The General Protocol Clause Samples

The General Protocol. Lemma 3.12. Let PXYZ be a probability distribution over X × Y × Z and PUV|X a conditional probability distribution over X × X × X which maximizes H(U|ZV) — H(U|YV). Let n, k, and a code C : [2k ] → X n be given for the channel C which, on in- put x ∈ X, chooses U, V, and Y according to PUVY and outputs (x ⊕ U, V, Y). Assume that C has rate k = log(|X |) — H(U|YV) — ε and decoding error 2 be given. γ κ2 > n bits, soundness 1 — γ and secrecy 1 — 2—nκ2 . The protocol has the properties that ▇▇▇▇▇ sends at most 3n[log(|X |)| bits, ▇▇▇▇▇ encodes one word of C, and Bob decodes one noisy word of C. The protocol needs inputs κ2, n, and a description of PUV|X.