Producing Quality Pseudorandomness with a Generalized Gauss Continued-Fraction Map
For cryptographers and random number generator designers, this work demonstrates a new chaotic map family as a viable source of high-quality pseudorandomness.
The paper introduces a family of r-continued-fraction maps, generalizing the Gauss map, to generate pseudorandom numbers that outperform standard generators like the Mersenne Twister in statistical tests (Dieharder, PractRand, TestU01).
Well-known chaotic maps, such as the logistic and tent maps, have been used to generate cryptographically secure pseudorandomness, yet we know of no efforts which attempt to use the Gauss continued-fraction map, a known chaotic map, as a starting point for producing quality pseudorandom output. In this paper, we consider the family of $r$-continued-fraction maps, which generalize the Gauss map, and use them to generate pseudorandom output which outperforms many standard generators, such as the Mersenne Twister, in statistical quality, as ascertained by use of the Dieharder, PractRand, and TestU01 suites. In this way, we demonstrate the potential viability of these maps as a starting point for novel generators, and provide practical motivation for further study of the properties of both the exact and finite-precision $r$-continued fraction maps.