Code-based
cryptosystems are promising candidates for post-quantum cryptography,
such as the McEliece and Niederreiter cryptosystems. Their security is
based on the difficulty of decoding a general linear code.
In this thesis, we study the security of algebraic geometry codes in
code-based cryptography. These codes include very well-known families
like generalized Reed-Solomon, BCH and Goppa codes. Furthermore, they
can be described using certain tools, e.g. the theory of algebraic
function fields, which we will focus on.