Encrypted system identification as-a-service via reliable encrypted matrix inversion

Encrypted computation opens up promising avenues across a plethora of application domains, including machine learning, health-care, finance, and control. Arithmetic homomorphic encryption, in particular, is a natural fit for cloud-based computational services. However, computations are essentially limited to polynomial circuits, while comparisons, transcendental functions, and iterative algorithms are notoriously hard to realize. Against this background, the paper presents an encrypted system identification service enabled by a reliable encrypted solution to least squares problems. More precisely, we devise an iterative algorithm for matrix inversion and present reliable initializations as well as certificates for the achieved accuracy without compromising the privacy of provided I/O-data. The effectiveness of the approach is illustrated with three popular identification tasks.