We present sTile, a technique for distributing trust-needing computation onto insecure networks, while providing probabilistic guarantees that malicious agents that compromise parts of the network cannot learn private data. With sTile, we explore the fundamental cost of achieving privacy through data distribution and bound how much less efficient a privacy-preserving system is than a non-private one. This paper focuses specifically on NP-complete problems and demonstrates how sTile-based systems can solve important real-world problems, such as protein folding, image recognition, and resource allocation. We present the algorithms involved in sTile and formally prove that sTile-based systems preserve privacy. We develop a reference sTile-based implementation and empirically evaluate it on several physical networks of varying sizes, including the globally distributed PlanetLab testbed. Our analysis demonstrates sTile's scalability and ability to handle varying network delay, as well as verifies that problems requiring privacy-preservation can be solved using sTile orders of magnitude faster than using today's state-of-the-art alternatives.