Analysis and design of digital PRNGs based on the discretized sawtooth map

In this paper, the sawtooth map in its digital implementation is investigated as a source of pseudo-random binary numbers. Effects of precision in the arithmetic blocks used to implement the map, as well as approximation strategies and value of the map slope are discussed in terms of period and statistical properties of bits generated. Optimum values of design parameters to achieve a good quality of output bit sequences are identified, and an area-efficient implementation on a programmable device is discussed. Comparison to traditional PRNGs based on Linear-Feedback Shift Registers shows that the discretized sawtooth map is a viable solution for implementing integrated PRNG circuits.