Random number generators Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular ou ...

are important in many kinds of technical applications, including

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

computer studies (e.g.,

Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...

simulations),

cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

and

gambling Gambling (also known as betting or gaming) is the wagering of something of value ("the stakes") on a random event with the intent of winning something else of value, where instances of strategy are discounted. Gambling thus requires three el ...

(on

game server A game server (also sometimes referred to as a host) is a server which is the authoritative source of events in a multiplayer video game. The server transmits enough data about its internal state to allow its connected clients to maintain their ...

s). This list includes many common types, regardless of quality.

Pseudorandom number generators (PRNGs)

Whenever using a

pseudorandom number generator A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generate ...

, keep in mind

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

's dictum "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." The following algorithms are pseudorandom number generators.

Cryptographic algorithms

Cipher algorithms and

cryptographic hash A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output ...

es can be used as very high-quality pseudorandom number generators. However, generally they are considerably slower (typically by a factor 2-10) than fast, non-cryptographic random number generators. These include: *

Stream cipher stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream ...

s. Popular choices are

Salsa20 Salsa20 and the closely related ChaCha are stream ciphers developed by Daniel J. Bernstein. Salsa20, the original cipher, was designed in 2005, then later submitted to the eSTREAM European Union cryptographic validation process by Bernstein. Cha ...

ChaCha Cha-Cha, Cha Cha, ChaCha or Chacha may refer to: Music * Cha-cha-cha (dance), a dance of Cuban origin * Cha-cha-cha (music), a genre of Cuban music * ''Cha Cha'' (album), a 1978 album by Herman Brood & His Wild Romance * ''Cha Cha'' (soundtrack), ...

(often with the number of rounds reduced to 8 for speed),

ISAAC Isaac; grc, Ἰσαάκ, Isaák; ar, إسحٰق/إسحاق, Isḥāq; am, ይስሐቅ is one of the three patriarchs of the Israelites and an important figure in the Abrahamic religions, including Judaism, Christianity, and Islam. He was the ...

HC-128 HC-256 is a stream cipher designed to provide bulk encryption in software at high speeds while permitting strong confidence in its security. A 128-bit variant was submitted as an eSTREAM cipher candidate and has been selected as one of the four fi ...

and

RC4 In cryptography, RC4 (Rivest Cipher 4, also known as ARC4 or ARCFOUR, meaning Alleged RC4, see below) is a stream cipher. While it is remarkable for its simplicity and speed in software, multiple vulnerabilities have been discovered in RC4, ren ...

. * Block ciphers in counter mode. Common choices are AES (which is very fast on systems supporting it in hardware),

TwoFish In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard contest, but it was not selected for standardization. Twof ...

Serpent Serpent or The Serpent may refer to: * Snake, a carnivorous reptile of the suborder Serpentes Mythology and religion * Sea serpent, a monstrous ocean creature * Serpent (symbolism), the snake in religious rites and mythological contexts * Serp ...

and

Camellia ''Camellia'' (pronounced or ) is a genus of flowering plants in the family Theaceae. They are found in eastern and southern Asia, from the Himalayas east to Japan and Indonesia. There are more than 220 described species, with some controversy ...

. *

Cryptographic hash function A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output re ...

s A few cryptographically secure pseudorandom number generators do not rely on cipher algorithms but try to link mathematically the difficulty of distinguishing their output from a `true' random stream to a computationally difficult problem. These approaches are theoretically important but are too slow to be practical in most applications. They include: *

Blum–Micali algorithm The Blum–Micali algorithm is a cryptographically secure pseudorandom number generator. The algorithm gets its security from the difficulty of computing discrete logarithms.Bruce Schneier, ''Applied Cryptography: Protocols, Algorithms, and Source ...

(1984) *

Blum Blum Shub Blum Blum Shub (B.B.S.) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub that is derived from Michael O. Rabin's one-way function. __TOC__ Blum Blum Shub takes the form :x_ = x_n^2 \bmod M, where ...

(1986) *

Naor–Reingold pseudorandom function In 1997, Moni Naor and Omer Reingold described efficient constructions for various cryptographic primitives in private key as well as public-key cryptography. Their result is the construction of an efficient pseudorandom function. Let ''p'' and ''l' ...

(1997)

Random number generators that use external entropy

These approaches combine a pseudo-random number generator (often in the form of a block or stream cipher) with an external source of randomness (e.g., mouse movements, delay between keyboard presses etc.). * /dev/random –

Unix-like A Unix-like (sometimes referred to as UN*X or *nix) operating system is one that behaves in a manner similar to a Unix system, although not necessarily conforming to or being certified to any version of the Single UNIX Specification. A Unix-li ...

systems *

CryptGenRandom CryptGenRandom is a deprecated cryptographically secure pseudorandom number generator function that is included in Microsoft CryptoAPI. In Win32 programs, Microsoft recommends its use anywhere random number generation is needed. A 2007 paper from ...

–

Microsoft Windows Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for serv ...

Fortuna Fortuna ( la, Fortūna, equivalent to the Greek goddess Tyche) is the goddess of fortune and the personification of luck in Roman religion who, largely thanks to the Late Antique author Boethius, remained popular through the Middle Ages until at ...

RDRAND RDRAND (for "read random"; known as Intel Secure Key Technology, previously known as Bull Mountain) is an instruction for returning random numbers from an Intel on-chip hardware random number generator which has been seeded by an on-chip entropy s ...

instructions (called ''Intel Secure Key'' by

Intel Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the developers of the x86 seri ...

), available in Intel x86 CPUs since 2012. They use the AES generator built into the CPU, reseeding it periodically. *''True Random Number Generator using Corona Discharge.''True Random Number Generator using Corona Discharge: Indian Patent Office. Patent Application Number: 201821026766 *

Yarrow ''Achillea millefolium'', commonly known as yarrow () or common yarrow, is a flowering plant in the family Asteraceae. Other common names include old man's pepper, devil's nettle, sanguinary, milfoil, soldier's woundwort, and thousand seal. The ...

References

External links

SP800-90 series on Random Number Generation

NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

Random Number Generation in the GNU Scientific Library Reference Manual
* ttp://www.lomont.org/Math/Papers/2008/Lomont_PRNG_2008.pdf Chris Lomont's overview of PRNGs, including a good implementation of the WELL512 algorithmbr>Source code to read data from a TrueRNG V2 hardware TRNG
{{DEFAULTSORT:Random number generators Computing-related lists Mathematics-related lists * *

Pseudorandom number generators (PRNGs)

Cryptographic algorithms

Random number generators that use external entropy

See also

References

External links