In 1998 Gerhard Frey firstly proposed using trace zero varieties for cryptographic purpose. These varieties are subgroups of the divisor class group on a low genus hyperelliptic curve defined over a finite field. These groups can be used to establish asymmetric cryptography using the discrete logarithm problem as cryptographic primitive. Trace zero varieties feature a better scalar multiplication performance than elliptic curves. This allows fast arithmetic in these groups, which can speed up the calculations with a factor 3 compared with elliptic curves and hence speed up the cryptosystem.