Abstract
In their 1985 paper, Goldwasser, Micali and Rackoff set forth the notion of zero-knowledge interactive proofs [GMR1]. This seminal paper generated considerable activity around the world. In the span of a few years, a substantial number of results were obtained by different groups of researchers. Among those, the following two theorems make an intriguing pair:
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Fortnow [F], together with Boppana, Hastad and Zachos [BHZ]: The existence of a perfect zero-knowledge protocol for an NP-complete problem would imply that the polynomial hierarchy collapses.
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Brassard, Chaum and Crépeau [BCC]: There exists a perfect zero-knowledge protocol for satisfiability.
Nevertheless, the polynomial hierarchy has not collapsed! Of course, the resolution of this apparent paradox is that the above two results strongly depend on fundamentally incompatible definitions of what a protocol is.
Supported in part by Canada NSERC grant A4107.
Supported in pm by an NSERC postgraduate scholarship; part of this research was performed while this author was visiting the Université de Montrtéal.
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Brassard, G., Crepeau, C. (1990). Sorting out zero-knowledge. In: Quisquater, JJ., Vandewalle, J. (eds) Advances in Cryptology — EUROCRYPT ’89. EUROCRYPT 1989. Lecture Notes in Computer Science, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46885-4_20
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