Secure Function Collection with Sublinear Storage

Consider a center possessing a trusted (tamper proof) device that wishes to securely compute a public function over private inputs that are contributed by some network nodes. In network scenarios that support direct communication of nodes with the center, the computation can be done by the nodes encrypting their inputs under the device’s public key and sending the ciphertexts to the center which, in turn, feeds them to the trusted device that computes the function. In many modern networking scenarios, however, the center and the contributing nodes are not directly connected/connectable, in which case the discovery and collection of inputs can only be performed by an agent (or agents) released to the network by the center. This introduces a new set of issues for secure computation. In this work we consider an agent that is released, sweeps the network once and then returns to its origin. The direct solution, in this case, is for the agent to possess a certified public key of the trusted device and for the nodes to contribute their inputs as ciphertexts under this key; once the agent collects all inputs it reconnects with the center for function computation. The above single-sweep simple collection requires the agent to store a linear number of ciphertexts. The goal of this work is to formalize and solve the above problem for a general set of functions by an agent that employs sub-linear storage while maintaining input privacy (an important technical requirement akin of that of “Private Information Retrieval” protocols).