The discrete logarithm problem plays a crucial rule in public key cryptosystems. Usually one takes an elliptic curve for which all known algorithms have exponential complexity. However, such curves allow a so-called ’side channel attack’ - which may break the system - since the addition demands two different formulas (depending on doubling or adding two different points). In 2007 H. Edwards discovered a new class of curves which are closely related to elliptic curves but for which the addition law is described by only one formula. We shall give an introduction to this new class of curves which may have an impact on public key cryptosytems.