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.

To decouple the multi-axis motion in the 6 degrees of freedom magnetically levitated actuators (MLAs), this paper introduces a numerical method to model the force and torque distribution. Taking advantage of the Gaussian quadrature, the concept of coil node is developed to simplify the Lorentz integral into the summation of the interaction between each magnetic node in the remanence region and each coil node in the coil region. Utilizing the coordinate transformation in the numerical method, the computation burden is independent of the position and the rotation angle of the moving part. Finally, the experimental results prove that the force and torque predicted by the numerical model are rigidly consistent with the measurement, and the force and torque in all directions are decoupled properly based on the numerical solution. Compared with the harmonic model, the numerical wrench model is more suitable for the MLAs undertaking both the translational and rotational displacements.