Fully homomorphic encryption (FHE) allows an untrusted party to efficiently compute any compact function directly on ciphertexts. When made available over an untrusted cloud server, data is submitted and returned in encrypted form, and the execution remains secure against malicious users. Early FHE proposals had rather disappointing efficiencies. Recently new FHE schemes based on the difficulty of the learning with errors (LWE) problem emerged with orders of magnitude improvement over earlier constructions. This project addresses a variety of problems in engineering, computer science and mathematics all centered around the goal of bringing LWE-based homomorphic encryption techniques closer to practice which could impact the way society utilizes computing services. The project team explores three research components. The first research component investigates algorithmic optimizations to speed up LWE-based schemes, and to develop optimized software implementations on CPUs and graphics processing units. Specifically, the investigators apply optimization techniques including changing the representation of the operands, batching, and precomputation. The team also aims to build a LWE-FHE based homomorphic instruction set. In another research component the project team develops application specific custom hardware to overcome inefficiencies of software platforms. Finally, we investigate the customization of parameters to match the needs of select lightweight cryptographic primitives.
TWC: Small: Towards Practical Fully Homomorphic Encryption