Random Number Generators

Random Number Generator: How Do Computers Generate Random Numbers?

People have been using random numbersfor millennia. Therefore, this concept isn't new. From the lottery games 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 end result to random luck.

But gambling aside, randomnesshas numerous uses in science, statistics cryptographyand more. However, using dice, coins or similar materials as a random device comes with limitations.

Due to the mechanical nature of these methods, generatinglarge quantities of random numbers takes a great quantity of effort and time. Because of human creativity, we have more powerful equipment and methods at our disposal.

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 techniques used to generate random numbers. The first methodis based on physical processes, and harvests the source of randomness from a physically occurring phenomenon expected to have random.

The phenomenon is observed out of the computer. It is measured and adjusted to account for biases due to an assessment process. Examples include photoelectric effect, cosmic background radiation, atmospheric noise (which we will utilize in this article) and many further.

Thus, random numbers generated from this randomness can be said to be " true" random numbers.

The hardware comprises a gadget that transforms energy from one form to another (for instance, radiation converts to the form of an electric signal) or an amplifier and an analog-to-digital converter to transform the output into digital number.

What are Pseudorandom Numbers?

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

As an alternative as an alternative to "true" random numbers, the second approach in generating random numbers involves computational algorithms that may produce random results.

How can this be so? The final results are in fact completely determined by an initial value also known as the key value or the key. Therefore, if you knew the key value and the way the algorithm functions you could duplicate the seemingly random results.

Random number generators that are of this type are usually referred to as Pseudorandom numbers generators. They, as consequently, generate Pseudorandom Numbers.

Even though this kind of generator usually doesn't gather any information from sources of naturally occurring randomness, gathering keys is possible when needed.

Let's compare some aspects of true random number generators or TRNGs and pseudorandom number generators , also known as PRNGs.

PRNGs are more efficient than TRNGs. Because they are deterministic, they are useful when you want to replay an entire sequence of random events. This can be very helpful in testing code for instance.

On the other hand TRNGs aren't periodic and perform better in secure roles, like encryption.

A duration is the number of iterations a PRNG go through before it repeats itself. So, all else being equal, a PRNG running more time would require more computing resources to anticipate and crack.

Example Algorithm for Pseudo-Random Number Generator

A computer runs code that is dependent on a set rules to be observed. For all PRNGs the rules are the following:

  1. Accept an initial input code, which is a key or seed.
  2. Apply the seed to the sequence of mathematical calculations to produce the final result. That result is the random number.
  3. Use that resulting random number as the basis for your following iteration.
  4. Repeat the process in order to simulate randomness.

We'll now take a look at an example.

The Linear Congruential Generator

The generator creates a series of random numbers. Based on an initial seed X0 , with integer parameters that act as multipliers, B as the increment and the modulus m, the generator is defined using the linear relationship: Xn (aXn-1 + b)mod mod. For a more programming-friendly formula: X n = (a * X n-1 + b) % m.

Each of them has to meet the following criteria:

  • m > 0.(the modus of the HTML0 is positive),
  • 0 . a m(the multiplier has a positive value, but lower than modulus),
  • 0.<= the modulus is b (the increment is not negative, however it is less then the modulus), and
  • 0equals the value of X 0 < (m)(the seed isn't negative however it is less in comparison to the modulus).

Let's design an JavaScript function that will take the initial values as arguments and then return an assortment of random numbers that are of an appropriate 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

Linear Congruential Generator one of the most popular and oldest PRNG algorithms.

In the case of random number generator algorithms that are able to be executed by computers, they are in use as early as the 1940s and 50s (the Middle-square method and Lehmer generator for instance) and are still being implemented today ( Xoroshiro128+, Squares RNG and many more).

A Sample Random Number Generator

When I was deciding to write this post about embedding the random number generator in a web page, faced a decision to make.

I could've used JavaScript's Math.random()function for the base and generated results in pseudorandom amounts, as I have done in previous articles (see Multiplication Chart Code Your Own Time Table).

But this article itself concerns generating random numbers. So I decided to find out how to gather "true" randomness based data and share my discovery with you.

Below are the "true" Random Number Generator. Make the settings and hit Generate.True Random Number GeneratorBinary Decimal Hexadecimal GenerateResult

The code pulls data from one of the APIs, via Random.org. The site has numerous useful tools that can be customized and comes with a great documentation with it.

The randomness is caused by atmospheric noise. I was able to use asynchronous functions. This is an enormous benefit for the future. The basic function of the system is 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 accepts permit the user to modify random number output. For example, min and max permit users to set upper and lower limits for generated output. Furthermore, base determines if output is printed as binary, decimal or hexadecimal.

Again, I chose this one, however there are a lot more configurations available at the source.

When you press the Generate button When you click Generate, you will see the handleGenerate() function is called. It then invokes the getRandom() asynchronous function, manages error handling, and outputs the result: 

// Output handling const handleGenerate = () => the following code:

The rest of the code deals in HTML style, layout, and styling.

The source code is ready to be embedded and utilized on this page. I divided it into components parts and then provided full instructions. It can be easily modified. You can also modify the functions and styles as the requirements of your business require.

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