Modern cryptography is based on security-proofs. We will demonstrate how these work, why they are desirable and what their limitations are.
Even the use of secure primitives like AES or RSA does not guarantee that the end-result is secure as well. In recent years breaks of modern primitives have in fact become exceedingly rare, yet stories like the KRACK-attack or ROBOT keep appearing.
The obvious answer to these problems would be to proof that our protocols are secure. While that may sound great in theory, there are many issues as well: