Example and One-Message Key Rate Sample Clauses

Example and One-Message Key Rate. In order to illustrate the basic idea, we start with an example probability distribution PXYZ, and give a simple protocol for this distribution. The protocol has the disadvantage that it requires a huge amount of commu- nication. The distribution is best described by the following random process: Al- ice gets a uniform random bit X, Bob gets the same bit after it has been sent through an erasure channel which outputs a special erasure sym- bol with probability p, and ▇▇▇ also gets X but erased with probability q > p (see Figure 3.1, one can imagine that these random variables are distributed by a trusted third party). Clearly, in such a scenario ▇▇▇▇▇ and ▇▇▇ have a certain advantage over ▇▇▇, and one hopes that this advantage can be exploited in order to get a secure key. In this case, our protocol has two steps. First, information reconciliation makes sure ▇▇▇▇▇ and ▇▇▇ get a common string over which ▇▇▇ has some uncertainty. Then, privacy amplification transforms this bit string into a se- cret key. We now describe these steps for this distribution in more detail.