What are the mainstream techniques borrowed from algebraic geometry (or some other branch of mathematics) which are currently used in cryptography/coding theory? I've only heard about a small subset of elliptic curves and hermitian curves. I've also heard about research of hyperelliptic curves but I don't know if some software has already implemented it.
Could you mention some other branches of mathematics being strongly used in cryptography/coding theory and its state? (mainstream/in research)