Implementation and Analysis of the Nonlinear Decomposition Attack on Polycyclic Groups

Abstract

Around two years ago, Roman\u27kov introduced a new type of attack called the nonlinear decomposition attack on groups with solvable membership search problem. To analyze the precise efficiency of the algorithm, we implemented the algorithm on two protocols: semidirect product protocol and Ko-Lee protocol. Because polycyclic groups were suggested as possible platform groups in the semidirect product protocol and polycyclic groups have a solvable membership search problem, we used poly- cyclic groups as the platform group to test the attack. While the complexity could vary regarding many different factors within the group, there was always at least one exponential factor in the complexity analysis of the algorithm