Random number generators using Cellular Automata implemented on FPGAs

Abstract

Cellular Automata (CA) have been found to make good pseudo-random number generators (PRNGs), and these CA-based PRNGs are well suited for implementation on Field Programmable Gate Arrays (FPGAs). To improve the quality of the random numbers that are generated, the basic CA structure is enhanced in two ways. First, the addition of a super-rule to each CA cell is considered. The resulting Self-Programmable CA (SPCA) uses the super-rule to determine when to make a dynamic rule change in each CA cell. The super-rule takes its inputs from neighboring cells and can be considered itself a second CA working in parallel with the main CA. When implemented on an FPGA, the use of lookup tables in each logic cell removes any restrictions on how the super-rules should be defined. Second, a hybrid configuration is formed by combining a CA with a Linear Feedback Shift Register (LFSR). This is advantageous for FPGA designs due to the compactness of the LFSR implementations. The suite of statistical tests found in the DIEHARD program is utilized to evaluate the quality of random numbers. Some of the hybrid CA/LFSR were found to pass all the DIEHARD tests. P 44th IEEE Southeastern Symposium on System Theory

Survey on hardware implementation of random number generators on FPGA: Theory and experimental analyses

“…Ranq1 is a MCG working modulo 2 64 , while its seed is produced by a 64-bits right XORshift [36]. Let us first recall that the XORshift takes an input and iteratively executes an exclusive or (XOR) of the binary number with a bit shifted translation (left and right) of itself.…”

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AEC: A Practical Scheme for Authentication with Error Correction

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