Lecture 20: Verifiable Mixnets Twobytwo Verifiable Mixes
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چکیده
Observed that the above expression is a conjunction of four disjunctions. We will give a protocol which allows the prover to prove a single disjunction. The prover can then prove the entire expression by separately proving that each of the four disjunctions is true. First we recall from last lecture the ChaumPedersen honest zero knowledge protocol for proving that two El Gamal ciphertexts, C1 = (α1, β1) = (g,m1 · yt) and C � = (α1 , β1 ) 1 = (g,m1 · yu) have the same plaintext (where the prover knows the reencryption factor, v = u− t).2 Let (a1, a2, b1, b2) be the quadruple (g, y, (α1 /α1), (β1 /β1)) = (g, y, g Then m1 v , (m1 � /m1)· yv ). = m2 if and only if loga1 (b1) = loga2 (b2) = v. (Proof left as an easy exercise.) To prove equality, use the following protocol:
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