Abstract

We study the computational complexity of languages which have interactive proofs of logarithmic knowledge complexity. We show that all such languages can be recognized in ${\cal BPP}^{\cal NP}$. Prior to this work, for languages with greater-than-zero knowledge complexity only trivial computational complexity bounds were known. In the course of our proof, we relate statistical knowledge complexity to perfect knowledge complexity; specifically, we show that, for the honest verifier, these hierarchies coincide up to a logarithmic additive term.

MSC codes

  1. 68Q15

Keywords

  1. zero knowledge
  2. interactive proofs
  3. knowledge complexity
  4. randomness
  5. complexity classes
  6. cryptography.

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 1116 - 1141
ISSN (online): 1095-7111

History

Published online: 28 July 2006

MSC codes

  1. 68Q15

Keywords

  1. zero knowledge
  2. interactive proofs
  3. knowledge complexity
  4. randomness
  5. complexity classes
  6. cryptography.

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