But of course, math is used in other crypto areas too.I think different crypto areas are basically depending on different underlying assumptions :) For instance, you can check functional encryption for some interesting assumptions.Crypto seems to cover everything related to security that can be formally proved.
I am now styding for first year bachelor's degree in Mathematics for IT. Even though I have a long journey ahead, I am thinking about trying to write a "scientific bachelor's thesis" (that's how we call bachelor's thesis with scientific results on my university in my language) when the time comes.
In the future I would like to major in the same field and possibly continue trying to get a Ph. Is cryptography a field with interesting and imporant problems to solve?
Additionally, we present a number of generic solutions (compilers) that can be applied to independently designed group key exchange protocols in order to enhance security thereof with respect to various goals considered by our security model.
Finally, we present a concrete group key exchange protocol that provably satisfies the apparently strongest currently available formally specified security requirements.
In any case, mathematics are always useful for anything related to computers. But Cryptography plays a role to connect them somehow.
A lot of computer users and developers can get along with a very low understanding of the underlying principles, but the maths are what I studied math in college, but now am a Ph. So math background can be helpful, but cryptography has its own "language".
We give an analytical overview of the state-of-the-art research in this area and identify strengths and weaknesses of many previous approaches.
We suggest a new approach in form of a security model those stronger definitions provide background for more confident security analyzes and proofs.
Moreover, cryptography is an applied field, by which I mean that it has immediate practical applications.
This means money: you can make a very nice living out of cryptographic expertise.