### Abstract

We show that Trevisan's extractor and its variants [22,19] are secure against bounded quantum storage adversaries. One instantiation gives the first such extractor to achieve an output length Θ(K-b), where K is the source's entropy and b the adversary's storage, together with a poly-logarithmic seed length. Another instantiation achieves a logarithmic key length, with a slightly smaller output length Θ((K-b)/K^{γ}) for any γ>0. In contrast, the previous best construction [21] could only extract (K/b) ^{1/15} bits. Some of our constructions have the additional advantage that every bit of the output is a function of only a polylogarithmic number of bits from the source, which is crucial for some cryptographic applications. Our argument is based on bounds for a generalization of quantum random access codes, which we call quantum functional access codes. This is crucial as it lets us avoid the local list-decoding algorithm central to the approach in [21], which was the source of the multiplicative overhead.

Original language | English (US) |
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Title of host publication | STOC'10 - Proceedings of the 2010 ACM International Symposium on Theory of Computing |

Pages | 161-170 |

Number of pages | 10 |

DOIs | |

State | Published - 2010 |

Event | 42nd ACM Symposium on Theory of Computing, STOC 2010 - Cambridge, MA, United States Duration: Jun 5 2010 → Jun 8 2010 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Other

Other | 42nd ACM Symposium on Theory of Computing, STOC 2010 |
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Country | United States |

City | Cambridge, MA |

Period | 6/5/10 → 6/8/10 |

### Keywords

- bounded quantum storage
- extractors
- random access codes

### ASJC Scopus subject areas

- Software

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## Cite this

*STOC'10 - Proceedings of the 2010 ACM International Symposium on Theory of Computing*(pp. 161-170). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/1806689.1806713