### 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, alternative to the dense model theorem, seed-dependent condensers and improved entropy loss for the leftover hash lemma.

Original language | English (US) |
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Title of host publication | Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings |

Pages | 1-22 |

Number of pages | 22 |

Volume | 7785 LNCS |

DOIs | |

State | Published - 2013 |

Event | 10th Theory of Cryptography Conference, TCC 2013 - Tokyo, Japan Duration: Mar 3 2013 → Mar 6 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7785 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 10th Theory of Cryptography Conference, TCC 2013 |
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Country | Japan |

City | Tokyo |

Period | 3/3/13 → 3/6/13 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings*(Vol. 7785 LNCS, pp. 1-22). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7785 LNCS). https://doi.org/10.1007/978-3-642-36594-2_1

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

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

*Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings.*vol. 7785 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7785 LNCS, pp. 1-22, 10th Theory of Cryptography Conference, TCC 2013, Tokyo, Japan, 3/3/13. https://doi.org/10.1007/978-3-642-36594-2_1

}

TY - GEN

T1 - Overcoming weak expectations

AU - Dodis, Yevgeniy

AU - Yu, Yu

PY - 2013

Y1 - 2013

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, alternative to the dense model theorem, 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, alternative to the dense model theorem, seed-dependent condensers and improved entropy loss for the leftover hash lemma.

UR - http://www.scopus.com/inward/record.url?scp=84873970779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873970779&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36594-2_1

DO - 10.1007/978-3-642-36594-2_1

M3 - Conference contribution

AN - SCOPUS:84873970779

SN - 9783642365935

VL - 7785 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 22

BT - Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings

ER -