A Youtube channel about breaking down complex math systems and how they apply to everyday life has done a nice piece on how Elliptic Curve Cryptography works, and how the NSA subverted the algorithm.
Professor Edward Frenkel discusses the mathematics behind elliptic curves and the nature of what makes it a secure encryption technique.
It is important to note that while this piece puts emphasis on email, using DUAL_EC_DBRG for your number generator can break any cryptosystem that relies on it. This is why it is very significant that it has now come to light that American security company RSA Security accepted a $10,000,000 contract with the NSA to make DUAL_EC_DBRG their default random number generator.
So, bearing the huge scope of this scandal in mind, enjoy this video. It gives a nice visual look of how the DUAL_EC_DBRG works and why it is a problem.
View the video here:
And the follow-up video here has some additional information about the scandal: