First of all, if constructing a formal specification for PKIX is not possible, then that should be telling you that it either needs to be simplified, better specified or scrapped altogether for something better (the latter would require an extremely large transition period, I'm imagining, so the first two are much preferred in this situation).
Otherwise, how can you be sure that any implementation in fact implements it correctly?
> And there had better be no bugs in the formal descriptions you construct from all these specs!
Well, I don't think that is true. You should in fact allow bugs in the formal description, otherwise how will you ever get anything done in such a project?
You see, having a formal description with a bug is much better than having no formal description at all.
If you have no formal description, you can't really tell if your code has bugs. If you have a buggy formal description, then you are able to catch some bugs in the implementation and the implementation can also catch some bugs in the formal description.
Also, some parts of the formal description can catch bugs in other parts of the formal description.
So the end result can be strictly better than the status quo.
> Plus, it's all a moving target.
Sure, but hopefully it's a moving target moving in the direction of simplification rather than getting more complex, otherwise things will just get worse rather than get better, regardless if we keep with the status quo or not. I'm not a TLS expert by any means but I think TLS 1.3 moved in that direction for some parts of the protocol, at least (if I'm not mistaken).
Also, I think you are not fully appreciating that formal verification can be done incrementally.
You can start by doing the minimum possible, i.e. simply verifying that your code is free of runtime errors, which would eliminate all memory safety-related bugs, including Heartbleed.
This would already be better than reimplementing in Rust, because the latter can protect from memory safety bugs but not other runtime bugs (such as division by zero, unexpected panics, etc).
BTW, this minimal verification effort would already eliminate the second bug in this security advisory.
You can then verify other simple properties, even function by function, no complicated models are even necessary at first.
For example, you could verify that your function that verifies a CA certificate, when passed the STRICT flag, is really more strict than when not passed the STRICT flag.
This would eliminate the first bug in this security advisory and all other similar bugs in the same function call-chain.
BTW, what I just said is really easy to specify, and I'm guessing it's also very easy to prove, since I'm guessing that the strict checks are just additional checks, while the normal checks are shared between the two verification modes.
Many other such properties are also easy to prove. The more difficult properties/models, or even full functional verification, can be implemented by more expert developers or even mathematicians.
I think the problem is also that OpenSSL devs, like the vast majority of devs, probably have no desire/intention/motivation/ability to do formal verification, otherwise you could even do this in the OpenSSL code base itself (although that is not ideal because verifying a program written in C requires more manual work than verifying it in a simpler language whose code extracts to C).
I'm also guessing that your budget estimate is an exaggeration since miTLS and EverCrypt, although admittedly projects whose scope has still not reached your ambitious goals (i.e. full functional verification of all layers in the stack), was probably done with a much smaller budget.
And it's not like you can't build on top of that and incrementally verify more properties over time, e.g. more layers of the stack or whatever.
You don't need a huge mega-project, just a starting point, and sufficient motivation.