Theorem to Generate Independently and Uniformly Distributed Chaotic Key Stream via Topologically Conjugated Maps of Tent Map

Table 4

Mean 𝑃 value and the passing ratio in SP800-22 tests with 100 random 𝑥₀.

Test	Mean 𝑃 value	Passing ratio	Results
Frequency (monobit) test	0.4750	0.9900	Success
Frequency test within a block	0.8343	1.0000	Success
Runs test	0.8343	0.9900	Success
Test for the longest run of ones in a block	0.5749	1.0000	Success
Binary matrix rank test	0.0376	1.0000	Success
Discrete fourier transform test	0.2133	0.9800	Success
Nonoverlapping template matching test	0.4871	0.9907	Success
Overlapping template matching test	0.1719	0.9800	Success
Maurer’s “universal statistical” test	0.4750	0.9900	Success
Linear complexity test	0.4944	0.9700	Success
Serial test	0.2739	1.0000	Success
Approximate entropy test	0.4944	0.9800	Success
Cumulative sums test	0.7488	0.9900	Success
Random excursions test	0.3408	0.9871	Success
Random excursions variant test	0.3988	0.9837	Success