Abstract
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.
| Original language | English (US) |
|---|---|
| Title of host publication | 2012 IEEE Information Theory Workshop, ITW 2012 |
| Pages | 109-113 |
| Number of pages | 5 |
| DOIs | |
| State | Published - 2012 |
| Event | 2012 IEEE Information Theory Workshop, ITW 2012 - Lausanne, Switzerland Duration: Sep 3 2012 → Sep 7 2012 |
Other
| Other | 2012 IEEE Information Theory Workshop, ITW 2012 |
|---|---|
| Country | Switzerland |
| City | Lausanne |
| Period | 9/3/12 → 9/7/12 |
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ASJC Scopus subject areas
- Information Systems
Cite this
Overcoming weak expectations. / Dodis, Yevgeniy; Yu, Yu.
2012 IEEE Information Theory Workshop, ITW 2012. 2012. p. 109-113 6404636.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Overcoming weak expectations
AU - Dodis, Yevgeniy
AU - Yu, Yu
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
UR - http://www.scopus.com/inward/citedby.url?scp=84873136980&partnerID=8YFLogxK
U2 - 10.1109/ITW.2012.6404636
DO - 10.1109/ITW.2012.6404636
M3 - Conference contribution
AN - SCOPUS:84873136980
SN - 9781467302234
SP - 109
EP - 113
BT - 2012 IEEE Information Theory Workshop, ITW 2012
ER -