Abstract
In a companion paper [DeYu] we have developed the tool of non-interactive proof-system we call “Metaproof” (μ-NIZK proof system); this provides a proof of “the existence of a proof to a statement”. Using a reduction of the theorem to a set of claims about encrypted values, enabled us to develop a crucial proof-system property which we called “on-line simulatable NIZK proof-system”. This was used to implement the “Many-Prover Non-Interactive Proof-System” where independent users can send proofs (which was not known in the original system and was open), and a “Self-Referential NIZK proof system” where the random reference string is available to the polynomial-time opponent who chooses the theorem to prove, (this was an intriguing question regarding such systems).
In this abstract we present an introduction to the basic tools and their possible applications. The subject of this paper is a variety of cryptographic applications provided by the new tools. We demonstrate its applicability in enhancing security and properties of a methodology for signature and authentication developed by Bellare and Goldwasser [BeGo] (by using the Metaproof system to solve the open problem of many-prover NIZK system). We also show, among other things, how the tools can be used to provide security mechanisms such as an “Oblivious Warden” which translates non-interactive proofs to random ones independently of the proof itself, and the notion of “Gradual opening of a zero-knowledge computation” which is first demonstrated to be correct using a non-interactive proof, and then is opened gradually and fast (i.e., without further proofs).
Part of this work was done while the author was visiting IBM Research Division, T. J. Watson Research Ctr, Yorktown Heights, NY 10598.
Preliminary Version
Chapter PDF
References
L. Babai and S. Moran, Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes, Journal of Computer and System Sciences, vol. 36, 1988, pp. 254–276.
M. Bellare and S. Goldwasser, New Paradigms for Digital Signatures and Message Authentication based on Non-interactive Zero-knowledge Proofs, Crypto 1989.
M. Bellare and S. Micali, Non-interactive Oblivious Transfer and Applications, Crypto 1989.
M. Blum, A. De Santis, S. Micali, and G. Persiano, Non-Interactive Zero-Knowledge Proof Systems, preprint.
M. Blum, P. Feldman, and S. Micali, Non-Interactive Zero-Knowledge Proof Systems and Applications, Proceedings of the 20th Annual ACM Symposium on Theory of Computing, Chicago, Illinois, 1988.
M. Blum, How to Prove a Theorem So No One Else Can Claim It, Proceedings of the International Congress of Mathematicians, Berkeley, California, 1986, pp. 1444–1451.
S. A. Cook, The Complexity of Theorem-Proving Procedures, Proc. 3rd Ann. ACM Symp. on Theory of Computing, New York, pp. 151–158.
Y. Desmeth, Abuse-free Cryptosystems: Particularly Subliminal-Free Authentication and Signature, preprint.
W. Diffie and M. E. Hellman, New Directions in Cryptography, IEEE Transactions on Information Theory, vol. IT-22, no. 6, Nov. 1976, pp. 644–654.
A. De Santis and G. Petsiano, Public-Randomness in Public-key Cryptosystems, Eurocrypt-90.
A. De Santis, S. Micali, and G. Persiano, Non-Interactive Zero-Knowledge Proof-Systems, in “Advances in Cryptology — CRYPTO 87”, vol. 293 of “Lecture Notes in Computer Science”, Springer Verlag.
A. De Santis, S. Micali, and G. Persiano, Non-Interactive Zero-Knowledge Proof-Systems with Preprocessing, Crypto 1988.
A. De Santis and M. Yung, Non-Interactive Metaproofs and Non-Interactive Protocols, Manuscript.
S. Even, O. Goldreich, and S. Micali, On-line/Off-line Digital Signatures, Crypto 1989.
U. Feige, D. Lapidot and A. Shamir, Multiple Non-Interactive Zero Knowledge Proofs Based on a Single Random String, Focs 90.
U. Feige, and A. Shamir, Witness-Hiding Protocols, Proceedings of the 22th Annual ACM Symposium on Theory of Computing, 1990, announcement in Crypto-89.
M. Garey and D. Johnson, Computers and Intractability: a Guide to the Theory of NP-Completeness, W. H. Freeman & Co., New York, 1979.
O. Goldreich, A Uniform-Complexity Treatment of Encryption and Zero-Knowledge, Technical Report no. 568, Technion, June 1989.
O. Goldreich, S. Goldwasser, and S. Micali, How to Construct Random Functions, Journal of the Association for Computing Machinery, vol. 33, no. 4, 1986, pp. 792–807.
S. Goldwasser and S. Micali. Probabilistic Encryption. Journal of Computer and System Science, vol. 28, n. 2, 1984, pp. 270–299.
S. Goldwasser, S. Micali, and C. Rackoff, The Knowledge Complexity of Interactive Proof-Systems, SIAM Journal on Computing, vol. 18, n. 1, February 1989.
S. Goldwasser, S. Micali, and R. Rivest, A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attack, SIAM Journal of Computing, vol. 17, n. 2, April 1988, pp. 281–308.
O. Goldreich, S. Micali, and A. Wigderson, Proofs that Yield Nothing but their Validity and a Methodology of Cryptographic Design, Proceedings of 27th Annual Symposium on Foundations of Computer Science, 1986, pp. 174–187.
O. Goldreich, S. Micali, and A. Wigderson, How to Play Any Mental Game, Proceedings of the 19th Annual ACM Symposium on Theory of Computing, New York, pp. 218–229.
J. Håstad, Pseudorandom Generation under Uniform Assumptions, Proceedings of the 22th Annual ACM Symposium on Theory of Computing, 1990.
R. Impagliazzo, L. Levin, and M. Luby, Pseudo-Random Generation from One-way Functions, Proceedings of 21st STOC, May 1989.
R. Impagliazzo and M. Naor, Efficient Cryptographic Schemes Provably Secure as Subset Sum, Proceedings of 30th FOCS, 1989.
R. Impagliazzo and M. Yung, Direct Minimum Knowledge Computations, in “Advances in Cryptology — CRYPTO 87”, vol. 293 of “Lecture Notes in Computer Science”, Springer Verlag pp. 40–51.
D. Lapidot and A. Shamir, These Proceedings.
M. Naor, Bit Commitment using Pseudo-randomness, Crypto 1989.
M. Naor and M. Yung, Public-key Cryptosystems Probably Secure Against Chosen Ciphertext Attacks, Proceedings of the 22th Annual ACM Symposium on Theory of Computing, 1990.
J. Rompel, One-way functions are Necessary and Sufficient for Secure Signatures, STOC 90.
A. Yao, Theory and Applications of Trapdoor Functions, Proc. 23rd IEEE Symp. on Foundations of Computer Science, 1982, pp. 80–91.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
De Santis, A., Yung, M. (1991). Cryptographic Applications of the Non-Interactive Metaproof and Many-prover Systems. In: Menezes, A.J., Vanstone, S.A. (eds) Advances in Cryptology-CRYPTO’ 90. CRYPTO 1990. Lecture Notes in Computer Science, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-38424-3_27
Download citation
DOI: https://doi.org/10.1007/3-540-38424-3_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54508-8
Online ISBN: 978-3-540-38424-3
eBook Packages: Springer Book Archive