We present the first efficient (i.e., polylogarithmic overhead) method for securely and privately processing large data sets over multiple parties with parallel, distributed algorithms. More specifically, we demonstrate load-balanced, statistically secure computation protocols for computing Parallel RAM (PRAM) programs, handling (1/3 - ∈) fraction malicious players, while preserving up to polylogarithmic factors the computation, parallel time, and memory complexities of the PRAM program, aside from a one-time execution of a broadcast protocol per party. Additionally, our protocol has polylog communication locality-that is, each of the n parties speaks only with polylog(n) other parties.
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