2006 | OriginalPaper | Buchkapitel
On the Relation Between the Ideal Cipher and the Random Oracle Models
verfasst von : Yevgeniy Dodis, Prashant Puniya
Erschienen in: Theory of Cryptography
Verlag: Springer Berlin Heidelberg
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The Random Oracle Model and the Ideal Cipher Model are two of the most popular idealized models in cryptography. It is a fundamentally important practical and theoretical problem to compare the relative strengths of these models and to see how they relate to each other. Recently, Coron et al. [8] proved that one can securely instantiate a random oracle in the ideal cipher model. In this paper, we investigate if it is possible to instantiate an ideal block cipher in the random oracle model, which is a considerably more challenging question. We conjecture that the
Luby-Rackoff construction
[19] with a sufficient number of rounds should suffice to show this implication. This does not follow from the famous Luby-Rackoff result [19] showing that 4 rounds are enough to turn a pseudorandom function into a pseudorandom permutation, since the results of the intermediate rounds are known to everybody. As a partial step toward resolving this conjecture, we show that random oracles imply ideal ciphers in the
honest-but-curious model
, where all the participants are assumed to follow the protocol, but keep all their intermediate results. Namely, we show that the
Luby-Rackoff construction
with a superlogarithmic number of rounds can be used to instantiate the ideal block cipher in any honest-but-curious cryptosystem, and result in a similar honest-but-curious cryptosystem in the random oracle model. We also show that securely instantiating the ideal cipher using the Luby Rackoff construction with upto a logarithmic number of rounds is equivalent in the honest-but-curious and malicious models.