Programs are under continuous attack for disclosing secret information, and defending against these attacks is becoming increasingly vital. An attractive approach for protection is to measure the amount of secret information that might leak to attackers. A fundamental issue in computing information leakage is that given a program and attackers with various knowledge of the secret information, what is the maximum amount of leakage of the program? This is called channel capacity. In this paper, two notions of capacity are defined for concurrent probabilistic programs using information theory. These definitions consider intermediate leakage and the scheduler effect. These capacities are computed by a constrained nonlinear optimization problem. Therefore, an evolutionary algorithm is proposed to compute the capacities. Single preference voting and dining cryptographers protocols are analyzed as case studies to show how the proposed approach can automatically compute the capacities. The results demonstrate that there are attackers who can learn the whole secret of both the single preference protocol and dining cryptographers protocol. The proposed evolutionary algorithm is a general approach for computing any type of capacity in any kind of program.

Probabilistic model checking is a formal verification method, which is used to guarantee the correctness of the computer systems with stochastic behaviors. Reachability probabilities are the main class of properties that are proposed in probabilistic model checking. Some graph-based pre-computation can determine those states for which the reachability probability is exactly zero or one. Iterative numerical methods are used to compute the reachability probabilities for the remaining states. In this paper, we focus on the graph-based pre-computations and propose a heuristic to improve the performance of these pre-computations. The proposed heuristic approximates the set of states that are computed in the standard pre-computation methods. The experiments show that the proposed heuristic can compute a main part of the expected states, while reduces the running time by several orders of magnitude.