A set of clawfree functions is a set of functions that are all easily computable, but for which it is hard to simultaneously find preimages of an element under different functions. In this thesis we develop a formalism for describing such functions, and show several techniques for building them, some new and others well known. We show how clawfree functions can be extremely useful, in the construction of for example collision free hash functions and of cryptographic protocols in general. In particular, we show how to solve the famous multiparty computation problem, while achieving un conditional privacy protection for one participant. This is the optimal result in the model of communication we consider
