High-Speed FPGA-Based Pseudorandom Generators with Extremely Long Periods

In this paper, we propose the use of a field programmable gate array (FPGA) to construct high-speed pseudorandom generators with extremely long periods of generated number sequences. The output streams pass all statistical tests from the NIST 800-22 statistical test suite. The numbers are encoded using only 31 bits. We show that by implementing many generators in a single FPGA, a new source of pseudorandom sequences with extremely long periods can be obtained. This source produces sequences that pass the NIST 800-22 statistical tests and the bit rate of the output stream is k times greater, where k is the number of 31-bit generators used. The upper limit of the bit rate depends on the number of 31-bit generators that produce streams passing all NIST 800-22 statistical tests. Although the new generator is not secure, it can be used in cryptography if an auxiliary source of pseudorandom numbers is implemented in the same FPGA.