Attacking Tropical Stickel Protocol by MILP and Heuristic Optimization Techniques

Known attacks on the tropical implementation of Stickel protocol involve finding minimal covers for a certain covering problem, and this leads to an exponential growth in the worst case time required to recover the secret key as the used polynomial degree increases. The computational inefficiency of this attack is also observed in practice, unless the number of explored covers is limited, on the expense of the success rate of the attack. Consequently, it can be argued that Alice and Bob can still repel these attacks on tropical Stickel protocol by utilizing very high polynomial degrees, a feasible approach due to the efficiency of tropical operations. The same is true for the implementation of Stickel protocol over some other semirings with idempotent addition (such as the max–min or digital semiring). In this paper, we propose alternative methods to attack the Stickel protocols that avoid solving the covering problem. These methods involve framing the attacks as a mixed integer linear programming (MILP) problem or applying certain heuristic global optimization techniques. We also include a number of numerical experiments to analyze the success rate and the time required to execute the suggested attacks in practice.