### 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) |
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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 |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems

### Cite this

*2012 IEEE Information Theory Workshop, ITW 2012*(pp. 109-113). [6404636] https://doi.org/10.1109/ITW.2012.6404636

**Overcoming weak expectations.** / Dodis, Yevgeniy; Yu, Yu.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2012 IEEE Information Theory Workshop, ITW 2012.*, 6404636, pp. 109-113, 2012 IEEE Information Theory Workshop, ITW 2012, Lausanne, Switzerland, 9/3/12. https://doi.org/10.1109/ITW.2012.6404636

}

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

SN - 9781467302234

SP - 109

EP - 113

BT - 2012 IEEE Information Theory Workshop, ITW 2012

ER -