Andrey Sidorenko (Eindhoven): Efficient pseudorandom generators based on the DDH assumption
A family of pseudorandom generators based on the decisional
Diffie-Hellman (DDH) assumption is proposed. 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 compared to many 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 efficiently
computable function that in some sense enumerates the elements of the
group). Two specific instances are presented. The techniques used to
design the instances, for example, the new probabilistic randomness
extractor are of independent interest for other applications.