Privacy-Preserving Gossip Algorithms
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We propose gossip algorithms that can preserve the sum of network values (and therefore the average), and in the meantime fully protect node privacy in terms of their initial values even against external eavesdroppers possessing the entire information flow and network knowledge. At each time step, a node is selected to interact with one of its neighbors via deterministic or random gossiping. Such node generates a random number as its new state, and sends the subtraction between its current state and that random number to the neighbor. Then the neighbor updates its state by adding the received value to its current state. It turns out that this type of privacy-preserving gossiping algorithms can be used as a simple encryption step in a number of consensus-based distributed computation or optimization algorithms, so that we can fully protect the individual algebraic equations or cost functions from being observed or reconstructed throughout the processing of such algorithms. With deterministic gossiping we establish its concrete privacy-preservation guarantee by proving impossibilities for the reconstruction of the node initial values, and potential strategies of adversarial eavesdroppers are investigated in details. With randomized gossiping, the desired privacy encryption is achieved by fully distributed and self-organized node updates. In both cases, we manage to characterize the convergence limits explicitly and analytically, with clear speed of convergence being established. Finally, we attempt to illustrate that the proposed algorithms can be generalized in real-world applications for making trade-offs between resilience against node dropout or communication failure and privacy preservation capabilities.
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