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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Shrinking the Keys of Discrete-Log-Type Lossy Trapdoor Functions
verfasst von : Xavier Boyen, Brent Waters
Erschienen in: Applied Cryptography and Network Security
Verlag: Springer Berlin Heidelberg
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To this day, realizations in the standard-model of (lossy) trapdoor functions from discrete-log-type assumptions require large public key sizes, e.g., about Θ(
λ
2
) group elements for a reduction from the decisional Diffie-Hellman assumption (where
λ
is a security parameter). We propose two realizations of lossy trapdoor functions that achieve public key size of only Θ(
λ
) group elements in bilinear groups, with a reduction from the decisional Bilinear Diffie-Hellman assumption.
Our first construction achieves this result at the expense of a long common reference string of Θ(
λ
2
) elements, albeit reusable in multiple LTDF instantiations. Our second scheme also achieves public keys of size Θ(
λ
), entirely in the standard model and in particular without any reference string, at the cost of a slightly more involved construction.
The main technical novelty, developed for the second scheme, is a compact encoding technique for generating compressed representations of certain sequences of group elements for the public parameters.