The rabbit hole goes deeper: how are you sure the compiler is correct? See the paper by John Regehr and his group: http://blog.regehr.org/archives/492 I'm not just saying this randomly in any subject that is concerned with correctness, as Regehr's work clearly shows that the places where compilers make the most mistakes are the places that cryptographic functions play in: numeric calculations at the boundaries of wha…
Turing award lecture by Ken Thompson, "Reflections on trusting trust".
Recommended if you haven't read it already.
https://www.ece.cmu.edu/~ganger/712.fall02/papers/p761-thomp...