This book provides an introduction to the key concepts of Fully Homomorphic Encryption (FHE)-based computing, and discusses the challenges associated with architecting FHE-based computing systems. Readers will see that due to FHE's ability to compute on encrypted data, it is a promising solution to address privacy concerns arising from cloud-based services commonly used for a variety of applications including healthcare, financial, transportation, and weather forecasting. This book explains the fundamentals of the FHE operations and then presents an architectural analysis of the FHE-based computing. The authors also highlight challenges associated with accelerating FHE on various commodity platforms and argue that the FPGA platform provides a sweet spot in making privacy-preserving computing plausible.