Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

This paper discusses a cryptographic protocol to evaluate an and-gate such that a party can keep his or her input bit secret from the other party. Such a protocol is of interest, because it can be generalized to any logical circuit for any number of participants. A formal statement of this generalization reads as follows: n participants want to compute together a function f(x1; x2; :::; xn) with xi being their inputs; nobody wants to reveal information about his or her input except what can be logically be deduced from one's input and the output. The paper contains no new results but provides an illustration of a sub-eld of cryptography, and describes several interesting protocols and protocol design techniques.

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