Is there even literature that formalizes the possible types of CPU backdoors and attempts to layout means of defense? Let's assume there's some high level rootkit above any virtualization/signed code/etc. It seems like there's probably a continuum of how much effort is required to utilize this rootkit:
1. Sandboxed user code can control rootkit (through sequence of instructions or whatnot)
2. Raw network packets can control rootkit (what looked like a weirdly-fragmented http request contained extra data that instructed the rootkit)
3. Nondeterministic crypto primitives are actually deterministic (anything encrypted with them looks scrambled, but is easy to decrypt.)
4. Anything that appears to be a crypto instruction sequence is side-channeled into tiny correlated delays on network DMA.
In addition it seems like there's bounds on the complexity of this rootkit (surviving audits), and bounds on what/when detectable changes it can actually make (corrupting deterministic crypto functions on every CPU would be a non-starter).
I'm rambling on this because I think that even assuming widespread microprocessor backdoors, it seems that it should be possible to work our way to creating things that are actually trustable in certain situations. For example, much slower auditable processors handle all network communication and check results from the faster possibly-backdoored microprocessor computing only deterministic functions.