Randomness and complexity

Abstract

Random choices have an unexpected power. From a database search to traffic analysis of the Web, from data mining to cryptography, several hard problems can be efficiently solved with the help of probabilistic algorithms. But random choices are also very elusive. If they were too powerful, some cryptographic algorithms used daily would no longer be trusted. At the heart of this phenomenon, the interplay between randomness and complexity creates a fascinating world that is almost entirely unexplored. This is a world where the most sophisticated algorithms meet their analytical limitations, and the reasons for their effectiveness in real applications still remains a mystery.