TY - GEN

T1 - Overcoming weak expectations

AU - Dodis, Yevgeniy

AU - Yu, Yu

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - 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, seed-dependent condensers and improved entropy loss for the leftover hash lemma.

AB - 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, seed-dependent condensers and improved entropy loss for the leftover hash lemma.

UR - http://www.scopus.com/inward/record.url?scp=84873136980&partnerID=8YFLogxK

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U2 - 10.1109/ITW.2012.6404636

DO - 10.1109/ITW.2012.6404636

M3 - Conference contribution

AN - SCOPUS:84873136980

SN - 9781467302234

T3 - 2012 IEEE Information Theory Workshop, ITW 2012

SP - 109

EP - 113

BT - 2012 IEEE Information Theory Workshop, ITW 2012

T2 - 2012 IEEE Information Theory Workshop, ITW 2012

Y2 - 3 September 2012 through 7 September 2012

ER -