Chaotic Pseudo Random Number Generators: A Case Study on Replication Study Challenges

Abstract

Chaotic Pseudo Random Number Generators have been seen as a promising candidate for secure random number generation. Using the logistic map as state transition function, we perform number generation experiments that illustrate the challenges when trying to do a replication study. Those challenges range from uncertainties about the rounding mode in arithmetic hardware over chosen number representations for variables to compiler or programmer decisions on evaluation order for arithmetic expressions. We find that different decisions lead to different streams with different security properties, where we focus on period length, but descriptions in articles often are not detailed enough to deduce all decisions unambiguously. Similar problems might, to some extent, appear in other types of replication studies for security applications. Therefore we propose recommendations for descriptions of numerical experiments on security applications to avoid the above challenges.