Exponential separation for one-way quantum communication complexity, with applications to cryptography

Dmitry Gavinsky, Julia Kempe, Iordanis Kerenidis, Ran Raz, Ronald De Wolf

Research output: Contribution to journalArticlepeer-review


We give an exponential separation between one-way quantum and classical communication protocols for a partial Boolean function (a variant of the Boolean hidden matching problem of Bar-Yossef et al.). Previously, such an exponential separation was known only for a relational problem. The communication problem corresponds to a strong extractor that fails against a small amount of quantum information about its random source. Our proof uses the Fourier coefficients inequality of Kahn, Kalai, and Linial. We also give a number of applications of this separation. In particular, we show that there are privacy amplification schemes that are secure against classical adversaries but not against quantum adversaries; and we give the first example of a key-expansion scheme in the model of bounded-storage cryptography that is secure against classical memory-bounded adversaries but not against quantum ones.

Original languageEnglish (US)
Pages (from-to)1695-1708
Number of pages14
JournalSIAM Journal on Computing
Issue number5
StatePublished - 2008


  • Bounded-storage model
  • Communication complexity
  • Exponential separation
  • Extractor
  • Hidden matching problem
  • One-way communication
  • Quantum communication
  • Quantum cryptography
  • Streaming model

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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