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Efficient Pseudorandom Generators Based on the DDH Assumption
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Efficient Pseudorandom Generators Based on the DDH Assumption
Reza Rezaeian Farashahi1, 2, Berry Schoenmakers1 and Andrey Sidorenko1
| (1) |
Dept. of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
| (2) |
Dept. of Mathematical Sciences, Isfahan University of Technology, P.O. Box 85145 Isfahan, Iran |
Abstract
A family of pseudorandom generators based on the decisional Diffie-Hellman 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 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 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.
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