No abstract

In this work, we explore distributed optimization problems, as they are often stated in energy and resource optimization. More precisely, we consider systems consisting of a number of subsystems that are solely connected through linear constraints on the optimized solutions. The focus is put on two approaches; namely dual decomposition and alternating direction method of multipliers (ADMM), and we are interested in the case where it is desired to keep information about subsystems secret. To this end, we propose a privacy preserving algorithm based on secure multiparty computation (SMPC) and secret sharing that ensures privacy of the subsystems while converging to the optimal solution. To gain efficiency in our method, we modify the traditional ADMM algorithm.

Privacy preservation in distributed computations is an important subject as digitization and new technologies enable collection and storage of vast amounts of data, including private data belonging to individuals. To this end, there is a need for a privacy preserving computation framework that minimises the leak of private information during computations while being efficient enough for practical usage. This paper presents a step towards such a framework with the proposal of a real number secret sharing scheme that works directly on real numbers without the need for conversion to integers which is the case in related schemes. The scheme offers computations like addition, multiplication, and division to be performed directly on secret shared data (the cipher text version of the data). Simulations show that the scheme is much more efficient in terms of accuracy than its counterpart version based on integers and finite field arithmetic. The drawback with the proposed scheme is that it is not perfectly secure. However, we provide a privacy analysis of the scheme, where we show that the leaked information can be upper bounded and asymptotically goes to zero. To demonstrate the scheme, we use it to perform Kalman filtering directly on secret shared data.

The paper presents a fully distributed private aggregation protocol that can be employed in dynamical networks where communication is only assumed on a neighbor-to-neighbor basis. The novelty of the scheme is its low overhead in communication and computation due to a pre-processing phase that can be executed even before the participants know their input to aggregation. Moreover, the scheme is resilient to node drop-outs, and it is defined without introducing any trusted or untrusted third parties. We prove the privacy of the scheme itself and subsequently, we discuss the privacy leakage caused by the output of the scheme. Finally, we discuss implementation of the proposed protocol to solve distributed optimization problems using two versions of the alternating direction method of multipliers (ADMM).

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