Efficient pseudorandom generators based on the DDH assumption

A family of pseudorandom generators based on the decisional Di±e- Hellman assumption is proposed. The new construction is a modi¯ed 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 modi¯ed ver- sion is provably secure and very e±cient in comparison with the other pseudorandom generators based on discrete log assumptions. Our generator can be based on any group of prime order provided that an additional requirement is met (i.e., there exists an e±ciently computable function that in some sense enumerates the elements of the group). Two speci¯c instances are presented. The techniques used to design the instances, for example, the new probabilistic randomness extractor are of independent interest for other applications