diffie–Hellman, problem being hard is a common foundation for security in cryptography.) However if you are choosing the parameters, you can just choose Q and e and compute P = Q^e yourself.