How to prove all NP-statements in zero-knowledge, and a methodology of cryptographic protocol design

  • Authors:
  • Oded Goldreich;Silvio Micali;Avi Wigderson

  • Affiliations:
  • Technion, Haifa, Israel;Massachusetts Institute of Technology, Cambridge;Hebrew Univ., Jerusalem, Israel

  • Venue:
  • Proceedings on Advances in cryptology---CRYPTO '86
  • Year:
  • 1987

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Abstract

Under the assumption that encryption functions exist, we show that all languages in NP possess zero-knowledge proofs.That is, it is possible to demonstrate that a CNF formula is satisfiable without revealing any other property of the formula. In particular, without yielding neither a satisfying assignment nor weaker properties such as whether there is a satisfying assignment in which x1=TRUE, or whether there is a satisfying assignment in which x1=x3 etc.The above result allows us to prove two fundamental theorems in the field of (two-party and multi-party) cryptographic protocols. These theorems yield automatic and efficient transformations that, given a protocol that is correct with respect to an extremely weak adversary, output a protocol correct in the most adversarial scenario. Thus, these theorems imply powerful methodologies for developing two-party and multiparty cryptographic protocols.