Formulating Cyber-Security as Convex Optimization Problems

Mission-centric cyber-security analysts require a complete overview and understanding of the state of a mission and any potential threats to their completion. To facilitate this, we propose optimization based algorithms that can be used to predict in real-time how an attacker may try to compromise a cyber-mission with a limited amount of resources, based on a model that takes into account potential damage to the mission and probabilistic uncertainty. Two different optimization schemes are considered: one where all the mission data is known a priori to the attacker and another where system identification and a moving horizon optimization is used to produce the estimates based on historical data. Our schemes are compared with real attacks carried our by human players in the 2011 international Capture The Flag (iCTF) hacking competition.