Secure Adaptive Filtering

In an increasingly connected world, the protection of digital data when it is processed by other parties has arisen as a major concern for the general public, and an important topic of research. The field of Signal Processing in the Encrypted Domain (SPED) has emerged in order to provide efficient and secure solutions for preserving privacy of signals that are processed by untrusted agents. In this work, we study the privacy problem of adaptive filtering, one of the most important and ubiquitous blocks in signal processing today. We present several use cases for adaptive signal processing, studying their privacy characteristics, constraints, and requirements, that differ in several aspects from those of the already tackled linear filtering and classification problems. We show the impossibility of using a strategy based solely on current homomorphic encryption systems, and we propose several novel secure protocols for a privacy-preserving execution of the least mean squares (LMS) algorithm, combining different SPED techniques, and paying special attention to the error analysis of the finite-precision implementations. We seek the best trade-offs in terms of error, computational complexity, and used bandwidth, showing a comparison among the different alternatives in these terms, and we provide the experimental results of a prototype implementation of the presented protocols, as a proof of concept that showcases the viability and efficiency of our novel solutions. The obtained results and the proposed solutions are straightforwardly extensible to other adaptive filtering algorithms, providing a basis and master guidelines for their privacy-preserving implementation.