The number field sieve has been designed for factoring large numbers. It was also used for solving the discrete logarithm problem over prime fields.

In this talk, we discuss its applications to class group and unit group computation in a number field.

In the first part, we will describe the class group and the unit group of a number field and explain the relevance of their computation in computational number theory.

After an overview of the state of the art algorithms of such computations (mostly due to Buchmann), we will focus on the number field sieve. We will highlight the similarities between class group computation and factorization (and the resolution of the discrete logarithm problem), and then explain how to use the number field sieve for our purposes. Finally, we will present our implementation and discuss its performances.