Security aspects of PRNGs with large state spaces

The security of cryptographic functions such as pseudo random number generators (PRNGs) can usually not be mathematically proven. Instead, statistical properties of the generator are commonly evaluated using standardized test batteries on a limited number of output values. This paper demonstrates that valuable additional information about the properties of the algorithm can be gathered by analyzing the state space. As the state space for practical use cases is usually huge, two approaches are presented to make this analysis manageable. Results for a practical application of these approaches to the algorithms AKARI and A5/1 are provided, giving new insights about the suitability of these PRNGs for security applications.