Pseudo Random Number Generator (PRNG)

Pseudo-Random Number Generator (PRNG)

A pseudorandom number generator (PRNG) refers to an algorithm that uses mathematical formulas to produce sequences of random numbers. PRNG generates a sequence of numbers approximating the properties of random numbers.
A PRNG starts from an arbitrary starting state using a seed state. Many numbers are generated in a short time and can also be reproduced later if the starting point in the sequence is known. Hence, the numbers are deterministic and efficient.

Characteristics of PRNG

Efficient: PRNG can produce many numbers in a short time and is advantageous for applications that need many numbers.
Deterministic: A given sequence of numbers can be reproduced at a later date if the starting point in the sequence is known. Determinism is handy if you need to replay the same sequence of numbers again at a later stage.
Periodic: PRNGs are periodic, which means that the sequence will eventually repeat itself. While periodicity is hardly ever a desirable characteristic, modern PRNGs have a period that is so long that it can be ignored for most practical purposes.

Why do we need PRNG?

With the advent of computers, programmers recognized the need for a means of introducing randomness into a computer program.
However, surprising as it may seem, it is difficult to get a computer to do something by chance as the computer follows the given instructions blindly and is therefore completely predictable.
It is not possible to generate truly random numbers from deterministic things like computers so PRNG is a technique developed to generate random numbers using a computer.

Applications of PRNG

The generation of pseudo-random numbers is an important and common task in computer programming. While cryptography and certain numerical algorithms require a very high degree of apparent randomness, many other operations only need a modest amount of unpredictability where many random numbers are required and where it is useful that the same sequence can be replayed easily.
Popular examples of such applications are simulation and modeling applications, statistical sampling and other areas where producing an unpredictable result is desirable.
Random number generators are very useful in developing Monte Carlo-method simulations, as debugging is facilitated by the ability to run the same sequence of random numbers again by starting from the same random seed.
Presenting a user with a "Random Quote of the Day". Determining the result for a lottery. Randomly selects music tracks for a background music system. Rolling of dice, coin flipping, shuffling of playing cards through a computer program. Different moves made by a computer game.
Weaker forms of randomness are used in hash algorithms and in creating amortized searching and sorting algorithms.
PRNGs may be used in gambling and cryptography (data encryption) (as long as the seed is secret) though they are not suitable for these applications where it is important that the numbers are really unpredictable. Cryptographically secure pseudorandom number generators (CSPRNG) are used for that purpose.

Different Methods for Pseudo-Random Number Generator

Middle square method (1946) by John von Neumann. Middle Square Weyl Sequence PRNG
Lehmer random number generator (1951). Or, Park–Miller random number generator. Or, Multiplicative linear congruential generator (MLCG). Or, Multiplicative congruential generator (MCG).
Linear congruential generator (LCG) (1958)
Lagged Fibonacci Generator (1958)
Linear feedback shift register (LFSR) (1965)
Inversive congruential generator (ICG) (1986)
Blum Blum Shub (1986)
Naor–Reingold pseudorandom function (1997)

PreviousRandom Number NextLinear Congruential Generator (LCG)

Last updated 4 years ago

Pseudo-Random Number Generator (PRNG)

A pseudorandom number generator (PRNG) refers to an algorithm that uses mathematical formulas to produce sequences of random numbers. PRNG generates a sequence of numbers approximating the properties of random numbers.

A PRNG starts from an arbitrary starting state using a seed state. Many numbers are generated in a short time and can also be reproduced later if the starting point in the sequence is known. Hence, the numbers are deterministic and efficient.

Characteristics of PRNG

Efficient: PRNG can produce many numbers in a short time and is advantageous for applications that need many numbers.

Deterministic: A given sequence of numbers can be reproduced at a later date if the starting point in the sequence is known. Determinism is handy if you need to replay the same sequence of numbers again at a later stage.

Periodic: PRNGs are periodic, which means that the sequence will eventually repeat itself. While periodicity is hardly ever a desirable characteristic, modern PRNGs have a period that is so long that it can be ignored for most practical purposes.

Why do we need PRNG?

With the advent of computers, programmers recognized the need for a means of introducing randomness into a computer program.

However, surprising as it may seem, it is difficult to get a computer to do something by chance as the computer follows the given instructions blindly and is therefore completely predictable.

It is not possible to generate truly random numbers from deterministic things like computers so PRNG is a technique developed to generate random numbers using a computer.

Applications of PRNG

The generation of pseudo-random numbers is an important and common task in computer programming. While cryptography and certain numerical algorithms require a very high degree of apparent randomness, many other operations only need a modest amount of unpredictability where many random numbers are required and where it is useful that the same sequence can be replayed easily.

Popular examples of such applications are simulation and modeling applications, statistical sampling and other areas where producing an unpredictable result is desirable.

Random number generators are very useful in developing Monte Carlo-method simulations, as debugging is facilitated by the ability to run the same sequence of random numbers again by starting from the same random seed.

Presenting a user with a "Random Quote of the Day". Determining the result for a lottery. Randomly selects music tracks for a background music system. Rolling of dice, coin flipping, shuffling of playing cards through a computer program. Different moves made by a computer game.

Weaker forms of randomness are used in hash algorithms and in creating amortized searching and sorting algorithms.

PRNGs may be used in gambling and cryptography (data encryption) (as long as the seed is secret) though they are not suitable for these applications where it is important that the numbers are really unpredictable. Cryptographically secure pseudorandom number generators (CSPRNG) are used for that purpose.

Different Methods for Pseudo-Random Number Generator

Middle square method (1946) by John von Neumann. Middle Square Weyl Sequence PRNG

Lehmer random number generator (1951). Or, Park–Miller random number generator. Or, Multiplicative linear congruential generator (MLCG). Or, Multiplicative congruential generator (MCG).

Linear congruential generator (LCG) (1958)

Lagged Fibonacci Generator (1958)

Linear feedback shift register (LFSR) (1965)

Inversive congruential generator (ICG) (1986)

Blum Blum Shub (1986)

Naor–Reingold pseudorandom function (1997)