@MISC{Giuliani98randomness,pseudorandomness,, author = {Kenneth Giuliani}, title = {Randomness, Pseudorandomness, and its Applications to Cryptography}, year = {1998} }

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Abstract

Introduction What does it mean for something to be random? What is a random number? Is 2 a random number? If one has a truly random number, and then proceeds to show it to everyone in the world and use it in every application, does it remain a random number? Intuitively, we all have a feel for performing some sort of action "at random". It is natural to think of choosing something "randomly " by selecting it out of a set of objects without any indication as to which object is chosen. As a result, the notions of probability and uniformness are often mentioned. But what does this phrase really mean? Can it be defined quantitatively? In particular, can this be done in a mathematical sense? In the field of computer science, there is an overwhelming tendency to avoid answering these questions. A formal definition of randomness is often seen as unnecessary and tedious. In addition, the generation of random numbers is often seen as a "Black Box", i.e. one does not know how it is don