Pairwise Independence and Derandomization gives several applications of the following paradigm, which has proven extremely powerful in algorithm design and computational complexity. First, design a probabilistic algorithm for a given problem. Then, show that the correctness analysis of the algorithm remains valid even when the random strings used by the algorithm do not come from the uniform distribution, but rather from a small sample space, appropriately chosen. In some cases this can be proven directly (giving "unconditional derandomization"), and in others it uses computational assumptions, like the existence of 1-way functions (giving "conditional derandomization"). Pairwise Independence and Derandomization is self contained, and is a prime manifestation of the "derandomization" paradigm. It is intended for scholars and graduate students in the field of theoretical computer science interested in randomness, derandomization and their interplay with computational complexity.

An n-component system contains n components, where each component may be either failing or working. Each component i is failing with probability pi independently of the other components in the system. A system state is a specification of the states of the n components. Let F, the set of failure states, be a specified subset of all system states. In this paper we develop Monte Carlo algorithms to estimate Pr[F], the probability that the system is in a failure state.

A new formula for the probability of a union of events is used to express the failure probability fo an n-component system. A very simple Monte-Carlo algorithm based on the new probability formula is presented. The input to the algorithm gives the failure probabilities of the n components of the system and a list of the failure sets of the system. The output is an unbiased estimator of the failure probability of the system. We show that the average value of the estimator over many runs of the algorthm tends to converge quickly to the failure Probability of the system. The overall time to estimate the failure probability with high accuracy compares very favorably with the execution times of other methods used for solving this problem.

This separation allows us to independently address the important issues of how much security is preserved by a reduction and how many public random bits are used in the reduction. To exemplify these new definitions, we present reductions from weak one-way permutations to one- way permutations with strong security preserving properties that are simpler than previously known reductions."