# Research

The research group ''computer security'' headed by Joachim von zur Gathen deals with a variety of subjects from

- computer algebra,
- computational number theory,
- cryptography,
- cryptographic hardware.

We study problems mostly from an algorithmic point of view. Often problems that theoretically pose no more mysteries are algorithmically difficult. Not only solutions (algorithms) have to be found - they should also be fast. Factoring polynomials in theory only means to understand that they decompose uniquely into irreducible factors. Algorithmically, we also want to *find* them and do that efficiently. The same problem for numbers is still open and thought to be unsolvable efficiently. This conjecture is the basis for the security of a prominent cryptographic protocol: RSA.

Our topics include

- factoring polynomials,
- exponentiation,
- functional decomposition of polynomials,
- cryptographic protocols,
- parallel computation,
- complexity theory,
- symbolic integration and summation.