  With the expansion of cloud services, serious concerns about the privacy of
users' data arise due to the exposure of the unencrypted data to the server
during computation. Various security primitives are under investigation to
preserve privacy while evaluating private data, including Fully Homomorphic
Encryption (FHE), Private Set Intersection (PSI), and others. However, the
prohibitive processing time of these primitives hinders their practical
applications. This work proposes and implements an architecture for
accelerating third-generation FHE with Amazon Web Services (AWS) cloud FPGAs,
marking the first hardware acceleration solution for third-generation FHE. We
also introduce a novel unbalanced PSI protocol based on third-generation FHE,
optimized for the proposed hardware architecture. Several
algorithm-architecture co-optimization techniques are introduced to allow the
communication and computation costs to be independent of the Sender's set size.
The measurement results show that the proposed accelerator achieves $>21\times$
performance improvement compared to a software implementation for various
crucial subroutines of third-generation FHE and the proposed PSI.
