Table 4 NIST randomness test of the 6D hyperchaotic system.

Frequency (Monobit)

0.7535

0.0424

0.9952

0.3919

0.2855

0.0851

\(\checkmark\)

Frequency Test within a Block

0.2319

0.2855

0.1744

0.9418

0.7998

0.9348

\(\checkmark\)

Runs

0.1651

0.4167

0.3544

0.4480

0.9465

0.6679

\(\checkmark\)

Longest-Run-of-Ones in a Block

0.1424

0.9137

0.5062

0.0695

0.0266

0.2841

\(\checkmark\)

Binary Matrix Rank

0.8796

0.66181

0.2943

0.2132

0.4963

0.0549

\(\checkmark\)

Spectral

0.8890

0.3568

0.2249

0.3953

0.9560

0.9560

\(\checkmark\)

Non-overlapping Template Matching

0.6825

0.5067

0.7783

0.8078

0.3494

0.5334

\(\checkmark\)

Overlapping Template Matching

0.9856

0.8357

0.1745

0.3964

0.8149

0.5544

\(\checkmark\)

Maurer’s “Universal Statistical”

0.7504

0.2339

0.0631

0.3737

0.1681

0.0287

\(\checkmark\)

Linear Complexity

0.4173

0.1617

0.2319

0.5114

0.1563

0.1364

\(\checkmark\)

Statistical

0.3633

0.0919

0.6525

0.5209

0.5642

0.2075

\(\checkmark\)

0.1651

0.4191

0.3554

0.4496

0.9489

0.6715

\(\checkmark\)

Approximate Entropy

0.6642

0.1093

0.8852

0.5689

0.5097

0.3584

\(\checkmark\)

Cumulative Sums (Cusums)

0.6374

0.0291

0.9532

0.5407

0.4791

0.1269

\(\checkmark\)

0.6918

0.5306

0.9781

0.7872

0.6976

0.5463

\(\checkmark\)

Random Excursions

0.0735

0.1226

0.1153

0.2399

0.2041

0.3312

\(\checkmark\)

Random Excursions Variant

0.0113

0.1744

0.3580

0.1790

0.0995

0.0352

\(\checkmark\)