Pseudorandomness and Random Number Generation

2.

Statistical Testing of Random Number Generators

2.1.

The Need for Empirical Testing

2.1.1.

Detecting Bias and Patterns

2.1.2.

Ensuring Suitability for Applications

2.1.3.

Limitations of Statistical Testing

2.2.

Test Batteries and Suites

2.2.1.

Overview of Test Suites

2.2.2.

2.2.2.1.

2.2.2.2.

Historical Significance

2.2.3.

2.2.3.1.

SmallCrush Battery

2.2.3.2.

2.2.3.3.

BigCrush Battery

2.2.4.

NIST Statistical Test Suite

2.2.4.1.

Scope and Usage

2.2.4.2.

SP 800-22 Standard

2.3.

Common Statistical Tests

2.3.1.

Frequency Tests

2.3.1.1.

2.3.1.2.

Frequency Test within a Block

2.3.2.

2.3.2.1.

Basic Runs Test

2.3.2.2.

Test for Longest Run of Ones

2.3.3.

2.3.3.1.

Binary Matrix Rank Test

2.3.4.

2.3.4.1.

Discrete Fourier Transform Test

2.3.5.

Template Matching Tests

2.3.5.1.

Non-overlapping Template Matching

2.3.5.2.

Overlapping Template Matching

2.3.6.

Complexity Tests

2.3.6.1.

Maurer's Universal Statistical Test

2.3.6.2.

Linear Complexity Test

2.3.7.

2.3.7.1.

2.3.7.2.

Approximate Entropy Test

2.3.8.

Cumulative Tests

2.3.8.1.

Cumulative Sums Test

2.3.8.2.

Random Excursions Test

2.4.

Interpreting Test Results

2.4.1.

Understanding p-values

2.4.2.

Setting Significance Levels

2.4.3.

Pass/Fail Criteria

2.4.4.

Common Pitfalls in Testing

2.4.4.1.

Overfitting to Test Suites

2.4.4.2.

Misinterpretation of Results

2.4.4.3.

Multiple Testing Problem

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1. Introduction to Randomness

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3. Classical Pseudorandom Number Generators