Complex software and network based information server systems may exhibit failures. Quite often, such failures may not be accidental. Instead some failures may be caused by deliberate security intrusions with the intent ranging from simple mischief, theft of confidential information to loss of crucial and possibly life saving services. Not only it is important to prevent and/or tolerate security intrusions, it is equally important to treat security as a QoS attribute at par with other QoS attributes such as availability and performance. This paper deals with various issues related to quantifying the security attributes of an intrusion tolerant system, such as the SITAR system. A security intrusion and the response of an intrusion tolerant system to an attack is modeled as a random process. This facilitates the use of stochastic modeling techniques to capture the attacker behavior as well as the system's response to a security intrusion. This model is used to analyze and quantify the security attributes of the system. The security quantification analysis is first carried out for steady-state behavior leading to measures like steady-state availability. By transforming this model to a model with absorbing states, we compute a security measure called the "mean time (or effort) to security failure" (MTTSF) and also compute probabilities of security failure due to violations of different security attributes.