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## The knowledge complexity of interactive proof systems (1989)

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Citations: | 1246 - 39 self |

### Citations

1390 | Probabilistic encryption - Goldwasser, Micali - 1984 |

1050 | The complexity of theorem-proving procedures. - Cook - 1971 |

576 | Knowledge and common knowledge in a distributed environment. distributed computing - Halpern, Moses - 1990 |

363 | A.: Zero knowledge proofs of identity - Fiege, Fiat, et al. - 1987 |

353 | Trading group theory for randomness. - Babai - 1985 |

339 | Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. - Babai, Moran - 1988 |

221 | Private coins versus public coins in interactive proof systems. - Goldwasser, Sipser - 1986 |

179 | Proofs that yield nothing but their validity and a methodology of cryptographic protocol design (extended abstract - Goldreich, Micali, et al. - 1986 |

147 | Belief , awareness and limited reasoning , in : - in, Halpern - 1985 |

144 | S.Zachos, Does co-NP have short interactive proofs ?, - Boppana - 1987 |

117 | Games against nature. - Papadimitriou - 1985 |

114 | Coin flipping by telephone - Blum - 1982 |

92 | The complexity of perfect zero-knowledge. - Fortnow - 1989 |

78 | Random selfreducibility and zero knowledge interactive proofs of possession of information,” - Tompa, Woll - 1987 |

65 | A model-theoretic analysis of knowledge - Fagin, Halpern, et al. - 1991 |

60 | Nontransitive Transfer of Confidence: A Perfect Zero-Knowledge Interactive Protocol for SAT and Beyond. - Brassard, Crepeau - 1986 |

36 | How to simultaneously exchange a secret bit by flipping a symmetrically biased coin - Luby, Micali, et al. - 1983 |

32 | A private interactive test of a boolean predicate and minimum-knowledge public key cryptosystems - Galil, Haber, et al. - 1985 |

26 | Interactive proof systems: Provers that never fail and random selection. - Goldreich, Mansour, et al. - 1987 |

23 | On the Power of Interaction - Aiello, Goldwasser, et al. - 1990 |

18 | Perfect Zero-Knowledge Languages can be Recognized in Two Rounds - Aiello, Hastad - 1987 |

1 |
Trading Group Theov for Randomness
- Babai
(Show Context)
Citation Context ...length tl, halts within f(n) turns. Here f is a non decreasing function from natural numbers to natural numbers. Interactive proof-systems should be contrasted with the “Arthur-Merlin” games of Babai =-=[B]-=-. In those games Merlin plays the role of n and Arthur the role of R. The big difference is that Merlin sees all results of Arthur’s coin tosses. This allows Babai to prove that arbitrary interaction ... |

1 |
Coin flipping by relephone
- Blum
- 1982
(Show Context)
Citation Context ...current knowledge about proving lower-bounds. We know of two interesting languages that have knowledge complexity 0. Both are algebraic. The first one is the following language BL proposed by Blum in =-=[Bll]-=- where he gives all the essential ingredients to prove BL UC(O). Let )I be an integer with prime factorization n =p:l -p:‘. Then n f BL if the number of different p,s congruent to 3 mod 4 is even. The... |

1 | Three uppkuriom of rhe oblivious fransfer, Unpublished manuscript - Blum - 1981 |

1 | Ow Jxing rhe Oblivious I ‘rurzsfer - Berger, Tedrick |

1 |
The Complexity of Theorem-Proving Procedures
- SCook
- 1971
(Show Context)
Citation Context ... procedure, NP constitutes a very successful formalization of this notion. Loosely speaking, a theorem is in provable in NP if its proof is easy to verify once it has been found. Let us recall Cook’s =-=[C]-=- (and independently Letin’s [t]) influential definition of NP in this light. The NP proof-system consists of two communicating Turing machines A and a : respectively, the prover and the verifier. The ... |

1 |
Lempel, A randomized profocol for Signirlg Co~fmcrs
- Even
- 1983
(Show Context)
Citation Context ...ious Transfer (OT) has been introduced by Rabin [HR] who also proposed the first protocol implementing it. OT appears useful as a design tool. See for example Blum [B12] and Even Goldreich and Lempel =-=[EGL]-=-. Rabin introduced OT (to be described below) in a number theoretic setting. Mom generally tbc OT can bc vicwcd as a protocol for transfer* a large amounf of knowledge with probability 112 [EGL]. Bcrg... |

1 |
A modelthcorctic analysis .of knowhzdge
- Fagin, Halpem, et al.
- 1984
(Show Context)
Citation Context ...t :method of communicating a proof. 3. K~~owledge Complexity Communication is a tool for transferring or exchanging knowledge. Knowlcdgc has received a lot of attention in a model-theoretic framework =-=[FHV]-=-, [HM]. In this context, roughly speaking, 1) All parricipanrs are considered to have i&ire cotqxuing power. (E.g. each participant “knows” all logical conscqucnccs of the information in his hands) an... |

1 |
A Secure Protocol for rhe Oblivious Transfer, Eurocrypt
- Fischer, Micali, et al.
- 1984
(Show Context)
Citation Context ...unicated. Model theoretic knowledge has been used to analyze protocols. For example, in [HR] it has been used co prove Rabin’s “Oblivious Transfer” correct In some setting. Howcvcr. as pointed out in =-=[FMR]-=-, Rabin’s oblivious transfer still lacks a proof of correctness in a complexity theoretic framework. We believe that knowledge complexity provides the right framework to discuss the correctness of cry... |

1 |
Knowledge gnnd Common Knowledge in a Dislributed Knvironmenf
- Halpern, Moses
- 1984
(Show Context)
Citation Context ...od of communicating a proof. 3. K~~owledge Complexity Communication is a tool for transferring or exchanging knowledge. Knowlcdgc has received a lot of attention in a model-theoretic framework [FHV], =-=[HM]-=-. In this context, roughly speaking, 1) All parricipanrs are considered to have i&ire cotqxuing power. (E.g. each participant “knows” all logical conscqucnccs of the information in his hands) and 2) T... |

1 |
On Solving A System of Simulkzrteous Alodtilar Polynomial Equations of Low Degree In preparation
- Hastad
(Show Context)
Citation Context ...col about the sccrct, may pin point weaknesses in the design of the protocol. For example the amount of knowledge revealed in a protocol of [BDJ appeared to be unreasonably large. Further analysis by =-=[H]-=- showed that this protocol could be broken if the encryption function used in the protocol is RSA with low exponents or Rabin’s function. A most important application of these ideas is that it allows ... |

1 |
A Logic 10 reason aboul likehood
- Halpcrn, Rabin
- 1983
(Show Context)
Citation Context ...municating the knowlcdgc efficiently, but the whole problem is making sure not too ntuch knowledge has been communicated. Model theoretic knowledge has been used to analyze protocols. For example, in =-=[HR]-=- it has been used co prove Rabin’s “Oblivious Transfer” correct In some setting. Howcvcr. as pointed out in [FMR], Rabin’s oblivious transfer still lacks a proof of correctness in a complexity theoret... |

1 | On fhe Security of Linearly Truncated Sequences, this proceedings - Hastad, Shamir |

1 |
Proofi with Unrntsred Oracles, Unpublished Manuscript
- Goldwasser, Mlcali
- 1983
(Show Context)
Citation Context ...ole for deciding whether a certain cryptographic protocol may be played securely more than once using the same secret key). Related notions of indistinguishability. have been previously considered in =-=[GM]-=- in the context of probabilistic encryption and then in [y] and [GGMJ in the context of pseudo-random number generation. 3.2 The knowledge computable from a communication Which communications convey k... |

1 | Sequen,rial Search Problems, Probl - cvin - 1973 |

1 | Games against nature, Proc. 24th ann. Symp. on Foundations of Computer Sciende - Papadimitriou - 1983 |

1 | The relative efficiency ofpropositionalproofsystems - COOK, RECKHOW |

1 | A secure protocol for the oblivious transfer, unpublished manuscript - FISCHER, MICALI, et al. - 1986 |

1 | to play any mental game - Ho - 1987 |

1 | On the cunning power of cheating verifiers: some observations of zero-knowledge proofs - OREN - 1987 |