Replication study challenges and new number formats for chaotic pseudo random number generators

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. However, descriptions in articles often are not detailed enough to deduce all decisions unambiguously. To address similar problems in other replication studies for security applications, we propose recommendations for descriptions of numerical experiments on security applications to avoid the above challenges. Moreover, we use the results to propose the use of higher-radix and mixed-radix representations to trade storage size for period length, and investigate if exploiting the symmetry of the logistic map function for number representation is advantageous.