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.
Keywords
- Elliptic Curve
- Discrete Logarithm
- Seed Length
- Discrete Logarithm Problem
- Quadratic Residue
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Farashahi, R.R., Schoenmakers, B., Sidorenko, A. (2007). Efficient Pseudorandom Generators Based on the DDH Assumption. In: Okamoto, T., Wang, X. (eds) Public Key Cryptography – PKC 2007. PKC 2007. Lecture Notes in Computer Science, vol 4450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71677-8_28
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