# Everything Provable is Provable in Zero-Knowledge

Conference paper

First Online:

- 72 Citations
- 2 Mentions
- 2k Downloads

## Abstract

Assuming the existence of a secure probabilistic encryption scheme, we show that every language that admits an interactive proof admits a (computational) zero-knowledge interactive proof. This result extends the result of Goldreich, Micali and Wigderson, that, under the same assumption, all of *NP* admits zero-knowledge interactive proofs. Assuming envelopes for bit commitment, we show tht every language that admits an interactive proof admits a perfect zero-knowledge interactive proof.

## Keywords

Proof System Oblivious Transfer Common Input Interactive Proof Public History
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Download
to read the full conference paper text

## References

- [AH]Adleman, L., and M. Huang, “Recognizing Primes in Random Polynomial Time,”
*Proceedings of the 19th STOC*, 1987, pp. 462–469.Google Scholar - [Babtano]Babai, L., “Trading Group Theory for Randomness,”
*Proceedings of the 17th STOC*, 1985, pp. 421–429.Google Scholar - [Bartano]Barrington, D., “Bounded Width Polynomial Size Branching Programs Recognize Exactly Those Languages in
*NC*^{1},”*Proceedings of the 18th STOC*, 1986, pp. 1–5.Google Scholar - [BaM]Babai, L. and S. Moran, “Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes,” manuscript.Google Scholar
- [Bl]Blum, M., “Coin Flipping by Telephone,”
*IEEE COMPCON*, 1982, pp. 133–137.Google Scholar - [BHZ]Boppana, R., J. Håstad, and S. Zachos, “Does co-NP Have Short Interactive Proofs?”, Information Processing Letters, 1987, pp. 127–132.MathSciNetCrossRefGoogle Scholar
- [Br]Brassard, G.,
*personal communication*, Augest 1988.Google Scholar - [CDG]Chaum, D., I. Damgård, and J. van de Graaf, “Multiparty Computations Ensuring Privacy of Each Party’s Input and Correctness of the Result,” Proceedings of Crypto-87, pp. 87–119.Google Scholar
- [Fe]Feldman, P., “The Optimum Prover Lives in
*PSPACE*,” manuscript.Google Scholar - [Fo]Fortnow, L., “The Complexity of Perfect Zero-Knowledge,”
*Proceedings of the 19th STOC*, 1987, pp. 204–209.Google Scholar - [G]Goldreich, O., “Randomness, Interactive Proofs and Zero-Knowledge (a survey),” Technion Technical Report, 1987.Google Scholar
- [GK]Goldwasser, S., and J. Kilian, “Almost All Primes Can Be Quickly Certified,”
*Proceedings of the 18th STOC*, 1986, pp. 316–329.Google Scholar - [GM]Goldwasser., S., and S. Micali, “Probabilistic Encryption,”
*Journal of Computer and System Sciences*, Vol. 28, No. 2, 1984, pp. 270–299.MathSciNetCrossRefGoogle Scholar - [GMR]Goldwasser, S., S. Micali, and C. Rackoff, “Knowledge Complexity of Interactive Proofs,”
*Proceedings of the 17th STOC*, 1985, pp. 291–305Google Scholar - [GMS]Goldreich, M., Y. Mansour, and M. Sipser, “Interactive Proof Systems: Provers that Never Fail and Random Selection,”
*Proceedings of the 28th FOCS*, 1987, pp. 449–461.Google Scholar - [GMW1]Goldreich, O., S. Micali, and A. Wigderson, “Proofs that Yield Nothing but their Validity and a Methodology of Cryptographic Protocol Design,”
*Proceedings of the 27th FOCS*, 1986, pp. 174–187.Google Scholar - [GMW2]Goldreich, O., S. Micali, and A. Wigderson, “How to Play Any Mental Game, or, A Completeness Theorem for Protocols with Honest Majority,”
*Proceedings of the 19th STOC*, 1987, pp. 218–229.Google Scholar - [GS]Goldwasser, S., and M. Sipser, “Arthur Merlin Games versus Interactive Proof Systems,”
*Proceedings of the 18th STOC*, 1986, pp. 59–68.Google Scholar - [I]Impagliazzo, R.,
*personal communications*, 1987.Google Scholar - [IY]Impagliazzo, R., and M. Yung, “Direct Minimum-Knowledge Computations,” Proceedings of Crypto-87, pp. 40–51.Google Scholar
- [K1]Kilian, J., “Founding Cryptography on Oblivious Transfer,”
*Proceedings of the 20th STOC*, 1988, pp. 20–31.Google Scholar - [K2]Kilian, J., “Primality Testing and the Cryptographic Complexity of Noisy Communications Channels,” MIT Ph.D. Thesis (in preparation), 1988.Google Scholar
- [L]Levin, L., “One-way Functions and Pseudorandom Generators,”
*Proceedings of the 17th STOC*, 1985, pp. 363–368.Google Scholar - [MRS]Micali, S., C. Rackoff and R. Sloan, “The Notion of Security for Probabilistic Cryptosystems,”
*SIAM Journal of Computing*, 17(2):412–426, April 1988.MathSciNetCrossRefGoogle Scholar - [O]Oren, Y., “On the Cunning Power of Cheating Verifiers: Some Observations about Zero Knowledge Proofs,”
*Proceedings of the 28th FOCS*, 1987, pp. 462–471.Google Scholar - [TW]Tompa, M., and H. Woll, “Random Self-Reducibility and Zero Knowledge Interactive Proofs of Possession of Information,”
*Proceedings of the 28th FOCS*, 1987, pp. 472–482.Google Scholar - [Ya]Yao, A.C., “Theory and Applications of Trapdoor Functions,”
*Proceedings of the 23rd FOCS*, 1982, pp. 80–91.Google Scholar - [Yu]Yung, M.,
*personal communication*, Augest 1988.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1990