Abstract
We consider the function ensembles emerging from the construction of Goldreich, Goldwasser and Micali (GGM), when applied to an arbitrary pseudoramdon generator. We show that, in general, such functions fail to yield correlation intractable ensembles. Specifically, it may happen that, given a description of such a function, one can easily find an input that is mapped to zero under this function.
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References
Canetti, R., Goldreich, O., Halevi, S.: The Random Oracle Methodology. In: 30th STOC, pp. 209–218 (1998) (revisited)
Goldreich, O., Goldwasser, S., Micali, S.: How to Construct Random Functions. JACM 33(4), 792–807 (1986)
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Goldreich, O. (2011). The GGM Construction Does NOT Yield Correlation Intractable Function Ensembles. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_12
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DOI: https://doi.org/10.1007/978-3-642-22670-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22669-4
Online ISBN: 978-3-642-22670-0
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