Pengdeng Li

Security Evaluation of the Cyber Networks Under Advanced Persistent Threats

Advanced persistent threats (APTs) pose a grave threat to cyberspace, because they deactivate all the conventional cyber defense mechanisms. This paper addresses the issue of evaluating the security of the cyber networks under APTs. For this purpose, a dynamic model capturing the APT-based cyber-attack-defense processes is proposed. Theoretical analysis shows that this model admits a globally stable equilibrium. On this basis, a new security metric known as the equilibrium security is suggested. The impact of several factors on the equilibrium security is revealed through theoretical analysis or computer simulation. These findings contribute to the development of feasible security solutions against APTs.

Reducing the Spectral Radius of a Torus Network by Link Removal

The optimal link removal (OLR) problem aims at removing a given number of links of a network so that the spectral radius of the residue network obtained by removing the links from the network attains the minimum. Torus networks are a class of regular networks that have witnessed widespread applications. This paper addresses three subproblems of the OLR problem for torus networks, where two or three or four edges are removed. For either of the three subproblems, a link-removing scheme is described. Exhaustive searches show that, for small-sized tori, each of the proposed schemes produces an optimal solution to the corresponding subproblem. Monte-Carlo simulations demonstrate that, for medium-sized tori, each of the three schemes produces a solution to the corresponding subproblem, which is optimal when compared to a large set of randomly produced link-removing schemes. Consequently, it is speculated that each of the three schemes produces an optimal solution to the corresponding subproblem for all torus networks. The set of links produced by each of our schemes is evenly distributed over a network, which may be a common feature of an optimal solution to the OLR problem for regular networks.

Defending against the Advanced Persistent Threat: An Optimal Control Approach

The new cyberattack pattern of advanced persistent threat (APT) has posed a serious threat to modern society. This paper addresses the APT defense problem, that is, the problem of how to effectively defend against an APT campaign. Based on a novel APT attack-defense model, the effectiveness of an APT defense strategy is quantified. Thereby, the APT defense problem is modeled as an optimal control problem, in which an optimal control stands for a most effective APT defense strategy. The existence of an optimal control is proved, and an optimality system is derived. Consequently, an optimal control can be figured out by solving the optimality system. Some examples of the optimal control are given. Finally, the influence of some factors on the effectiveness of an optimal control is examined through computer experiments. These findings help organizations to work out policies of defending against APTs.