One-Message Sample Clauses

One-Message. Key Agreement In this chapter we study the following scenario: Xxxxx, Xxx, and Xxx have access to many independent instances of random variables X, Y, and Z, respectively, distributed according to some fixed and commonly known distribution PXYZ. Xxxxx and Xxx want to agree on a key with a single message from Xxxxx to Bob, and using as few random variables as possi- ble. In this chapter we will see for which distributions PXYZ this is possi- ble and give protocols for this task. Further, we give lower bounds on the number of random variables needed. Overview of this chapter In Section 3.1 we start by giving an intuition of the protocol and explain the three basic steps. In the first step, a preprocessing step, Xxxxx manipu- lates her random variables individually to obtain random variables which are better suited for the subsequent protocol. In the next step, called infor- mation reconciliation, Xxxxx sends Bob information which allows him (but not Xxx) to find the random variables of Xxxxx. This gives Xxxxx and Xxx a common string about which Xxx has imperfect knowledge. In the third step, called privacy amplification, Xxxxx and Xxx use this common string to obtain a secure key. The discussion of Section 3.1 also leads to the defi- nition of the one-message key rate, the rate at which Xxxxx and Xxx can use their random variables to obtain key bits. In Section 3.2 we give a detailed study of the preprocessing step, and Section 3.3 contains a description of our information reconciliation proto- col. As privacy amplification is simple to implement (we apply a strong extractor) we do not need a section in order to describe it. Section 3.4 then describes the complete protocol in detail.