FGb: A Library for Computing Gröbner Bases

International audienceFGb is a high-performance, portable, C library for computing Gröbner bases over the integers and over finite fields. FGb provides high quality implementations of state-of-the-art algorithms ($F_4$ and $F_5$) for computing Gröbner bases. Currently, it is one of the best implementation of these algorithms, in terms of both speed and robustness. For instance, FGb has been used to break several cryptosystems