Abstract

We survey definitions, known results, and open questions in the area of locally random reductions and explore the ramifications of these reductions in complexity theory. This paper is based on a survey talk given at the DIMACS Workshop on Structural Complexity and Cryptography, Rutgers University, New Brunswick NJ, December 1990. 1 Introduction We consider the question of whether a probabilistic polynomial-time machine A can compute a function f in the following manner. A interacts with one or more machines B 1 , . . ., B k that are not restricted to probabilistic polynomial time. At the end of the interaction, A can use the information obtained from the B i 's to compute f(x). However, the information that A sends to the B i 's is locally random. Informally, this means that no individual B i can use it to figure out what A's private input x is. This study can be motivated by the practical problem of using shared resources for private computations. For example, f may be a financial ...

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