High quality uniform random number generation through LUT optimised linear recurrences

This paper describes a class of FPGA-specific uniform random number generators with a 2^k - 1 length period, which can provide k random bits per cycle for the cost of k lookup tables (LUTs) and k flip flops. The generator is based on a binary linear recurrence, but with a recurrence matrix optimised for LUT based architectures. It avoids many of the problems and inefficiencies associated with LFSRs and Tausworthe generators, while retaining the ability to efficiently skip ahead in the sequence. In particular we show that this class of generators produces the highest sample rate for a given area compared to LFSR and Tausworthe generators. The statistical quality of this type of generators is very good, and can be used to create small and fast generators with long periods which pass all common empirical tests, such as Diehard, Crush, Big-Crush and the NIST cryptographic tests