SUMMARY

Homomorphic Encryption is a relatively new cryptographic method which, unlike traditional encryption, allows computations to be preformed on encrypted data. Robotic controllers can take advantage of these new techniques to increase system security by encrypting the entire motion control scheme including: sensor signals, model parameters, feedback gains, and perform computation in the ciphertext space to generate motion commands without a security hole. However, numerous challenges exist which have limited the wide spread adoption of homomorphically encrypted control systems. The following thesis address several of these pressing issues--cryptographic overflow and heterogenous deployment.

Cryptographic overflow is a phenomenon intrinsic to homomorphic ciphers. As encrypted data is computed on the level of 'noise' inside the ciphertext increases, until it becomes too great making decryption impossible, this is known as 'overflow'. The primary contributor to noise growth is multiplication. Thus, this thesis explores topological sorting methods to find semantically equivalent but syntactically simpler control expressions. This allows an encrypted control scheme to preform the same calculation but with fewer multiplications, thus reducing the total amount of noise injected into the system.

Furthermore, encrypted calculations impose a hefty computational burden as compared to its unencrypted counterparts. As such, heterogeneous mix of different computing technologies (i.e. CPU, GPU, FPGA) are needed to achieve real-time signal processing. As such, this thesis explores which aspects of an encrypted control system is best suited for which computing technology and describes a deployment strategy to take advantage of these differences.