Could a fully homomorphic cpu architecture with fully encrypted cache be immune to Spectre and similar side channel attacks? Could this be tested on an FPGA?
Unfortunately, FHE doesn't work this way. You're operating on encrypted data, so performing some branched operations doesn't work due to the security (IND-CPA) security.
IE: You have a value that you need to do `if <condition> then <statement> else <other statement>`
Problematically, if that condition could work, then it would violate the confidentiality of the encrypted value, thus breaking the CPA security. Now there are some workarounds and methods to getting around this problem sometimes, but in many cases it's not possible.
> A cryptosystem that supports arbitrary computation on ciphertexts is known as fully homomorphic encryption (FHE). Such a scheme enables the construction of programs for any desirable functionality, which can be run on encrypted inputs to produce an encryption of the result
I thought that meant the program itself could be fully encrypted, but after a second look it seems that it is just the inputs that are encrypted. Still, other areas of the wiki talk about support for boolean gates and even arbitrary gates. I don't know what to think, but it is motivating me to revisit coding theory :-)
IE: You have a value that you need to do `if <condition> then <statement> else <other statement>`
Problematically, if that condition could work, then it would violate the confidentiality of the encrypted value, thus breaking the CPA security. Now there are some workarounds and methods to getting around this problem sometimes, but in many cases it's not possible.