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We i n vestigate the outsourcing of numerical and scienti c computations using the following framework: A customer who needs computations done but lacks the computational resources computing power, appropriate software, or programming expertise to do these locally, w ould like to use an external agent to perform these computations. This currently arises in many practical situations, including the nancial services and petroleum services industries. The outsourcing is secure if it is done without revealing to the external agent either the actual data or the actual answer to the computations. The general idea is for the customer to do some carefully designed local preprocessing disguising of the problem and or data before sending it to the agent, and also some local postprocessing of the answer returned to extract the true answer. The disguise process should be as lightweight as possible, e.g., take time proportional to the size of the input and answer. The disguise preprocessing that the customer performs locally to hide" the real computation can change the numerical properties of the computation so that numerical stability m ust be considered as well as security and computational performance. We present a framework for disguising scienti c computations and discuss their costs, numerical properties, and levels of security. We show that no single disguise technique is suitable for a broad range of scienti c computations but their is an array of disguise techniques available so that almost any scienti c computation could be disguised at a reasonable cost and with very high levels of security. These disguise techniques can be embedded in a very high level, easy-to-use system problem solving environment that hides their complexity.

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The horizontal and vertical components of gravity change when tectonic stresses deform the earth because mass is redistributed relative to the gravity meter. We analyze the change in gravity resulting from deformation in a homogeneous elastic half-space. We derive expressions in closed form which give the change in horizontal and vertical components of gravity measured at the surface for any specified distribution of dislocations at depth. For example, the change in the vertical component of gravity observed by a gravity meter fixed in space above an infinitely long thrust fault is found to be proportional to the local change in height, whereas the change due to a spherically symmetric source of dilatation is zero. Analysis of the change in the horizontal component shows that error in measurements of uplift resulting from changes in level is negligible for these sources.