Analyses and Encryption Implementation of a New Chaotic System Based on Semitensor Product

Table 1

NIST test results for the random sequences of the new system, Lorenz system, and Qi system (the number of sequences is 100, and their lengths are 1000000).

Statistical test	value of cL (n)	value of cQ (n)	value of c (n)	Test results of c (n)	Proportion
Frequency	0.000000	0.236810	0.474986	√	100/100
Block frequency (m = 128)	0.289667	0.699313	0.946308	√	99/100
Cumulative sums	0.000000	0.108791	0.779188	√	100/100
Runs	0.000000	0.554420	0.075719	√	100/100
Longest run	0.419021	0.383827	0.289667	√	100/100
Rank	0.851383	0.996335	0.289667	√	100/100
FFT	0.911413	0.911413	0.213309	√	99/100
Nonoverlapping template (m = 9)	0.000003	0.181557	0.983453	√	100/100
Overlapping template (m = 9)	0.181557	0.935716	0.924076	√	100/100
Universal	0.616305	0.289667	0.014550	√	97/100
Approximate entropy (m = 10)	0.000000	0.798139	0.816537	√	99/100
Random excursions	0.008879	0.319084	0.739918	√	64/64
Random excursions variant	0.213309	0.289667	0.949602	√	64/64
Linear complexity (M = 500)	0.010988	0.013569	0.108791	√	99/100
Serial (m = 16)	0.616305	0.028817	0.262249	√	100/100