Fully-Homomorphic Encryption for Real-Time Control

An FPGA Implementation

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Currently, encryption is part of daily life, from commercial to industrial applications. Secure, long-distance communication is vital to the safe and reliable operation of industrial feedback control. Utilising public networks as a medium is often cost-effective at the risk of a security breach. Current industrial feedback control systems generally utilise end-to-end encryption to communicate control signals and gains securely. Data has to be decrypted for processing. Homomorphic encryption allows for manipulation of encrypted data. This eliminates the need for decryption to update controller states and calculating control effort. Partially Homomorphic Encryption supports either multiplication or addition of encrypted values, whereas Fully Homomorphic Encryption allows for both. Besides being flexible, Fully Homomorphic Encryption schemes are thought to be quantum safe. Unfortunately, Fully Homomorphic Encryption schemes are computationally expensive limiting practical applications. This thesis presents an enhanced version of the of the popular Fully Homomorphic Encryption scheme by Gentry. The encryption scheme is enhanced through the introduction of three alterations. New notation is introduced that streamlines its description. The main functions that compose the encryption scheme are all replaced with analytical equivalents. The so called reduced cipher is introduced. Rewriting the encryption scheme using the improved notation, analytical functions and reduced cipher leads to a more computationally and memory efficient implementation. The alterations make the encryption more suitable for implementation on Field Programmable Gate Arrays which decreases compute time. Such an implementation is presented and used to demonstrate the efficacy of the enhanced encryption scheme.