Game Design for Better Security of Combination Locks

Dial locks are commonly used to secure a person's items. Commercially available dial locks often use four or five wheels of letters, allowing a user to select a word as a combination. In order to evaluate the security of these locks, we create a game, with an instance created by the lock designer, and played by a lock owner and a thief. In the game, the lock owner chooses a word as a combination, and the thief creates a brute force strategy to try all possible combinations that yield words until the combination is found. To accomplish the task, the thief will solve a version of the Probabilistic Travelling Salesman Problem (PTSP) by creating an a priori tour through all the words a lock can create. The goal for the game designer, then, is to create a lock configuration that maximizes the expected length of the best possible PTSP tour. This paper describes a Genetic Algorithm (GA) approach to design a near-optimal game, i.e. a lock configuration that makes it as difficult for the thief to crack. An analysis of the output of the GA shows that the locks that the system creates are significantly more secure than both commercial locks, in the context of this game..