Moving permuted congruential generators beyond linear congruential generators

Abstract The permuted congruential generators is a set of pseudorandom number generators released by Melissa E. O’Neill in 2014. The original technical report outlined several lightweight scrambling techniques designed for the linear congruential generator. Each scrambling technique offered some improvement to the quality of the linear congruential generator. However, the real strength of the scrambling techniques was that they could be combined into multiple overall stronger scramblers. The technical report concludes with the creation of the PCG library, a popular pseudorandom number generation library that implements several generators described in the technical report. Starting from the observation that the paper’s work was narrowly focused on implementing their scrambling techniques for specific linear congruential generators, we explore the permuted congruential generator scrambling techniques and their potential for being applied to other pseudorandom number generators by generalizing the scrambling techniques to work across different pseudorandom number generators.