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 -