On relationships between statistical zero-knowledge proofs

This paper solves several fundamental open problems about statistical zero-knowledge interactive proofs (SZKIPS). Roughly speaking, this paper proves:

[1]  Ivan Damgård,et al.  Honest Verifier vs Dishonest Verifier in Public Coin Zero-Knowledge Proofs , 1995, CRYPTO.

[2]  Rafail Ostrovsky,et al.  One-way functions are essential for non-trivial zero-knowledge , 1993, [1993] The 2nd Israel Symposium on Theory and Computing Systems.

[3]  Rafail Ostrovsky,et al.  Computational Complexity and Knowledge Complexity , 1994, Electron. Colloquium Comput. Complex..

[4]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[5]  Oded Goldreich,et al.  Interactive proof systems: Provers that never fail and random selection , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[6]  Shafi Goldwasser,et al.  Private coins versus public coins in interactive proof systems , 1986, STOC '86.

[7]  Moti Yung,et al.  Direct Minimum-Knowledge Computations , 1987, CRYPTO.

[8]  Silvio Micali,et al.  Proofs that yield nothing but their validity and a methodology of cryptographic protocol design , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[9]  László Babai,et al.  Trading group theory for randomness , 1985, STOC '85.

[10]  Moni Naor,et al.  Bit Commitment Using Pseudo-Randomness , 1989, CRYPTO.

[11]  Rafail Ostrovsky,et al.  Computational complexity and knowledge complexity (extended abstract) , 1994, STOC '94.

[12]  Johan Håstad,et al.  Perfect zero-knowledge languages can be recognized in two rounds , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[13]  Yair Oren,et al.  On the cunning power of cheating verifiers: Some observations about zero knowledge proofs , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[14]  David Chaum,et al.  Minimum Disclosure Proofs of Knowledge , 1988, J. Comput. Syst. Sci..

[15]  Johan Håstad,et al.  Pseudo-random generators under uniform assumptions , 1990, STOC '90.

[16]  Leonid A. Levin,et al.  Pseudo-random generation from one-way functions , 1989, STOC '89.

[17]  Lance Fortnow,et al.  The Complexity of Perfect Zero-Knowledge , 1987, Proceeding Structure in Complexity Theory.

[18]  Moni Naor,et al.  Bit commitment using pseudo-randomness (extended abstract) , 1989, CRYPTO 1989.

[19]  Michael Sipser,et al.  A complexity theoretic approach to randomness , 1983, STOC.

[20]  Ivan Damgård,et al.  Interactive Hashing can Simplify Zero-Knowledge Protocol Design Without Computational Assumptions (Extended Abstract) , 1993, CRYPTO.

[21]  Rafail Ostrovsky,et al.  The (true) complexity of statistical zero knowledge , 1990, STOC '90.

[22]  Leonid A. Levin,et al.  A hard-core predicate for all one-way functions , 1989, STOC '89.

[23]  Rafail Ostrovsky,et al.  Interactive Hashing Simplifies Zero-Knowledge Protocol Design , 1994, EUROCRYPT.

[24]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[25]  Silvio Micali,et al.  Everything Provable is Provable in Zero-Knowledge , 1990, CRYPTO.