Simple designs for provable security in cryptographic primitives
to design something simply so it can be proved secure


We currently cannot prove the security of anything (well, other than informational secure things such as OTP), without making some assumptions.  The best we can do is:


This is secure, assuming that this abstract problem is hard (but that says nothing about whether the abstract problem is actually hard).  Public key cryptosystems tend to be in this category.
This is secure against these classes of attacks (but that says nothing about other types of attacks).  AES is in this category, as we have a proof of security against linear and differential cryptanalysis.



  and hope that it's not broken in its lifetime?


We don't know how that can be avoided, either in simple or in complex systems.