Analysis of FIPS 140-2 Test and Chaos-Based Pseudorandom Number Generator

Pseudo random numbers are used for various purposes. Pseudo random number generators (PRNGs) are useful tools to provide pseudo random numbers. The FIPS 140-2 test issued by the American National Institute of Standards and Technologyhas been widely used for the verifications the statistical properties of the randomness of the pseudo random numbers generated by PRNGs. First this paper analyzes the FIPS 140-2 test. The results show that • The required interval of the FIPS140-2 Monobit Test corresponds to the confident interval with significant level α = 0.0001(1− α). • The required interval of the FIPS140-2 Pork Test corresponds to χ test with significant level α = 0.0002(1 α). • The required intervals of the FIPS140-2 Run Test correspond to the confident interval with significant level α = 0.00000016(1− α). Second this study considers a novel chaotic map (NCM), whose prototype is the Lorenz three-dimensional Lorenz chaotic map. A NCP -based CPRNG is designed. Using the FIPS 140-2 test measures the 1000 keystreams randomly generated by the RC4 algorithm, and the 1000 keystreams generated by the CPRNG with perturbed randomly initial conditions in the range | | ∈ [10−16, 10−4]. The results show that the statistical properties of the randomness of the sequences generated via the CPRNG and the RC4 do not have significant differences. The results confirm once again that suitable designed chaos-based PRNGs may generate sound random sequences, in particular for a replacement for the one-time pad system.