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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Overcoming Weak Expectations
verfasst von : Yevgeniy Dodis, Yu Yu
Erschienen in: Theory of Cryptography
Verlag: Springer Berlin Heidelberg
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Recently, there has been renewed interest in basing cryptographic primitives on weak secrets, where the only information about the secret is some non-trivial amount of (min-) entropy. From a formal point of view, such results require to upper bound the expectation of some function
f
(
X
), where
X
is a weak source in question. We show an elementary inequality which essentially upper bounds such ‘weak expectation’ by two terms, the first of which is independent of
f
, while the second only depends on the ‘variance’ of
f
under uniform distribution. Quite remarkably, as relatively simple corollaries of this elementary inequality, we obtain some ‘unexpected’ results, in several cases noticeably simplifying/improving prior techniques for the same problem.
Examples include non-malleable extractors, leakage-resilient symmetric encryption, alternative to the dense model theorem, seed-dependent condensers and improved entropy loss for the leftover hash lemma.