A new family of pseudorandom generators based on the decisional Diffie-Hellman assumption is presented. The new construction is a modified and generalized version of the Dual Elliptic Curve generator proposed by Barker and Kelsey. Although the original Dual Elliptic Curve generator is shown to be insecure, the modified version is provably secure and very efficient in comparison with other pseudorandom generators based on discrete log assumptions. Our generator can be based on any group of prime order provided an additional requirement is met (i.e., there exists an efficiently computable function that in some sense ranks the elements of the group).