Differentially Private Coded Computing
Hsuan-Po Liu, Mahdi Soleymani, Hessam Mahdavifar · 2023
Distributed computing has attracted significant recent attention for speeding up large-scale computations by disseminating computational jobs from a central master node across several worker nodes/servers. However, worker nodes are often untrusted and can also collude to gain unauthorized access to sensitive data. Hence, sharing sensitive data with them raises data privacy concerns. Coded computing has emerged as a promising framework for speeding up distributed computing and can be also adapted to address security and privacy concerns utilizing tools from secret sharing and multi-party computing. However, ensuring perfect information-theoretic privacy imposes a strict threshold on the maximum number of colluding workers the protocol can tolerate and, also, necessitates quantizing/mapping data to finite fields. Differential privacy is a widely accepted practical measure to capture the privacy leakage of the shared data. The mainstream approach is then to add perturbations to the data via randomized mechanisms. In this paper, we revisit coded computing, and especially when it is adapted to handle real-valued data, and analyze the privacy guarantees through the lens of differential privacy in terms of the (ϵ,δ)-differential privacy metric, for the first time in the literature. All the computations are done over the field of real/complex numbers and data privacy, in terms of differential privacy, is attained by adding noise terms in a certain structured way. In particular, the noise is added through the secret sharing mechanism (which can be, in principle, decoded and cancelled out at the master) as means of ensuring differential privacy. Furthermore, we propose a differentially private distributed matrix multiplication protocol for matrix multiplications that keeps the privacy of data in the worst adversarial case.