Pseudorandomness and Random Number Generation - Classical Pseudorandom Number Generators

3.1.

3.1.1.

3.1.2.

3.1.2.1.

3.1.2.2.

3.1.3.

3.1.3.1.

3.1.3.2.

3.1.3.3.

3.1.4.

3.1.4.1.

3.1.4.2.

3.2.

3.2.1.

3.2.2.

3.2.3.

3.2.4.

3.3.

3.3.1.

3.3.2.

3.3.3.

3.3.4.

3.4.

3.4.1.

3.4.2.

3.4.3.

3.5.

3.5.1.

3.5.2.

3.5.3.

3.5.4.

3.5.5.

3.5.5.1.

3.5.5.2.

3.6.

3.6.1.

3.6.2.

3.6.2.1.

3.6.2.2.

3.6.2.3.

3.6.3.

3.6.4.

2. Statistical Testing of Random Number Generators

Go to top

4. Cryptographically Secure Pseudorandom Number Generators

Classical Pseudorandom Number Generators

Linear Congruential Generators

LCG Formula and Operation

Parameter Selection

Strengths and Weaknesses

Spectral Test for LCGs

Lagged Fibonacci Generators

Linear-Feedback Shift Registers

Generalised Feedback Shift Registers

Mersenne Twister

Algorithm Overview

Period Length

State Space and Initialization

Statistical Properties

Widespread Use and Limitations

Xorshift Generators

Basic Principle

Variants

Statistical Properties

Performance Characteristics