Computer security continues to grow in importance as computation and storage of sensitive data is increasingly outsourced to cloud-based computing services. Moreover, with the rapid development of quantum computers, we expect to see new classes of threats looming that can defeat the security of long trusted cryptosystems. Fully Homomorphic Encryption (FHE) is a potential solution to address both challenges. FHE enables computation directly on encrypted data, supporting secure computations on untrusted computing servers. The security of many modern FHE schemes is based on the hardness of the Ring Learning with Errors problem, which is presumed to be resistant to quantum attacks.

Although FHE offers a high degree of security, it suffers from prohibitively large computational costs. In the first year of this project, we characterized FPGA-based and GPU-based implementations of polynomial multiplication. The goal was to accelerate its two major computationally-expensive operations: 1) modular reduction and 2) the Number Theoretic Transform (NTT). We have already published two papers on our progress on this project [1][2] and have a paper under review describing the range of microarchitectural extensions that we have explored. We have leveraged a Xilinx FPGA in our work to implement some of our microarchitectural enhancements, which has allowed us to get timing, power and area parameters. From our analysis of FHE during the first year of this project, we have identified key bottlenecks that remain in our GPU-based FHE implementation. Our focus moving forward it to consider addressing these bottlenecks from both a memory technology solution and algorithmic optimizations.