Dynamical Analysis of a Quadratic Megastable Chaotic Oscillator and Its Application in Biometric Fingerprint Image Encryption

Table 2

The NIST 800-22 test performance results of the x, y, and z state variables of the chaotic QMO system.

Test type	value x	value y	value z	Result
Frequency (monobit) test	0.9378	0.7025	0.2627	Success
Frequency test within a block	0.2204	0.9218	0.1046	Success
Runs test	0.9076	0.7489	0.5165	Success
Test for the longest run of ones in a block	0.1097	0.8477	0.1085	Success
Binary matrix rank test	0.1308	0.4985	0.6488	Success
Discrete Fourier transform test	0.9780	0.0283	0.0651	Success
Nonoverlapping template matching test	0.9294	0.8947	0.4218	Success
Overlapping template matching test	0.6813	0.2080	0.1662	Success
Maurer’s universal statistical test	0.2050	0.8413	0.3269	Success
Linear complexity test	0.0758	0.9445	0.9277	Success
Serial test	0.9903	0.8832	0.4318	Success
	0.9077	0.7490	0.5144	Success
Approximate entropy test	0.2163	0.2737	0.4486	Success
Cumulative sums test	0.8883	0.7848		Success
Random excursions test
(x = −4)	0.0707	0.3537		Success
(x = −3)	0.9046	0.3775		Success
(x = −2)	0.7340	0.3514		Success
(x = −1)	0.7972	0.2836		Success
(x = 1)	0.7192	0.4131		Success
(x = 2)	0.2173	0.7693		Success
(x = 3)	0.1456	0.7260		Success
(x = 4)	0.3911	0.0434		Success
Random excursions variant test
(x = −9)	0.3383	0.9068		Success
(x = −8)	0.2474	0.9917		Success
(x = −7)	0.1845	0.7380		Success
(x = −6)	0.2828	0.8225		Success
(x = −5)	0.4540	0.8617		Success
(x = −4)	0.9120	0.9213		Success
(x = −3)	0.4611	0.7462		Success
(x = −2)	0.2658	0.2229		Success
(x = −1)	0.6513	0.0423		Success
(x = 1)	0.1588	0.1845		Success
(x = 2)	0.1248	0.3968		Success
(x = 3)	0.2663	0.9641		Success
(x = 4)	0.2626	0.6375		Success
(x = 5)	0.0749	0.9040		Success
(x = 6)	0.0451	0.9758		Success
(x = 7)	0.0768	0.7254		Success
(x = 8)	0.0748	0.6256		Success
(x = 9)	0.0367	0.6714		Success

Test not applicable. There are an insufficient number of cycles.