Table 1 NIST SP 800 − 22 statistical test results.

From: 2D logistic map with unit transfer function and modulus operation based pseudorandom number generation for image encryption

 

Logistic map with additional input43 P-value

Non-stationary logistic map38 P-value

Digitalized modified logistic map44P-value

PRNG from chaotic logistic map34P-value

PRNG from mutual coupled 2D logistic map45 P-value

Proposed 2DLMGD P-value42

Proposed technique

Frequency

0.5171

0.6298

0.0061

0.6355

0.4216

0.3461

0.9869

Block frequency

0.1586

0.5621

0.3371

0.4568

0.3324

0.6497

0.6884

Cumulative sums(forward)

0.2147

0.7939

0.4626

0.2655

0.2149

0.2648

0.383331

Cumulative sums(reverse)

0.5351

–

–

0.5585

–

0.6587

0.3723

Runs

0.2753

0.2113

0.1283

0.9673

0.2487

0.8431

0.535966

Longest-runs

0.6699

0.8906

0.8881

0.0123

0.2567

0.8712

0.622422

Rank

0.1546

0.3274

0.4685

0.5749

0.193

0.1045

0.574491

FFT

0.7967

0.6073

0.1626

0.0001

0.41

0.8421

0.156734

Overlapping templates*

0.2757

0.4848

0.8043

0.3795

0.3177

0.4679

0.546487

Non-periodic templates

0.2262

–

0.4970

0.3521

–

0.1246

0.70946

Universal

0.0849

0.8795

0.3241

0.4038

0.4102

0.1002

0.691846

Approximate entropy

0.0147

0.5549

0.4846

0.906

0.3497

0.0846

0.614823

Random-excursions

*

0.7653

0.9742

0.1473

0.0158

0.3014

0.8318

0.5412

Random-excursions variant

*

0.2686

0.5033

0.0013

0.5707

0.2987

0.3479

0.3780

Serial 1

0.3613

0.9005

0.2881

0.9329

0.2419

0.4399

0.885531

Serial 2

0.0365

–

–

–

–

0.1484

0.978562

Linear complexity

0.1478

0.6337

0.0083

0.1252

0.5167

0.3464

0.76795

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