An Efficient FPGA Random Number Generator using LFSRs and Cellular Automata

Linear Feedback Shift Registers (LFSRs) and Cellular Automata (CA) are commonly used in the implementation of pseudo-random number generators (PRNGs). However, these designs typically cannot produce high quality random numbers due to adjacent bit correlations and the appearance of repetitive structures in the bit sequences. This paper explores the implementation of an efficient hybrid configuration which combines the bit streams from an LFSR and a CA. In particular, designs that are suitable for implementation on a Field Programmable Gate Arrays (FPGAs) rather than on ICs are investigated. The proposed configurations take advantage of the FPGA's ability to realize compact LFSR implementations. Site spacing is utilized to lessen the effect of adjacent bit correlations and hence improve the random number quality. The concept of entropy is one figure of merit employed to evaluate the quality of the random numbers. The suite of statistical tests found in the DIEHARD program is also used in this regard. Hybrid LFSR/CA with varying degrees of site spacing are presented which were found to pass all the DIEHARD tests.