Random Numbers are generated by Random Number Generators (RNG). It plays a vital role in todayâ€™s world where security and entertainment is an important aspect. This post will discuss what is Random Number Generator (RNG), it’s types, How it works, techniques for generation, architecture, applications, advantages and disadvantages.

Table of Contents

**What is Random Number Generator (RNG)**

RNG is designed to generate Random sequence. To generate Random Numbers it requires input which is an information source with positive entropy. The source of entropy could be atmospheric noise, variations in mouse movements or it may be a radioactive source. It has a memory and generates non-likely random variables. Randomness is an event whose state cannot be predicted easily and accurately. Ideally, RNG, is memory less that outputs unlikely sequence of random variables.

**Fig. 1 â€“ Introduction to Random Number Generator**

Random Numbers are widely used in various applications like computer programs, cryptography, casino games, mobile applications like music players, digital games like lottery, lotto etc. The development of quantum cryptography and quantum information processing has given a new dimension to the applications using RNGâ€™s.Â Fig. 2 shows the physical view of RNG. The range of this device as mentioned is 1 to 4 i.e. it allows the selection of 1 to 3 Random Numbers. It displays the numbers generated on LCD and outputs via serial port.

**Fig. 2 â€“ Physical View of RNG**

**Types of Random Number Generators**

There are two types of Random Number Generators. They are:

- True Random Number Generators (Non-Deterministic Random Number Generators)
- Pseudo Random Number Generators (Deterministic Random Number Generators)

**True Random Number Generators**

The numbers generated by this type of device are not predictable by any mathematical logic and and mainly depend on the physical information like atmospheric noise. They are also called as Non-Deterministic Random Numbers generated through hardware.

**Pseudo Random Number Generators**

The Random Numbers generated by this device is predictable as it uses mathematical algorithms through software. They are also called as Deterministic Random Numbers.

**Techniques for Generating Random Numbers**

There are three techniques for generating Random Numbers. They are:

- Linear Congruential Method
- Combined Linear Congruential Generators
- Random Number Streams

**Linear Congruential Method**

These are the most widely used Random Number Generator in use today. This method produces sequence of integers between 0 and m-1 according to the equation:

Where:

a = Multiplier

c = Increment

m = modulus

To generate Uniform Random Numbers, we use the equation:

According to Hull-Dobell theorem, Linear Congruential Generator whose cycle length is m, has full period, if the conditions mentioned, holds good. They are:

- If q is a prime number, that divides m, then q divides a-1.
- The only positive integer that divides both m and c is 1.
- If 4 divides m, then it also divides a-1.

**Combined Linear Congruential Generator**

Some of the application systems require longer period length due to the increase in complexity of the system. Hence two or more multiplicative congruential generators are combined to achieve this.

Let the nth output from k different multiplicative Congruential Generators be Xn1, Xn2, â€¦â€¦. Xnk.

Therefore, Xj is defined as :

**X _{n+1, j Â }= ( a_{j}X_{n }+ c_{j }) mod m_{j }**, Where;

**m _{j }= **prime modulus

**a _{j }= **multiplier

**c = **increment

**Random Number Streams**

Random Number Stream refers to the starting seed taken from the sequence X_{0, }X_{1 }â€¦â€¦. X_{p. }and considering â€˜bâ€™ values apart and the Stream â€˜iâ€™ could be defined by starting seed i.e.

S_{i }= X _{b(i â€“ 1)}

Seed is an integer value that initializes Random Number Sequence for a Generator. If the RNG has k streams, then it acts like k distinct virtual RNGâ€™s.

**Architecture of RNG**

The system consists of modules namely:

- Sensor Module
- Generation Module

**Fig. 3 â€“ Architecture of Random Number Generator**

**Sensor Module **

This module is responsible for capturing data. Sensor acquires the data and provides an interface to transfer the collected information to the computer. The sensor converts physical information such as noise (analog) signal to digital signal.

**Generation Module**

In this module, the process ofÂ Post-processing happens where the data is binarized. This data is transferred to output module.

**Output Module**

The output module accepts the binary data and stores it as a file. Random Number is generated using this file and is displayed.

**How does RNG Work**

Let us consider RNG, that uses the randomness of Radioactive decay as an entropy source to generate random numbers. According to Quantum Mechanics, the decay of atoms is random and cannot be predicted. The System has PIC (Programmable Interface Controller) Microcontroller and special type of counter called as Geiger Counter which detects ionizing radiation. Shift Registers are used that act as RAM for the system.

**Fig. 4 â€“ Working of RNG**

The entropy or the random event acts as input to the system. The counter detects the radiation and is controlled by the Microcontroller. The Microcontroller rotates the numbers inside the Register which is around 10,00,000 numbers per second. When the Microcontroller detects the random event (Radioactive particle), it terminates the rotation of numbers, reads the current number and stores in Shift Register.

Shift Registers act as RAM for the system. The Shift Register accepts the input and shifts for every clock cycle and outputs the data on LCD via serial port.Â Thus sequence of numbers are generated and these numbers are known as Random Numbers.

**Applications of Random Number Generator**

The applications include:

- The Random numbers are widely used in Digital games.
- They are also used in Statistical Sampling.
- Used in Cryptography, computations in statistical physics.
- Widely used in casino games like Roulette wheel.
- Also used in Radio communications.
- RNGâ€™s are used for numerical analysis.

**Advantages of Random Number Generator**

The advantages are:

- RNGâ€™s provide security to diverse systems.
- Pseudo Random Generators are easier to implement.
- Pseudo Random Numbers can be generated faster compared to True Random Numbers.
- Reproduction of the existing sequence is possible if the initial point is known.

**Disadvantages of Random Number Generator**

The disadvantages are:

- Few Pseudo Random Generators have shorter periods for some Seed values.
- True Random Number Generators are expensive to implement.
- The random numbers generated by Linear Congruential Generator depends on the bit position and lower bits will be less random than the upper bits.

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