On multivariate cryptosystems based on maps with logarithmically invertible decomposition corresponding to walk on graph

The paper illustrates the concept of the map with logarithmically invertible decomposition. We introduce families of multivariate cryptosystems such that there security level is connected with discrete logarithm problem in Cremona group. The private key of such cryptosystem is a modification of graph based stream ciphers which use stable multivariate maps. Modified version corresponds to a stable map with single disturbance. If the disturbance (or initial condition) allows fast computation then modified version is almost as robust as original one. Methods of modification improve the resistance of such stream ciphers implemented on numerical level to straightforward linearisation attacks.