Analog Privacy-Preserving Coded Computing

Abstract

The state-of-the-art approaches to privacy-preserving coded computing rely on quantizing the data into a finite field, so that Shamir's secret sharing can be employed. Such coded computing solutions, however, are not properly scalable with the size of dataset, mainly due to computation overflows. To address such a critical issue, we propose a novel extension of certain coded computing schemes to the analog domain. This includes distributed polynomial evaluation and Lagrange coded computing (LCC) that are widely used in the literature. All the operations in the proposed protocols are done over the infinite fields of R/C but for practical implementations floating-point numbers are used. We characterize the privacy of data in our proposed protocols, against any subset of colluding servers up to a certain size, in terms of the distinguishing security (DS) and the mutual information security (MIS) metrics. Also, the accuracy of outcome is characterized in a practical setting assuming operations are performed using floating-point numbers. Consequently, fundamental trade-offs between the accuracy of the outcome and their privacy level are observed in the analog domain and are numerically evaluated. Moreover, we implement analog LCC (ALCC) to perform matrix-matrix multiplication over a batch of matrices. It is observed that ALCC is superior compared to LCC, implemented using fixed-point numbers, assuming both schemes use an equal number of bits to represent data symbols.