A Quantum Goldreich-Levin Theorem with Cryptographic Applications

  • Authors:
  • Mark Adcock;Richard Cleve

  • Affiliations:
  • -;-

  • Venue:
  • STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
  • Year:
  • 2002

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Abstract

We investigate the Goldreich-Levin Theorem in the context of quantum information. This result is a reduction from the problem of inverting a one-way function to the problem of predicting a particular bit associated with that function. We show that the quantum version of the reduction is quantitatively more efficient than the known classical version. If the one-way function acts on n-bit strings then the overhead in the reduction is by a factor of O(n/驴2) in the classical case but only by a factor of O(1/驴) in the quantum case, where 1/2 + 驴 is the probability of predicting the hard-predicate. We also show that, using the Goldreich-Levin Theorem, a quantum bit (or qubit) commitment scheme that is perfectly binding and computationally concealing can be obtained from any quantum one-way permutation.