If you read that article you'll see that current approaches don't even attempt some kinds of proofs such as proof of security against side channel attacks. It goes by other names as well such as proof of code correctness:
A major problem with current attempts at proofs is you can at best create a proof based on a system specification and what you want it to be secure against, which basically means you have to already know all possible attacks including zero day attacks. So far the field has resulted in nothing practically useful as far as I know. Homomorphic encryption might be close to being practical for a limited set of problems and could be provably secure for a limited set of attacks, though I don't know if anyone has attempted such a proof yet.
https://en.wikipedia.org/wiki/Provable_security
If you read that article you'll see that current approaches don't even attempt some kinds of proofs such as proof of security against side channel attacks. It goes by other names as well such as proof of code correctness:
https://www.schneier.com/blog/archives/2009/10/proving_a_com...
A major problem with current attempts at proofs is you can at best create a proof based on a system specification and what you want it to be secure against, which basically means you have to already know all possible attacks including zero day attacks. So far the field has resulted in nothing practically useful as far as I know. Homomorphic encryption might be close to being practical for a limited set of problems and could be provably secure for a limited set of attacks, though I don't know if anyone has attempted such a proof yet.