Producing Quality Pseudorandomness with a Generalized Gauss Continued-Fraction Map

Abstract

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 utilize 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 the 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.

arXiv comment18 pages, 6 figures. The algorithm was simplified and retested using the same randomness testing suites as previous versions. The code for the generator is now included in the paper. The mathematical description of the algorithm was substantially revised. Some superfluous analysis of test results was omitted to improve readability. Two paragraphs were added to the concluding section