This paper discusses an asymmetric cryptosystem based on fractions, the Rk-system, which can be implemented fast using only additions and multiplications. Also it is very simple to initialize the system and to generate new keys. The Rk-system makes use of the difficulty to compute the numerator and the denumerator of a fraction only knowing the rounded floating point representation. It is also based on the difficulty of a simultaneous diophantine approximation with many parameters and only a little error bound.