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On Monotone Formula Composition of Perfect Zero-Knowledge Languages

On Monotone Formula Composition of Perfect Zero-Knowledge Languages,10.1137/S0097539798346123,Siam Journal on Computing,Alfredo De Santis,Giovanni Di

On Monotone Formula Composition of Perfect Zero-Knowledge Languages   (Citations: 1)
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We investigate structural properties of interactive perfect zero-knowledge (PZK) proofs. Specifically, we look into the closure properties of PZK languages under monotone boolean formula composition. This gives rise to new protocol techniques. We show that interactive PZK for random self-reducible languages (RSR) (and for co-RSR) is closed under monotone boolean formula composition. Namely, we present PZK proofs for monotone boolean formulae whose atoms are statements about membership in a PZK language which is RSR (or whose complement is RSR). We also discuss extensions, recent applications and generalizations of the techniques.
Journal: Siam Journal on Computing - SIAMCOMP , vol. 38, no. 4, pp. 1300-1329, 2008
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    • ...accurate statement of their results) and [12] on the previously discussed protocol to prove statement ‘di = 1’ and the previously discussed protocol to prove statement ‘ ∨ i−1 j =1 ((dj = 1) ⊕ (tj = 1))’...
    • ...All these properties are directly implied from the results in [8, 12, 13] about the ORcomposition technique...
    • ...This can be done using the ‘AND-composition’ technique from [8, 12] on the just discussed protocol to prove statement Ui . This composition results in a 3-message proof system for proving statement Φ1(d, t) where the verifier sends a single challenge, satisfying completeness, soundness (under the discrete logarithm assumption), and honest-verifier zero-knowledge...
    • ...All these properties are directly implied from the results in [8, 12, 13] about the AND-composition technique...

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