In this paper the generality and wide applicability of zero-knowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs that, for the member...
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In this paper the generality and wide applicability of zero-knowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs that, for the members of a language, efficiently demonstrate membership in the language without conveying any additional knowledge. All previously known zero-knowledge proofs were only for number-theoretic languages in NP and CoNP. Under the assumption that secure encryption functions exist or by using "physical means for hiding information," it is shown that all languages in NP have zero-knowledge proofs. Loosely speaking, it is possible to demonstrate that a CNF formula is satisfiable without revealing any other property of the formula, in particular, without yielding neither a satisfying assignment nor properties such as whether there is a satisfying assignment in which x1 = x3 etc. It is also demonstrated that zero-knowledge proofs exist "outside the domain of cryptography and number theory." Using no assumptions, it is shown that both graph isomorphism and graph nonisomorphism have zero-knowledge interactive proofs. The mere existence of an interactive proof for graph nonisomorphism is interesting, since graph nonisomorphism is not known to be in NP and hence no efficient proofs were known before for demonstrating that two graphs are not isomorphic.
We present a method called Partitioned Encryption whose main property is its simplicity. It is an extension of Probabilistic Public-Key Encryption , which can be used in designing cryptographic protocols and can be ap...
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We present a method called Partitioned Encryption whose main property is its simplicity. It is an extension of Probabilistic Public-Key Encryption , which can be used in designing cryptographic protocols and can be applied to distributed problem solving. We also give a modification of Secret Sharing called Partitioned Secret Sharing . We demonstrate the power of Partitioned Encryption: combining it with the partitioning of the user set gives a solution scheme for ‘Verifiable Secret Sharing’ and ‘Simultaneous Broadcast in the Presence of faults’, which are important primitives of fault-tolerant distributed computing introduced by Chor, Goldwasser, Micali and Awerbuch (1985). The scheme is fully polynomial, simple, and efficient in terms of communication rounds. The basic partitioning methods are suggested as general tools for distributedcomputing, which are easy to implement and analyze.
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