Random Number Generators

Random Number Generator: How Do Computers Generate Random Numbers?

People have been using random numbersfor millennia, which means this concept isn't new. From the lottery of the ancient city of Babylon as well as roulette tables in Monte Carlo, to dice games in Vegas The aim is to leave the final result to chance.

Although gambling aside, randomnesshas numerous applications in statistics, science, cryptographyand and many more. However, using coins, dice or similar forms of media as a random device comes with its limitations.

Due to its mechanical basis for these methods, generatinglarge quantities of random numbers demands a huge deal of time and work. Thanks to the human brain, we are able to use more effective tools and methods that are available.

Methods of generating random numbers

True Random Numbers

Photo of the analog input digital output processing device. Photo by Harrison Broadbent

Let's consider two principal methods used to generate random numbers. The first methodis one called HTML1. It isbased on physical processes and harvests the source of randomness from some nature phenomenon believed as random.

This kind of phenomenon occurs beyond the computer. It is recorded and adjusted to account for biases resulting from measuring processes. Examples include photoelectric effect, cosmic background radiation, atmospheric noise (which we'll use within this post), and other sources.

So, random numbers created by this kind of randomness are thought to be " true" random numbers.

The technical aspect is comprised of a device that transforms energy from one form to another (for example, radiation is converted into electronic signals) along with an amplifier and an analog-to-digital conversion device to turn the output into a digital number.

What are Pseudorandom Numbers?

Picture of computer code flowing through computer screen. Photo by Markus Spiske.

In addition in lieu of "true" random numbers, the alternative approach that is used for generating random numbers involves computational algorithms that may produce random results.

Why apparently random? Because the final results are in fact completely determined by an initial value often referred to as"the "seed" value . It is also known as the the key. Therefore, if you know the value of the key and how the algorithm functions then you can reproduce the almost random results.

Random number generators of this kind are frequently called Pseudorandom number generators. They, as consequently, generate Pseudorandom Numbers.

Even though this kind of generator generally doesn't collect any information from natural randomness, such gathering of keys can be made feasible if needed.

Let's look at some of the differences between real random number generators, also known as TRNGs and pseudorandom numbers generators, or PRNGs.

PRNGs can be faster than TRNGs. Due to their deterministic nature they are helpful when you want to repeat an event that is random. This helps a great deal in testing your code, for instance.

However, TRNGs are not periodic and work better in areas that require security, such as encryption.

The term "period" refers to the length is the number of times a PRNG has to go through before it begins repeating itself. So, all else being identical, a PRNG having a longer period would take more computer resources to predict and then break.

Example Algorithm for Pseudo-Random Number Generator

The computer's execution is dependent on a set guidelines to be followed. For PRNGs as a whole they are governed by the following:

  1. Accept an initial input code, which is a seed or key.
  2. Apply the seed to a series of mathematical operations to create the result. This result is the random number.
  3. Use that random number as the basis for your following version.
  4. Then repeat the process to emulate randomness.

We'll now take a look at an example.

The Linear Congruential Generator

This generator generates a string of pseudorandom numbers. Based on an initial seed X0 and integer parameters such as a as the multiplier and B as the increment and the modulus m, the generator is described by the linear relationship: The formula is: Xn (aXn-1 + b)mod M. For a more programming-friendly syntax: X n = (a * X n-1 + b) % M.

Each member has to satisfy the following conditions:

  • m > 0(the Modulus can be positive),
  • 0 < a < M(the multiplier of the multiplier, which is positive but less than the modulus),
  • 0= B m (the increment is non negative but less than modulus) and
  • 0The seed is 0 < the m(the seed is non-negative however it is less than its modulus).

Let's design the JavaScript function that accepts the arguments as the starting values to return an array of numbers that are of the specified length: 

  // x0=seed; a=multiplier; b=increment; m=modulus; n=desired array length; const linearRandomGenerator = (x0, a, b, m, n) =>  const results = [] for (let i = 0; i < n; i++)  x0 = (a * x0 + b) % m results.push(x0)  return results

The Linear Congruential Generator (LCG) is among of the oldest and most well-known PRNG algorithms.

For random number generator algorithms that can be used by computers, they date back in the 1950s and 1940s (the Middle-square method and the Lehmer generator for instance) and continue to be developed today ( Xoroshiro128+, Squares RNG, and more).

A Sample Random Number Generator

When I decided to write this article on embedding a random number generator on a web page, made a decision.

It is possible to use JavaScript's Math.random()function as the base and generated output in pseudorandom numbers like I've done in the past (see Multiplication Chart Create Your Own Times Table).

However, this post involves generating random numbers. This is why I wanted to know how to collect "true" randomness based data and then share my findings with you.

So below are the "true" Random Number Generator. Choose the parameters and then hit Generate.True Random Number GeneratorBinary Decimal Hexadecimal GenerateResult

The code retrieves data using some API courtesy of Random.org. This online resource has numerous helpful tools that can be customized and comes with an excellent guideline to go with it.

The randomness comes from atmospheric noise. I was able to utilize the asynchronous function. This is a major benefit in the future. The core function looks like this: 

// Generates a random number within user indicated interval const getRandom = async (min, max, base) =>   const response = await  fetch("https://www.random.org/integers/?num=1&min="+min+"  &max="+max+"&col=1&base="+base+"&format=plain&rnd=new")  return response.text()

The parameters it uses allow the user to alter the output of random numbers. For instance, min and max permit users to define upper and lower levels for output. Also, base determines whether output is printed in decimal, binary or hexadecimal.

Again, I chose this configuration , however, there are many other options available from the source.

When you press the Generate button, that handleGenerate() function is called. It then invokes the getRandom() asynchronous function, manages error handling, and produces results: 

// Output handling const handleGenerate = () => (

The remainder of the code is concerned with HTML structures, look, and styling.

This code can be used to be embedded and utilized on this page. I separated it into component elements and included full instructions. It is easily customizable. You can also alter the functions and styles to suit your requirements demand.

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