Shafi Goldwasser, Silvio Micali, and Charles Rackoff. The knowledge complexity of interactive proofs. SIAM Journal of Computing, 18(1):186--208, 1989. 15 Home/Search Document Not in Database Summary Related Articles Check |
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Interactive Hashing Simplifies Zero-Knowledge Protocol.. - Ostrovsky, Venkatesan, .. (1998) (6 citations) (Correct)
....machine possessing additional private knowledge. It tries to convince the probabilistic polynomial time verifier that a given theorem is true. A zero knowledge (ZK) proof is an interactive proof with an additional privacy constraint: the verifier does not learn why the theorem is true [GMR]. That is, whatever the polynomialtime verifier sees in a ZK proof with the unbounded prover of a true theorem x, can be approximated by a probabilistic polynomial time machine working solely on input x. A statistical zero knowledge proof (SZK proof) is one for which this true view and approximate ....
....and ICSI. Part of this work wz done at Bellcore and part at IBM T.J. Watson Research Center. Bellcore, Room 2M 344, 445 South St, Morristown, NJ 07960. E mail: v,akieObelleora. con. IBM Research, T.J. Watson Research Center, Yorktown Heights, NY 10598. mai] nogieason. ibm. con. 268 proofs [GMR] were shown to be equivalent to the existence of general one way functions JILL, Ha 90, NY, Ro, OWl. Such efforts, not only develop the theoretical foundations of cryptography, but also enable the primitive implementations to be based on a larger possible concrete choices of underlying functions, ....
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Goldwasser, S., S. Micali, and C. Rackoff, "The Knowledge Complexity of Interactive Proofs," SIAM J. Cornput., 18(1), 186-208 (February 1989).
Proofs of Knowledge for Non-Monotone Discrete-Log Formulae.. - Bresson, Stern (2002) (3 citations) (Correct)
....signatures schemes with revocation of identity and multi signer features. Such features can be useful to protect privacy or for collabrative use of group signatures, respectively. 1 Introduction 1. 1 Proof of Knowledge Zero knowledge has been introduced by Goldwasser, Micali and Racko in [23] to quantify the amount of information leaked in an interactive protocol. The (interactive) protocols are thus proved zero knowledge when they reveal no information apart from the validity of the statement. Almost at the same time, the concept of proof of knowledge [21] introduced the notion of ....
S. Goldwasser, S. Micali, and C. W. Racko . Knowledge complexity of interactive proofs. In Proc. of STOC '85, pages 291-304. ACM Press, May 1985.
Efficient and Concurrent Zero-Knowledge from any public.. - Micciancio, Petrank (2002) (Correct)
....based on a perfectly binding commitment scheme based on the Decisional Die Hellman (DDH) assumption which satis es some special properties. Note that our transformation works for many interesting protocols. In fact, many of the known zero knowledge proof systems are public coin (see for example [26, 23, 21]) A weaker result that follows from our technique is a transformation of (non concurrent) computational public coins honest veri er zero knowledge proofs into computational public coins zero knowledge proofs that are good also for non honest veri ers. Such a transformation clearly follows from ....
S. Goldwasser, S. Micali, C. Racko . The Knowledge Complexity of Interactive Proofs. Proc. 17th STOC, 1985, pp. 291-304.
Free Bits, PCPs and Non-Approximability - Towards Tight.. - Bellare, Goldreich, Sudan (1995) (9 citations) (Correct)
....be of interest to indicate that for every s 1, FPCP 1;s [poly; 0] coNP (2) FPCP 1;s [poly; 1] PSPACE (3) It seems that FPCP 1;1=2 [poly; 0] is not contained in BPP, since Quadratic Non Residuosity and Graph Non Isomorphism belong to the former class. Specifically, the interactive proofs of [GMR] and [GMW] can be viewed as a pcp system with polynomial randomness, query complexity 1 and free bit complexity 0. Thus, it seems that the obvious observation PCP 1;s [poly; 1] AM (for every s 1, where AM stands for one round Arthur Merlin games) would also be hard to improve upon. ....
....and Johnson [GJ1] showing that it is NPhard to approximate the chromatic factor within a factor less than two. The indication of higher factors, and results for other problems, had to wait for the interactive proof approach. Interactive proofs were introduced by Goldwasser, Micali and Rackoff [GMR] and Babai [Bab] Ben Or, Goldwasser, Kilian and Wigderson [BGKW] extended these ideas to define a notion of multiprover interactive proofs. Fortnow, Rompel and Sipser [FRS] showed that the class, MIP, of languages possessing multi prover interactive proofs equals the class of languages which have ....
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S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proofs. SIAM J. Computing, Vol 18, No. 1, 1989, pp. 186--208.
Definitions And Properties Of Zero-Knowledge Proof Systems - Goldreich, Oren (1994) (34 citations) (Correct)
....Micali and Rackoff. We introduce and classify two definitions of zero knowledge: auxiliary Gamma input zero knowledge and blackbox Gamma simulation zero knowledge. We explain why auxiliary input zero knowledge is a definition more suitable for cryptographic applications than the original [GMR1] definition. In particular, we show that any protocol solely composed of subprotocols which are auxiliaryinput zero knowledge is itself auxiliary input zero knowledge. We show that blackboxsimulation zero knowledge implies auxiliary input zero knowledge (which in turn implies the [GMR1] ....
....[GMR1] definition. In particular, we show that any protocol solely composed of subprotocols which are auxiliaryinput zero knowledge is itself auxiliary input zero knowledge. We show that blackboxsimulation zero knowledge implies auxiliary input zero knowledge (which in turn implies the [GMR1] definition) We argue that all known zero knowledge proofs are in fact blackbox simulation zero knowledge (i.e. were proved zero knowledge using blackboxsimulation of the verifier) As a result, all known zero knowledge proof systems are shown to be auxiliary input zero knowledge and can be ....
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Goldwasser, S., S. Micali, and C. Rackoff, "Knowledge Complexity of Interactive Proofs", Proc. 17th STOC, 1985, pp. 291-304.
Statistical Zero-Knowledge Languages Can Be Recognized in Two.. - Aiello, Hastad (1991) (24 citations) (Correct)
.... Languages Can Be Recognized in Two Rounds William Aiello Johan Hastad Applied Math Department and Laboratory of Computer Science, MIT Abstract: Recently, a hierarchy of probabilistic complexity classes generalizing NP has emerged in the work of Babai [B] and Goldwasser, Micali, and Rackoff [GMR1], and Goldwasser and Sipser [GS] The class IP is defined through the computational model of an interactive prover verifier pair. Both Turing machines in a pair receive a common input and exchange messages. Every move of the verifier as well as its final determination of whether to accept or ....
....languages for which there exist polynomial length proofs of membership which can be verified in polynomial time. Recently, a hierarchy of probabilistic complexity classes generalizing this notion of efficient provability has emerged in the work of Babai [B] and Goldwasser, Micali, and Rackoff [GMR1], and Goldwasser and Sipser [GS] The class IP is defined through the Supported by an ONR fellowship and partially supported by NSF grant DCR 8509905. Supported by an IBM Post Doctoral Fellowship and partially supported by Air Force Contract AFOSR 86 0078. Currently at the Royal Institute of ....
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Goldwasser, S., S. Micali, and C. Rackoff, "The Knowledge Complexity of Interactive Proofs," Proc. of 17th Symposium on Theory of Computing, pp 291--305, Providence, 1985.
Probabilistically Checkable Proofs - Sudan, Guruswami (1 citation) (Correct)
....of PCP actually evolved over a series of surprising developments in the late 80s and early 90s. The notion of checking proofs in a probabilistic sense (where the verification process is allowed to err with small probability) dates back to the seminal work of Goldwasser, Micali and Rackoff [18] and Babai [4] on Interactive Proofs (IP) In the IP proof system, a probabilistic verifier interacts with a prover who wishes to convince the verifier that some assertion is true. The model of the interactive proofs evolved over time, partly motivated by efforts to understand the model better. ....
Shafi Goldwasser, Silvio Micali and Charles Rackoff. The knowledge complexity of interactive proofs. SIAM Journal on Computing, 18:186--208, 1989.
Perfect Zero-Knowledge in Constant Rounds - Bellare, Micali, Ostrovsky (1990) (21 citations) Self-citation (Micali) (Correct)
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Goldwasser, S., S. Micali, and C. Rackoff, "The Knowledge Complexity of Interactive Proofs," Proceedings of the 17th ACM Symposium on Theory of Computing , May 1985.
Lower Bounds for Concurrent Zero Knowledge - Kilian, Petrank, Rackoff Self-citation (Rackoff) (Correct)
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S. Goldwasser, S. Micali, C. Rackoff. The Knowledge Complexity of Interactive Proofs. Proc. 17th STOC, 1985, pp. 291-304.
New Tools in Cryptography: Mutually Independent Commitments.. - Liskov (2004) Self-citation (Micali) (Correct)
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Shafi Goldwasser, Silvio Micali, and Charles Racko#. Knowledge complexity of interactive proofs. In Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing, pages 291--304, Providence, Rhode Island, 6--8 May 1985.
The Complexity of Decision versus Search - Bellare, Goldwasser (1994) (21 citations) Self-citation (Goldwasser) (Correct)
....where it is sufficient for the prover to be able to decide membership in the language. Such power is also sufficient for almost all of the languages in IP that have been closely examined (specifically, the languages of graph isomorphism, graph non isomorphism [GMW] and quadratic non residuosity [GMR]) On the other hand all known interactive proofs for complete languages for coNP require the prover to do more than decide membership in the language. Similarly, all known interactive proofs for the language of quadratic residuosity require the prover to do more than decide quadratic ....
....to decide L. NP proof systems, however, are very restrictive. It becomes natural to ask: would the prover s task be alleviated if the parties were allowed interaction and the proof was now only required to be correct with high probability In other words, we now consider interactive proofs (cf. [GMR]) We recall that in an interactive proof both parties are allowed to be probabilistic and the parties are allowed to exchange messages, for a polynomial number of rounds, before the verifier decides whether or not to accept. Completeness and soundness are required to hold only with high ....
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S. Goldwasser, S. Micali and C. Rackoff. The Knowledge Complexity of Interactive Proofs. SIAM J. Computing 18(1), 186--208, 1989.
Encapsulated Key Escrow - Bellare, Goldwasser (1996) (11 citations) Self-citation (Goldwasser) (Correct)
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S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proofs. SIAM J. Comput. Vol. 18, No. 1, 186-208, February 1989.
Non-interactive Zaps and New Techniques for NIZK - Jens Groth Rafail (Correct)
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Shafi Goldwasser, Silvio Micali, and Charles Rackoff. The knowledge complexity of interactive proofs. SIAM Journal of Computing, 18(1):186--208, 1989. 15
Minimal Assumptions for Efficient Mercurial Commitments - Dodis (2005) (Correct)
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S. Goldwasser, S. Micali, and C. Rackoff. Knowledge complexity of interactive proofs. In Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing, pages 291--304, Providence, Rhode Island, 6--8 May 1985.
Zero-Knowledge Proofs for Mix-nets of Secret Shares.. - Marius-Calin Silaghi.. (2005) (Correct)
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S. Goldwasser, S. Micali, and C. Racko#. Knowledge complexity of interactive proofs. In Proc. of 17th STOC, pages 291--304, 1985. Earlier version: Knowledge complexity, unpublished manuscript, (submitted to FOCS, 1984).
The (True) Complexity of Statistical Zero Knowledge.. - Bellare, Micali.. (Correct)
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Goldwasser, S., S. Micali, and C. Rackoff, "The Knowledge Complexity of Interactive Proofs," SIAM J. Comput., 18(1), 186-208 (February 1989).
A Relationship between One-Wayness and Correlation Intractability - Hada, Tanaka (1999) (2 citations) (Correct)
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S. Goldwasser, S. Micali, and C. Racko#, "The Knowledge Complexity of Interactive Proofs," Proceedings of 17th STOC, pp.291-304, 1985.
On the Existence of 3-Round Zero-Knowledge Protocols - Hada, Tanaka (1999) (26 citations) (Correct)
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S. Goldwasser, S. Micali, and C. Racko#, "The Knowledge Complexity of Interactive Proofs," Proceedings of 17th STOC, pp.291-304, 1985.
Free Bits, PCPs and Non-Approximability--- - Towards Tight Results (Correct)
No context found.
S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proofs. SIAM J. Computing Vol 18, No. 1, 186--208, 1989.
Concurrent Zero-Knowledge Proofs for NP - Kilian, Petrank, Richardson (2001) (1 citation) (Correct)
No context found.
S. Goldwasser, S. Micali, C. Racko . The Knowledge Complexity of Interactive Proofs. Proc. 17th STOC, 1985, pp. 291-304.
Free Bits, PCPs and Non-Approximability - Towards Tight.. - Bellare, Goldreich.. (1995) (9 citations) (Correct)
No context found.
S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proofs. SIAM J. Computing Vol 18, No. 1, 186--208, 1989.
Efficient and Concurrent Zero-Knowledge from any public.. - Micciancio, Petrank (Correct)
No context found.
S. Goldwasser, S. Micali, C. Racko . The Knowledge Complexity of Interactive Proofs. Proc. 17th STOC, 1985, pp. 291-304.
Free Bits, PCPs and Non-Approximability--- - Towards Tight Results (Correct)
No context found.
S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proofs. SIAM J. Computing Vol 18, No. 1, 186--208, 1989.
Proofs of Knowledge for Non-Monotone Discrete-Log Formulae.. - Bresson, Stern (2002) (3 citations) (Correct)
No context found.
S. Goldwasser, S. Micali, and C. W. Racko#. Knowledge complexity of interactive proofs. In Proc. of STOC '85, pages 291--304. ACM Press, May 1985.
Free Bits, PCPs and Non-Approximability - Towards Tight.. - Bellare, Goldreich.. (1995) (9 citations) (Correct)
No context found.
S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proofs. SIAM J. Computing Vol 18, No. 1, 186--208, 1989.
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