| M. Tompa and H. Woll. Random Self-Reducibility and Zero-Knowledge Proofs of Possession of Information. Proceedings of the 28th Annual IEEE Symposium on the Foundations of Computer Science, IEEE (1987). |
.... an NP one (in previous solutions, even if the original proof system had been perfect ZK, the transformed one would be statistical) As in some of the results in [15, 24] one of the ideas in our proof is to make (appropriate) use of the auxiliary inputs that the definition of ZK provides (cf. [11, 15, 19, 24, 29]) Previous solutions [5, 25, 26] did not exploit this feature of ZK. We note that auxiliary inputs are important to the definition of ZK: Goldreich and Krawczyk [13] show that without auxiliary inputs in the definition, ZK would not even be closed under sequential composition. Another idea of our ....
....the interaction with b P is negligible (the auxiliary input of V is set to the empty string in both cases) The first condition is called the completeness condition and the second the soundness condition. Next we define zero knowledge (ZK) proofs [19] We remark that the auxiliary inputs (cf. [11, 15, 19, 24, 29]) are crucial to make the definition meaningful. For one thing, without them, the composition of zero knowledge protocols is not necessarily a zero knowledge protocol as we would like it to be [13] We recall also that any ZK proof which is black box simulation ZK (as all known ones are) is ZK in ....
M. Tompa and H. Woll. Random Self-Reducibility and Zero-Knowledge Proofs of Possession of Information. Proceedings of the 28th Annual IEEE Symposium on the Foundations of Computer Science, IEEE (1987).
....secrecy of an input x against an adversary B that has no input, or at least none related to x. Such inputs would be called auxiliary inputs. In computational zero knowledge, including auxiliary inputs in the definition proved necessary for the secrecy if a protocol is executed repeatedly [25, 28]. Similarly, such auxiliary inputs occur if a statistically hiding protocol is repeated. However, in this case we can show quite easily that secrecy in the setting with auxiliary input is a consequence of normal secrecy. We now describe this formally. An auxiliary input attacker B aux on a ....
M. Tompa and H. Woll, "Random self-reducibility and zero knowledge proofs of possession of information," in Proc. 28th IEEE Symp. Foundations of Computer Science, 1987, pp. 472--482.
.... verifier of the truth of an assertion, but it does not really make sense for the prover to convince the verifier that she 2 knows a proof of the assertion (of course she knows such a proof if it exists since she is all powerful) Nevertheless, Feige, Fiat and Shamir [FFS] and Tompa and Woll [TW] have given formal definitions of what should constitute a proof of knowledge in the context of interactive proof systems. Brassard, Chaum and Cr epeau have investigated a different setting, in which the prover s computing power is limited [BC1,C,BCC] The resulting protocols are convincing for ....
....tosses, it can take snapshots of the verifier, and it can restore the verifier to a previous state. Also, the simulator can talk to the verifier, making him believe that he is talking to the prover. Similarly, it is natural to consider yet a fourth actor (introduced implicitly by Tompa and Woll [TW], explicitly but namelessly by Feige, Fiat and Shamir [FFS] and named observer by Boyar, Lund and Peralta [BLP] We prefer to call this actor the extractor because we give it a more active role than Boyar, Lund and Peralta. Just as the 3 Nevertheless, the term reluctant was coined thinking ....
Tompa, M. and Woll, H. "Random self-reducibility and zero-knowledge proofs of possession of knowledge", Proceedings of the 28th IEEE Symposium on Foundations of Computer Science, 1987, pp. 472 -- 482.
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M. Tompa and H. Woll. Random Self-Reducibility and Zero-Knowledge Proofs of Possession of Information. Proceedings of the 28th Annual IEEE Symposium on the Foundations of Computer Science, IEEE (1987).
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