Discreetly Distributing Computation via Self-Assembly

One aspect of large networks, such as the Internet, is the colossal amount of computation its nodes could perform if that computation were distributed efficiently. The Internet has already led to solving some problems, e.g., NP-complete problems, that were unlikely to have been solved on individual computers. However, the methods leading to those solutions disclosed inputs, algorithms, and outputs to the Internet nodes. It has even been argued in the literature that it is not possible to ask an entity for help with solving NP-complete problems without disclosing the input and algorithm. In this paper, we present an architectural style that distributes computation over a network discreetly, such that no small group of computers (asymptotically smaller than Θ(n log n) for an n-bit input) knows the algorithm or the input. The style abstracts away the distribution and only requires writing non-parallel code, automating in turn the parallelization of computation. Further, the style is faultand adversary-tolerant (malicious, faulty, and unstable nodes may not break the computation) and scalable (communication among the nodes does not increase with network or problem size). Systems designed and constructed according to the style free the architect from having to worry about these non-functional properties. We formally argue that our architectural style has all three properties: discreetness, fault and adversary tolerance, and scalability.