The Secret Key Rate of a Class of Binary Distributions Sample Clauses

The Secret Key Rate of a Class of Binary Distributions. − In this section we study the one-way secret-key rate of a general class of distributions. Namely, for parameters α and β, we assume that Xxxxx and Xxx are given binary random variables X and Y which have the property that they are equal with probability at least (1 + α)/2 (i.e., X and Y have correlation at least α). Furthermore, we assume that with probability 1 β, the random variable Z does not give any information about X. This class will also be of interest for Sections 3 and 4. Definition 5. Let D(α, β) be the set of probability distributions PXY Z over {0, 1} × {0, 1} × Z satisfying – Pr[X = 0] = Pr[X = 1] = 1 , – Pr[X = Y ] ≥ 1+α, – there exists an event E such that H(X|ZE ) = 1 and Pr[E ] ≥ 1 − β. D D ǁ − ǁ ≥ ǁ − ǁ ≤| | | | It is not hard to see that we could similarly look at the distributions which satisfy PY X=0 PY X=1 α and PZ X=0 PZ X=1 β, where Y does not have to be binary. This condition implies that Xxx can apply a function to Y such that a distribution from (α, β) results. Furthermore, all distributions in (α, β) satisfy this characterization. D D Some distributions in (α, β) have a higher secret-key rate than oth- ers, of course. We will see that the following distribution has the lowest secret-key rate of all distributions in (α, β). Intuitively, this distribu- tion gives as much information to Eve as possible, and makes X and Y as independent as possible under the constraints of Definition 5. For a ran- dom variable X, let4 λ(X) be the random variable describing the out- put of a binary symmetric channel taking input X, i.e., P λ(X)|X=0(0) = P λ
Sample 1
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The Secret Key Rate of a Class of Binary Distributions. ‌ — In this section we study the one-way secret-key rate of a general class of distrib- utions. Namely, for parameters α and β, we assume that Xxxxx and Xxx are given binary random variables X and Y which have the property that they are equal with probability at least (1 + α)/2 (i.e., X and Y have correlation at least α). Furthermore, we assume that with probability 1 β, the random variable Z does not give any information about X. This class will also be of interest for Sections 3 and 4.
Sample 1

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