Sharing Random Bits with No Process Coordination

We present a method by which any polynomial-time randomized distributed algorithm is transformed in such way that each participating process needs only polylog local random bits and access to a server providing random strings. The method assumes no coordination among the processes. The error probability increases by only an additive negligible term, and the time complexity of each process increases by at most a polylog factor. The main contribution of the paper is in reducing the length of the local random string from (roughly) quadratic (as reported in [Zim97]) to (roughly) linear in the logarithm of the length of the input.