In many distributed computing systems, aspects related to security are getting more and more relevant. Security is ubiquitous and could not be treated as a separated problem or a challenge. In our opinion it should be considered in the context of resource management in distributed computing environments like Grids and Clouds, e.g. scheduled computations can be much delayed because of cyber-attacks, inefficient infrastructure or users valuable and sensitive data can be stolen even in the process of correct computation. To prevent such cases there is a need to introduce new evaluation metrics for resource management that will represent the level of security of computing resources and more broadly distributed computing infrastructures. In our approach, we have introduced a new metric called reputation, which simply determines the level of reliability of computing resources from the security perspective and could be taken into account during scheduling procedures. The new reputation metric is based on various relevant parameters regarding cyber-attacks (also energy attacks), administrative activities such as security updates, bug fixes and security patches. Moreover, we have conducted various computational experiments within the Grid Scheduling Simulator environment (GSSIM) inspired by real application scenarios. Finally, our experimental studies of new resource management approaches taking into account critical security aspects are also discussed in this paper.