Analysis of the Time Series Generated by a New High-Dimensional Discrete Chaotic System

Table 4

Randomness test of by NIST SP800.

Test	8		16		32
	value	Ratio	value	Ratio	value	Ratio
Frequency	0.455937	100/96	0.181557	99/96	0.055361	99/96
Block frequency	0.129620	100/96	0.224821	99/96	0.012650	99/96
Cumulative sums	0.401199	100/96	0.262249	98/96	0.798139	98/96
Runs	0.020548	98/96	0.867692	96/96	0.897763	98/96
Longest run	0.911413	99/96	0.153763	99/96	0.816537	99/96
Rank	0.851383	99/96	0.401199	100/96	0.924076	100/96
FFT	0.004981	98/96	0.699313	99/96	0.657933	98/96
Nonoverlapping template	0.007694	99/96	0.014550	96/96	0.004981	98/96
Overlapping template	0.455937	98/96	0.779188	100/96	0.574903	100/96
Universal	0.383827	99/96	0.779188	100/96	0.867692	99/96
Approximate entropy	0.419021	100/96	0.366918	98/96	0.867692	99/96
Random excursions	0.03200	75/72	0.001254	75/71	0.076389	69/67
Random excursions variant	0.007234	75/72	0.069925	74/71	0.063958	71/67
Serial	0.334538	99/96	0.115387	95/96	0.437274	98/96
Linear complexity	0.678686	96/96	0.534146	99/96	0.304126	95/96

The asterisk “” in Table 4 indicate that the corresponding test failed.