I know that most of the math related to cryptography is number theory/abstract algebra/probability, but I was wondering if there are some algorithms that make use of other fields of math like real/complex analysis, differential equations or linear algebra? Also, what is highest level of mathematics required for cryptography?
It would be hard to find a category of mathematics not related in some way to cryptography, here is a list of applied mathematics by subject area. Even very abstract mathematics could be future cryptographic tools waiting to happen:
"A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. "