In recent years, quantitative security techniques have been providing effective measures of the security of a system against an attacker. Such techniques usually assume that the system produces a finite amount of observations based on a finite amount of secret bits and terminates, and the attack is based on these observations. By modeling systems with Markov chains, we are able to measure the effectiveness of attacks on non-terminating systems. Such systems do not necessarily produce a finite amount of output and are not necessarily based on a finite amount of secret bits. We provide characterizations and algorithms to define meaningful measures of security for non-terminating systems, and to compute them when possible. We also study the bounded versions of the problems, and show examples of non-terminating programs and how their effectiveness in protecting their secret can be measured.

Quantitative techniques have been successfully employed in verification of information and communication systems. However, the use of such techniques are still rare in the area of security. In this paper, we present a toolkit that implements transient analysis on a key update method for wireless sensor networks. The analysis aims to find out the probability of a network key being compromised at a specific time point, which result in fluctuations over time for a specific key update method called Leave-based key update. For such a problem, the use of current tools is limited in many ways such as rapidly constructing a compact formal model, computing the time point where the risk is maximum, or terminating the transient analysis after the fluctuations disappear and system stabilizes. Our toolkit, LBTool, is not only resolving the above-mentioned issues, but also demonstrating how to construct models in an analytical way and how to speed up the analysis by eliminating redundant computations. The toolkit can be generalized to other key update methods by replacing the analytical model construction.

We present a simple Markovian framework for modeling packet traffic with variability over several time scales. We present a fitting procedure for matching second-order properties of counts to that of a second-order self-similar process. Our models essentially consist of superpositions of two-state Markov modulated Poisson processes (MMPPs). We illustrate that a superposition of four two-state MMPPs suffices to model second-order self-similar behavior over several time scales. Our modeling approach allows us to fit to additional descriptors while maintaining the second-order behavior of the counting process. We use this to match interarrival time correlations.

We present a modelling framework and a fitting method for modelling second order self-similar behaviour with the Markovian arrival process (MAP). The fitting method is based on fitting to the autocorrelation function of counts a second order self-similar process. It is shown that with this fitting algorithm it is possible closely to match the autocorrelation function of counts for a second order self-similar process over 3-5 time-scales with 8-16 state MAPs with a very simple structure, i.e. a superposition of 3 and 4 interrupted Poisson processes (IPP) respectively and a Poisson process. The fitting method seems to work well over the entire range of the Hurst (1951) parameter.