Secrets and Proofs: The Role of Randomness

Secrecy, which lays at the heart of cryptography, is an ancient art. This art form has been tranformed into a science in the last 30 years, using the tools and esthetics of computational complexity theory. Two essential ingredients of these developments are the use of randomization techniques, and redefining mathematical notions such as \"information\", \"randomness\" and \"what constitutes a proof\" from a computationally bounded point of view. In this talk I will describe highlights of the development of modern cryptography, emphasizing the role of these crucial ingredients.