This module we are going to discuss privacy amplification. This task forms the final step in the quantum key distribution protocols we’ll see in the coming modules, but it is also useful in other cryptographic contexts. Moreover, we’ll see that privacy amplification can be achieved using a beautiful family of objects from theoretical computer science called randomness extractors, themselves well worth studying in their own right!

4.1 introduces the task of privacy amplification and gives you a few examples.

4.2 discusses randomness extractors and explains how these constructions can be used to achieve privacy amplification.

4.3 gives a detailed construction of randomness extractor based on two-universal hashing.

4.4 introduces one of the key tools in the analysis of our extractor construction, the pretty-good measurement. The idea of the pretty-good measurement is useful all across quantum information, and this module is a stand-alone one.

4.5 puts all the pieces together, and explains how our construction of an extractor gives us a way to achieve privacy amplification, even when the adversary can be quantum.

The material in this module is more technical than previous modules. We’ll also take a more computer-science-y bent, and much of what you’ll learn is of interest outside of quantum information. So hang on! Privacy amplification is essential to making our protocol for key distribution, that you’ll discover next week, work. As usual, you’ll find pointers to many online resources in the “resources” page.