That first sentence is not a good way to sum up what happened. Dual EC isn't "weak"; it's pretty plainly a backdoor.
(I'm among an elite cadre† of cryptography-adjacents who felt it probably wasn't, but only because I thought it was too stupid to actually be used anywhere --- as soon as it was disclosed that (a) it was a default-yes algorithm in BSAFE and (b) big companies actually used BSAFE in important products, it was immediately clear what was going on).
The idea of Dual EC is essentially that your output is internal RNG state encrypted with a public key, leaving open the obvious question of "who has the private key?". I think we all know the answer to that now.
(I'm among an elite cadre† of cryptography-adjacents who felt it probably wasn't, but only because I thought it was too stupid to actually be used anywhere --- as soon as it was disclosed that (a) it was a default-yes algorithm in BSAFE and (b) big companies actually used BSAFE in important products, it was immediately clear what was going on).
The idea of Dual EC is essentially that your output is internal RNG state encrypted with a public key, leaving open the obvious question of "who has the private key?". I think we all know the answer to that now.
† i am being ironic