Abstract
We consider perfect zero-knowledge proof systems for “proving the power to decide whether a membership in a language is true or not”. We extend the definition of the model, and then extend the class of languages in it; (so far only the language of quadratic residuosity modulo a Blum integer was known to be applicable to this model). More precisely, we present a protocol for all known random self-reducible languages (i.e., graph isomorphism, quadratic residuosity, discrete log). This protocol can be executed with only 4 rounds of communication. Finally we extend a well-known lower bound for the number of rounds of zero-knowledge proofs of membership to our “decision power model”. This shows that (under some technical restrictions) our protocol is round-optimal unless the considered language is in BPP (which seems unlikely).
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© 1997 Springer-Verlag
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di Crescenzo, G., Sakurai, K., Yung, M. (1997). Zero-knowledge proofs of decision power: New protocols and optimal round-complexity. In: Han, Y., Okamoto, T., Qing, S. (eds) Information and Communications Security. ICICS 1997. Lecture Notes in Computer Science, vol 1334. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028458
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DOI: https://doi.org/10.1007/BFb0028458
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