The FPGA idea raises security questions of its own - how do you get the bitstream over securely, then the data and results, without leaking the data you're trying to protect or being vulnerable to evil clones of the bitstream? Or the FPGA debug JTAG interface?
Meanwhile Windows is requiring that every laptop have a small crypto processor for its own compliance processes (i.e. bitlocker).
I would assume the bitstream would only contain non-secret implementation details and keys would be loaded at runtime rather than being synthesized into the design.
In terms of moving the data over to the FPGA, I have no idea. But if it's all on the same die, it doesn't seem like there's a big physical attack surface that's different than just doing stuff on the CPU.
Meanwhile Windows is requiring that every laptop have a small crypto processor for its own compliance processes (i.e. bitlocker).