Theory of Cryptography pp 1-22
Overcoming Weak Expectations
- Cite this paper as:
- Dodis Y., Yu Y. (2013) Overcoming Weak Expectations. In: Sahai A. (eds) Theory of Cryptography. Lecture Notes in Computer Science, vol 7785. Springer, Berlin, Heidelberg
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.
Unable to display preview. Download preview PDF.