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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.
2) Some crypto researchers are trying to attack the crypto schemes.
A couple of years ago, Wang attacked several prevalent hash functions (which is used as building blocks of many crypto schemes).
Crypto seems to cover everything related to security that can be formally proved.
But here proofs in Crypto often mean ''reductions'' (similar to those in Complexity) and depend on some underlying assumptions such as the well-known big integer factorization problem. Crypto research also covers building cryptographic schemes or attacking them (a.k.a., cryptoanalysis).
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.
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The rapid and promising development of applications and communication systems designed for groups of participants like groupware, computer supported collaborative work systems, or digital conference systems implies exigence of mechanisms providing adequate security properties.
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?