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.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Adleman, L., and M. Huang, “Recognizing Primes in Random Polynomial Time,” Proceedings of the 19th STOC, 1987, pp. 462–469.
Babai, L., “Trading Group Theory for Randomness,” Proceedings of the 17th STOC, 1985, pp. 421–429.
Barrington, D., “Bounded Width Polynomial Size Branching Programs Recognize Exactly Those Languages in NC 1,” Proceedings of the 18th STOC, 1986, pp. 1–5.
Babai, L. and S. Moran, “Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes,” manuscript.
Blum, M., “Coin Flipping by Telephone,” IEEE COMPCON, 1982, pp. 133–137.
Boppana, R., J. Håstad, and S. Zachos, “Does co-NP Have Short Interactive Proofs?”, Information Processing Letters, 1987, pp. 127–132.
Brassard, G., personal communication, Augest 1988.
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.
Feldman, P., “The Optimum Prover Lives in PSPACE,” manuscript.
Fortnow, L., “The Complexity of Perfect Zero-Knowledge,” Proceedings of the 19th STOC, 1987, pp. 204–209.
Goldreich, O., “Randomness, Interactive Proofs and Zero-Knowledge (a survey),” Technion Technical Report, 1987.
Goldwasser, S., and J. Kilian, “Almost All Primes Can Be Quickly Certified,” Proceedings of the 18th STOC, 1986, pp. 316–329.
Goldwasser., S., and S. Micali, “Probabilistic Encryption,” Journal of Computer and System Sciences, Vol. 28, No. 2, 1984, pp. 270–299.
Goldwasser, S., S. Micali, and C. Rackoff, “Knowledge Complexity of Interactive Proofs,” Proceedings of the 17th STOC, 1985, pp. 291–305
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.
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.
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.
Goldwasser, S., and M. Sipser, “Arthur Merlin Games versus Interactive Proof Systems,” Proceedings of the 18th STOC, 1986, pp. 59–68.
Impagliazzo, R., personal communications, 1987.
Impagliazzo, R., and M. Yung, “Direct Minimum-Knowledge Computations,” Proceedings of Crypto-87, pp. 40–51.
Kilian, J., “Founding Cryptography on Oblivious Transfer,” Proceedings of the 20th STOC, 1988, pp. 20–31.
Kilian, J., “Primality Testing and the Cryptographic Complexity of Noisy Communications Channels,” MIT Ph.D. Thesis (in preparation), 1988.
Levin, L., “One-way Functions and Pseudorandom Generators,” Proceedings of the 17th STOC, 1985, pp. 363–368.
Micali, S., C. Rackoff and R. Sloan, “The Notion of Security for Probabilistic Cryptosystems,” SIAM Journal of Computing, 17(2):412–426, April 1988.
Oren, Y., “On the Cunning Power of Cheating Verifiers: Some Observations about Zero Knowledge Proofs,” Proceedings of the 28th FOCS, 1987, pp. 462–471.
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.
Yao, A.C., “Theory and Applications of Trapdoor Functions,” Proceedings of the 23rd FOCS, 1982, pp. 80–91.
Yung, M., personal communication, Augest 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ben-Or, M. et al. (1990). Everything Provable is Provable in Zero-Knowledge. In: Goldwasser, S. (eds) Advances in Cryptology — CRYPTO’ 88. CRYPTO 1988. Lecture Notes in Computer Science, vol 403. Springer, New York, NY. https://doi.org/10.1007/0-387-34799-2_4
Download citation
DOI: https://doi.org/10.1007/0-387-34799-2_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97196-4
Online ISBN: 978-0-387-34799-8
eBook Packages: Springer Book Archive