### Abstract

We introduce strong blenders. A strong blender BLE(· ·) uses weak sources X, Y to produce BLE(X, Y) that is statistically random even if one is given Y. Strong blenders generalize strong extractors [15] and extractors from two weak random sources [25, 6]. We show that non-constructive strong blenders can extract all the randomness from X, as long as Y has logarithmic min-entropy. We also give explicit strong blenders which work provided the sum of the min-entropies of X and Y is at least their block length. Finally, we show that strong blenders have applications to cryptographic systems for parties that have independent weak sources of randomness. In particular, we extend the results of Maurer and Wolf [12] and show that parties that are not able to sample even a single truly random bit can still perform privacy amplification over an adversarially controlled channel.

Original language | English (US) |
---|---|

Pages (from-to) | 252-263 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2764 |

State | Published - 2003 |

### Fingerprint

### ASJC Scopus subject areas

- Biochemistry, Genetics and Molecular Biology(all)
- Computer Science(all)
- Theoretical Computer Science

### Cite this

**On extracting private randomness over a public channel.** / Dodis, Yevgeniy; Oliveira, Roberto.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 2764, pp. 252-263.

}

TY - JOUR

T1 - On extracting private randomness over a public channel

AU - Dodis, Yevgeniy

AU - Oliveira, Roberto

PY - 2003

Y1 - 2003

N2 - We introduce strong blenders. A strong blender BLE(· ·) uses weak sources X, Y to produce BLE(X, Y) that is statistically random even if one is given Y. Strong blenders generalize strong extractors [15] and extractors from two weak random sources [25, 6]. We show that non-constructive strong blenders can extract all the randomness from X, as long as Y has logarithmic min-entropy. We also give explicit strong blenders which work provided the sum of the min-entropies of X and Y is at least their block length. Finally, we show that strong blenders have applications to cryptographic systems for parties that have independent weak sources of randomness. In particular, we extend the results of Maurer and Wolf [12] and show that parties that are not able to sample even a single truly random bit can still perform privacy amplification over an adversarially controlled channel.

AB - We introduce strong blenders. A strong blender BLE(· ·) uses weak sources X, Y to produce BLE(X, Y) that is statistically random even if one is given Y. Strong blenders generalize strong extractors [15] and extractors from two weak random sources [25, 6]. We show that non-constructive strong blenders can extract all the randomness from X, as long as Y has logarithmic min-entropy. We also give explicit strong blenders which work provided the sum of the min-entropies of X and Y is at least their block length. Finally, we show that strong blenders have applications to cryptographic systems for parties that have independent weak sources of randomness. In particular, we extend the results of Maurer and Wolf [12] and show that parties that are not able to sample even a single truly random bit can still perform privacy amplification over an adversarially controlled channel.

UR - http://www.scopus.com/inward/record.url?scp=30744451262&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30744451262&partnerID=8YFLogxK

M3 - Article

VL - 2764

SP - 252

EP - 263

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -