Advantage Distillation Protocols Sample Clauses

Advantage Distillation Protocols. This section will describe the known advantage distillation protocols based on the aforementioned scenario. 2.2.1 The Repetition Code Protocol 2.2.1 Let n be the length of Xxxxx’s and Bob’s original strings, where Bob’s string is obtained from a transmission of Xxxxx’s string over a BSC with error probability p. Let Q be the side information that Xxxxx and Xxx exchanged over the public channel during an AD/IR protocol. The protocol ends with Xxxxx having obtained string A′ and Xxx X′. Let β be the a posteriori bit error probability between A′ and B′, and let I(A′ Q) denote Xxx’s information about A′ knowing Q. The information rate of the protocol is given by Rβ(p) = 1 − I(A′|Q)/n. If Xxxxx and Xxx discard the bits from their strings needed to compensate for the information leaked to Eve because of their discussion over the public channel, their strings have shrunk after the reconciliation protocol. Thus, the information rate is just the length of the final reconciled strings divided by the length of original strings. Without loss of generality, we may assume that it is always Bob who corrects the differences between his string and Xxxxx’s string. The aim of AD/IR protocols is to let p approach to 0, while keeping R0(p) as large as possible. The higher value of R0(p) the protocol can achieve, the better the protocol. The amount of information exchanged over the public channel for distillation/reconciliation is lower bounded by H(A B) = n h(p), where h(p) = p log(p) (1 p) log(1 p) denotes the binary entropy function. Therefore, an upper bound for R0(p) is 1 h(p). Recall that log is used to denote the binary logarithm. Note that the probability that Ai Bi, 1 ≤ i ≤ n, is given by ϵ0, so the information rate of the repetition code protocol is given by Rβ(ϵ0) = r = ϵN + (1 − ϵ0)N 0
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Advantage Distillation Protocols. In the following section, we present some required background to understand the proofs in Sections 4 and 5, and in particular we introduce the parity-check protocol that we use to lower bound the secret-key rate. The parity-check protocol is an example of a so-called advantage-distillation protocol, which is a type of protocol introduced in [11,14] to prove Theorem 1 in the satellite setting.

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