Abstract

This paper investigates the possibility of disposing of interaction between prover and verifier in a zero-knowledge proof if they share beforehand a short random string.
Without any assumption, it is proven that noninteractive zero-knowledge proofs exist for some number-theoretic languages for which no efficient algorithm is known.
If deciding quadratic residuosity (modulo composite integers whose factorization is not known) is computationally hard, it is shown that the NP-complete language of satisfiability also possesses noninteractive zero-knowledge proofs.

MSC codes

  1. 68Q15
  2. 94A60

Keywords

  1. interactive proofs
  2. randomization
  3. zero-knowledge proofs
  4. secure protocols
  5. cryptography
  6. quadratic residuosity

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 1084 - 1118
ISSN (online): 1095-7111

History

Submitted: 4 September 1990
Accepted: 15 February 1991
Published online: 13 July 2006

MSC codes

  1. 68Q15
  2. 94A60

Keywords

  1. interactive proofs
  2. randomization
  3. zero-knowledge proofs
  4. secure protocols
  5. cryptography
  6. quadratic residuosity

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