Choosing a hard-to-guess secret is a prerequisite in many security applications. Whether it is a password for user authentication or a secret key for a cryptographic primitive, picking it requires the user to trade-off usability costs with resistance against an adversary: a simple password is easier to remember but is also easier to guess; likewise, a shorter cryptographic key may require fewer computational and storage resources but it is also easier to attack. A fundamental question is how one can optimally resolve this trade-off. A big challenge is the fact that an adversary can also utilize the knowledge of such usability vs. security trade-offs to strengthen its attack. In this paper, we propose a game-theoretic framework for analyzing the optimal trade-offs in the face of strategic adversaries. We consider two types of adversaries: those limited in their number of tries, and those that are ruled by the cost of making individual guesses. For each type, we derive the mutually-optimal decisions as Nash Equilibria, the strategically pessimistic decisions as maximin, and optimal commitments as Strong Stackelberg Equilibria of the game. We establish that when the adversaries are faced with a capped number of guesses, the user's optimal trade-off is a uniform randomization over a subset of the secret domain. On the other hand, when the attacker strategy is ruled by the cost of making individual guesses, Nash Equilibria may completely fail to provide the user with any level of security, signifying the crucial role of credible commitment for such cases. We illustrate our results using numerical examples based on real-world samples and discuss some policy implications of our work.
Covering attack detection, malware response, algorithm and mechanism design, privacy, and risk management, this comprehensive work applies unique quantitative models derived from decision, control, and game theories to understanding diverse network security problems. It provides the reader with a system-level theoretical understanding of network security, and is essential reading for researchers interested in a quantitative approach to key incentive and resource allocation issues in the field. It also provides practitioners with an analytical foundation that is useful for formalising decision-making processes in network security.  Global threats of terrorism, drug-smuggling, and other crimes have led to a significant increase in research on game theory for security. Game theory provides a sound mathematical approach to deploy limited security resources to maximize their effectiveness. A typical approach is to randomize security schedules to avoid predictability, with the randomization using artificial intelligence techniques to take into account the importance of different targets and potential adversary reactions. This book distills the forefront of this research to provide the first and only study of long-term deployed applications of game theory for security for key organizations such as the Los Angeles International Airport police and the U.S. Federal Air Marshals Service. The author and his research group draw from their extensive experience working with security officials to intelligently allocate limited security resources to protect targets, outlining the applications of these algorithms in research and the real world. The book also includes professional perspectives from security experts Erroll G. Southers; Lieutenant Commander Joe DiRenzo III, U.S. Coast Guard; Lieutenant Commander Ben Maule, U.S. Coast Guard; Erik Jensen, U.S. Coast Guard; and Lieutenant Fred S. Bertsch IV, U.S. Coast Guard.