Biblio

This paper presents topological sorting methods to minimize the multiplicative depth of encrypted arithmetic expressions. The research aims to increase compatibility between nonlinear dynamic control schemes and homomorphic encryption methods, which are known to be limited by the quantity of multiplicative operations. The proposed method adapts rewrite rules originally developed for encrypted binary circuits to depth manipulation of arithmetic circuits. The paper further introduces methods to normalize circuit paths that have incompatible depth. Finally, the paper provides benchmarks demonstrating the improved depth in encrypted computed torque control of a dynamic manipulator and discusses how achieved improvements translate to increased cybersecurity.

We consider the problem of implementing a Linear Quadratic Gaussian (LQG) controller on a distributed system, while maintaining the privacy of the measurements, state estimates, control inputs and system model. The component sub-systems and actuator outsource the LQG computation to a cloud controller and encrypt their signals and matrices. The encryption scheme used is Labeled Homomorphic Encryption, which supports the evaluation of degree-2 polynomials on encrypted data, by attaching a unique label to each piece of data and using the fact that the outsourced computation is known by the actuator. We write the state estimate update and control computation as multivariate polynomials in the encrypted data and propose an extension to the Labeled Homomorphic Encryption scheme that achieves the evaluation of low-degree polynomials on encrypted data, with degree larger than two. We showcase the numerical results of the proposed protocol for a temperature control application that indicates competitive online times.