Near-optimal extractors against quantum storage

  • Authors:

  • Anindya De;Thomas Vidick

  • Affiliations:

  • UC Berkeley, Berkeley, CA, USA;UC Berkeley, Berkeley, CA, USA

  • Venue:
  • Proceedings of the forty-second ACM symposium on Theory of computing
  • Year:
  • 2010

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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)/Kγ) for any γ0. 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.