lecture20

# lecture20 - RESULTS OF A PROOF CSci 5403 By interacting...

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1 COMPLEXITY THEORY CSci 5403 LECTURE XX: ZERO KNOWLEDGE RESULTS OF A PROOF By interacting with a “traditional prover” the verifier gains access to new information: What about an interactive prover? G ˥ HAM: v 1 ,v 2 ,…,v n Quite So. Prover Verifier Prover Verifier x has a square root mod N knows y 2 =x mod N Pick r ˥ R Z N * w = r 2 mod N b ˥ R {0,1} z = y b r mod N ACCEPT if z 2 =x b w mod N Prover Verifier G 0 G 1 . knows π (G 0 ) = G 1 . H = ρ (G 1 ) b ˥ R {0,1} σ = ρπ b ACCEPT if H = ρπ b (G 1-b ) pick ρ ˥ R S n

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2 ZERO KNOWLEDGE Definition. An interactive proof system (P,V) for L is honest-verifier perfect zero-knowledge (HVPZK) if (P,V) has perfect completeness and there exists an efficient Simulator S, so that ˲ x ˥ L, ˲ σ ˥ {0,1}*, Pr r [S(x;r) = σ ] = Pr r’ [(P V)(x;r’) = σ ] Thus the output of the simulator on L is identically distributed to honest-verifier transcripts on L. Denote this by { S(x) } x ˥ L { (P V)(x) } x ˥ L . Prover Verifier h ˥ ʪ g ʫ mod P knows h = g x mod P γ = g y mod P z ˥ R Z P-1 w = xz+y mod P-1 ACCEPT if h z γ = g w mod P z = F (h,g, γ ) pick y ˥ R Z P-1 . ZERO KNOWLEDGE Definition. An interactive proof system (P,V) for L is perfect zero-knowledge (PZK) if for every PPT V* there is an efficient Simulator S V* , so that {S
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lecture20 - RESULTS OF A PROOF CSci 5403 By interacting...

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