Recycling random bits in parallel

Shows that r pseudo-random bits can be obtained by concatenating t blocks of r/t pseudo-random bits, where the blocks are generated in parallel. This can be considered as a parallel version of R. Impagliazzo and D. Zuckerman's (1989) method of recycling random bits by doing a random walk on an expander. The proof is based on the fact that t simultaneous independent random walks on an expander graph is equivalent to a random walk on a much larger expander. Impagliazzo and Zuckerman's method of generating the random walk required arithmetic operations with long integers. In the authors' parallel version, the integers involved are much shorter, and different segments of the pseudo-random bits are generated independently in parallel. Optimal speedup is also achieved.