Synchronization of two tree parity machines

One of the problems of cryptography based on the tree parity machine is how to recognize that two tree parity machines are synchronized. In this paper, one of the possible solutions based on polynomial function is described. The proposed method is focused on obtaining of one unique number by polynomial function. Consequently, two possible forms of an attack on the number are presented. The first one is based on brute force attack and the second is done by using genetic algorithm.