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词条 List of random number generators
释义

  1. Pseudorandom number generators (PRNGs)

  2. Cryptographic algorithms

  3. Random number generators that use external entropy

  4. Hardware (true) random number generators (TRNGs)

  5. Random number servers

  6. Well-known PRNG APIs

  7. See also

  8. References

  9. External links

{{external links|date=June 2016}}

Random number generators are important in many kinds of technical applications, including physics, engineering or mathematical computer studies (e.g., Monte Carlo simulations), cryptography and gambling (on game servers).

This list includes many common types, regardless of quality.

Pseudorandom number generators (PRNGs)

Whenever using a pseudorandom number generator, keep in mind John von Neumann's dictum "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin."[1]

The following algorithms are pseudorandom number generators.

GeneratorDateFirst proponentsReferencesNotes
Middle-square method1946J. von Neumann[2]In its original form, it's of poor quality and of historical interest only.
Lehmer generator1951D. H. Lehmer[3]One of the very earliest and most influential design.
Linear congruential generator (LCG)1958W. E. Thomson; A. Rotenberg[4][5]A generalisation of the Lehmer generator and historically the most influential and studied generator.
Lagged Fibonacci generator (LFG)1958G. J. Mitchell and D. P. Moore[6]
Linear feedback shift register (LFSR)1965R. C. Tausworthe[7]A hugely influential design. Also called Tausworthe generators.
Wichmann–Hill generator1982B. A. Wichmann and D. I. Hill[8]A combination of three small LCGs, suited to 16-bit CPUs. Widely used in many programs, e.g. it is used in Excel 2003 and later versions for the function RAND[9] and it was the default generator in the language Python up to version 2.2.[10]
Rule 301983S. Wolfram[11]Based on cellular automata.
Inversive congruential generator (ICG)1986J. Eichenauer and J. Lehn[12]
Park-Miller generator1988S. K. Park and K. W. Miller[13]A specific implementation of a Lehmer generator, widely used because built-in in the C and C++ languages as the function `minstd'.
ACORN generator1989R. S. Wikramaratna[14] [15]The Additive Congruential Random Number Generator.
MIXMAX generator1991G. K. Savvidy and N. G. Ter-Arutyunyan-Savvidy[16]It is a member of the class of matrix linear congruential generator, a generalisation of LCG. The rationale behind the MIXMAX family of generators relies on results from ergodic theory and classical mechanics.
Add-with-carry (AWC)1991G. Marsaglia and A. Zaman[17]A modification of Lagged-Fibonacci generators.
Subtract-with-borrow (SWC)1991G. Marsaglia and A. Zaman[17] A modification of Lagged-Fibonacci generators. A SWB generator is the basis for the RANLUX generator,[18] widely used e.g. for particle physics simulations.
Maximally periodic reciprocals1992R. A. J. Matthews[19]A method with roots in number theory, although never used in practical applications.
KISS1993G. Marsaglia[20]Prototypical example of a combination generator.
Multiply-with-carry (MWC)1994G. Marsaglia; C. Koç[21][22]
Complementary-multiply-with-carry (CMWC)1997R. Couture and P. L’Ecuyer[23]
Mersenne Twister (MT)1998M. Matsumoto and T. Nishimura[24]Closely related with LFSRs. In its MT19937 implementation is probably the most commonly used modern PRNG. Default generator in the Python language starting from version 2.3.
Xorshift2003G. Marsaglia[25]It is a very fast sub-type of LFSR generators. Marsaglia also suggested as an improvement the xorwow generator, in which the output of a xorshift generator is added with a Weyl sequence. The xorwow generator is the default generator is the CURAND library of the nVidia CUDA application programming interface for graphics processing units.
Well equidistributed long-period linear (WELL)2006F. Panneton, P. L'Ecuyer and M. Matsumoto[26]A LFSR closely related with Mersenne Twister, aiming at remedying some of its shortcomings.
A small noncryptographic PRNG (JSF)2009Bob Jenkins[27]
Advanced Randomization System (ARS)2011J. Salmon, M. Moraes, R. Dror and D. Shaw[28]A simplified version of the AES block cipher, leading to very fast performance on system supporting the AES-NI.
Threefry2011J. Salmon, M. Moraes, R. Dror and D. Shaw[28]A simplified version of the Threefish block cipher, suitable for GPU implementations.
Philox2011J. Salmon, M. Moraes, R. Dror and D. Shaw[28]A simplification and modification of the block cipher Threefish with the addition of an S-box.
SplitMix2014G. L. Steele, D. Lea and C. H. Flood[29]Based upon the final mixing function of MurmurHash3. Included in Java Development Kit 8 and above.
Permuted Congruential Generator (PCG)2014M. E. O'Neill[30]A modification of LCG.
Random Cycle Bit Generator (RCB)2016R. Cookman[31]RCB is described as a bit pattern generator made to overcome some of the shortcomings with Mersenne Twister and short periods/bit length restriction of shift/modulo generators.
Xoroshiro128+2018D. Blackman, S. Vigna[32]A modification of Marsaglia's Xoroshift generators, one of the fastest generators on modern 64-bit CPUs.

Cryptographic algorithms

Cipher algorithms and cryptographic hashes 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 ciphers. Popular choices are Salsa20 or ChaCha (often with the number of rounds reduced to 8 for speed), ISAAC, HC-128 and RC4.
  • Block ciphers in counter mode. Common choices are AES (which is very fast on systems supporting it in hardware), TwoFish, Serpent and Camellia.
  • Cryptographic hash functions

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 (1984)
  • Blum Blum Shub (1986)
  • Naor–Reingold pseudorandom function (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.).

  • CryptGenRandom - Microsoft Windows
  • Intel RdRand instructions (called by Intel Secure Key), available in Intel x86 CPUs since 2012. They use the AES generator built into the CPU, reseeding it periodically.
  • Yarrow
  • Fortuna
  • /dev/random - Linux and Unix

Hardware (true) random number generators (TRNGs)

The following is a list of companies that produce hardware random number generators:

  • Araneus Alea
  • ComScire
  • Entropy Key
  • Fox-IT Fox RandomCard
  • ID Quantique
  • Intel 810/815/840/845G chipsets
  • LETech
  • QuintessenceLabs
  • TectroLabs
  • TRNG98
  • VIA Padlock engine
  • Whitewood Entropy Engine
  • Kidekin TRNG
  • OneRNG
  • BitBabbler
  • ProtegoST
  • ubld.it TrueRN
  • Real Random EaaS

Random number servers

The following (non-exhaustive) list of websites claim to provide random numbers generated from a truly random source, with many providing additional randomisation services:

  • appIncredible.com
  • Australian National University[33]
  • Entropy as a Service
  • [https://www.getnetrandom.com Quantum TRNG Entropy as a Service]
  • EntropyPool
  • HotBits
  • Humboldt University of Berlin (registration required)
  • random.org
  • randomnumbers.info
  • Randomserver
  • Ubuntu Pollinate
  • [https://www.realrandom.co]

The following websites claim to generate pseudo-random numbers:

  • andrew.hedges.name
  • [https://csrng.net/ CSRNG.net]
  • randomnumbergenerator.com

Well-known PRNG APIs

  • Random class in the .NET Framework
  • Random class in the Java programming language
  • SecureRandom class in the Java programming language
  • Random module in the Haskell 98 specifications
  • Web Crypto API for web browsers

See also

  • Diceware
  • Diehard tests - statistical test suite for random number generators.
  • TestU01 - statistical test suite for random number generators.
  • Hardware random number generator
  • Random number generator attack
  • Randomness

References

1. ^{{cite journal | last= Von Neumann | first= John | title= Various techniques used in connection with random digits | journal= National Bureau of Standards Applied Mathematics Series | year= 1951 | volume= 12 | pages= 36–38 | url= https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf}}
2. ^Some of von Neumann's 1949 papers were printed only in 1951. John von Neumann, “Various techniques used in connection with random digits,” in A.S. Householder, G.E. Forsythe, and H.H. Germond, eds., Monte Carlo Method, National Bureau of Standards Applied Mathematics Series, vol. 12 (Washington, D.C.: U.S. Government Printing Office, 1951): pp. 36-38.
3. ^{{Cite journal|last=Lehmer|first=Derrick H.|date=1951|title=Mathematical methods in large-scale computing units|url=|journal=Proceedings of 2nd Symposium on Large-Scale Digital Calculating Machinery|pages=141–146|doi=|pmid=|access-date=|via=}}
4. ^{{Cite journal|last=Thomson|first=W. E.|date=1958|title=A Modified Congruence Method of Generating Pseudo-random Numbers|url=https://academic.oup.com/comjnl/article/1/2/83/425243|journal=The Computer Journal|volume=1|issue=2|pages=83|doi=10.1093/comjnl/1.2.83|pmid=|access-date=|via=}}
5. ^{{Cite journal|last=Rotenberg|first=A.|date=1960|title=A New Pseudo-Random Number Generator|url=https://dl.acm.org/citation.cfm?id=321019|journal=Journal of the ACM|volume=7|issue=1|pages=75–77|via=|doi=10.1145/321008.321019}}
6. ^D. E. Knuth, The Art of Computer Programming, Vol. 2 Seminumerical Algorithms, 3rd ed., Addison Wesley Longman (1998); See pag. 27.
7. ^{{Cite journal|last=Tausworthe|first=R. C.|date=1965|title=Random Numbers Generated by Linear Recurrence Modulo Two|url=http://www.ams.org/journals/mcom/1965-19-090/S0025-5718-1965-0184406-1/S0025-5718-1965-0184406-1.pdf|journal=Mathematics of Computation|volume=19|issue=90|pages=201–209|via=|doi=10.1090/S0025-5718-1965-0184406-1}}
8. ^{{Cite journal|last=Wichmann|first=Brian A.|last2=Hill|first2=David I.|date=1982|title=Algorithm AS 183: An Efficient and Portable Pseudo-Random Number Generator|journal=Journal of the Royal Statistical Society. Series C (Applied Statistics)|volume=31|issue=2|pages=188–190|doi=10.2307/2347988|jstor=2347988}}
9. ^{{Cite web|url=https://support.microsoft.com/en-us/help/828795/description-of-the-rand-function-in-excel|title=Microsoft Support - Description of the RAND function in Excel|last=|first=|date=Apr 17, 2018|website=|archive-url=|archive-date=|dead-url=|access-date=}}
10. ^{{Cite web|url=https://docs.python.org/2/library/random.html|title=Documentation » The Python Standard Library » 9. Numeric and Mathematical Modules » 9.6. random — Generate pseudo-random numbers|last=|first=|date=|website=|archive-url=|archive-date=|dead-url=|access-date=}}
11. ^{{cite journal|author = Wolfram, S.|title = Statistical mechanics of cellular automata|journal = Rev. Mod. Phys.|volume = 55|pages = 601–644|year = 1983|doi = 10.1103/RevModPhys.55.601|bibcode=1983RvMP...55..601W|issue = 3}}
12. ^{{Cite journal|last=Eichenauer|first=Jürgen|last2=Lehn|first2=Jürgen|date=1986|title=A nonlinear congruential pseudorandom number generator.|journal=Statistische Hefte|volume=27|pages=315–326|doi=10.1007/BF02932576}}
13. ^{{Cite journal|last=Park|first=Stephen K.|last2=Miller|first2=Keith W.|date=1988|title=Random Number Generators: Good Ones Are Hard To Find|url=http://www.firstpr.com.au/dsp/rand31/p1192-park.pdf|journal=Communications of the ACM|volume=31|issue=10|pages=1192–1201|via=|doi=10.1145/63039.63042}}
14. ^{{Cite journal|last=Wikramaratna|first=R. S.|date=1989|title=ACORN — A new method for generating sequences of uniformly distributed Pseudo-random Numbers|url=|journal=Journal of Computational Physics|volume=83|pages=16–31|via=|doi=10.1016/0021-9991(89)90221-0}}
15. ^Wikramaratna, R.S. Theoretical and empirical convergence results for additive congruential random number generators, Journal of Computational and Applied Mathematics (2009), doi:10.1016/j.cam.2009.10.015
16. ^{{cite journal |doi=10.1016/0021-9991(91)90015-D|title=On the Monte Carlo simulation of physical systems|journal=Journal of Computational Physics|volume=97|issue=2|pages=566|year=1991|last1=Savvidy|first1=G.K|last2=Ter-Arutyunyan-Savvidy|first2=N.G|bibcode=1991JCoPh..97..566S}}
17. ^1 {{Cite journal|last=George|first=Marsaglia|last2=Zaman|first2=Arif|date=1991|title=A new class of random number generators|url=https://projecteuclid.org/download/pdf_1/euclid.aoap/1177005878|journal=Annals of Applied Probability|volume=1|issue=3|pages=462–480|via=|doi=10.1214/aoap/1177005878}}
18. ^{{Cite journal|last=Martin|first=Lüscher|date=1994|title=A portable high-quality random number generator for lattice field theory simulations|url=https://www.sciencedirect.com/science/article/pii/0010465594902321|journal=Computer Physics Communications|volume= 79| issue = 1|pages=100–110|via=|doi=10.1016/0010-4655(94)90232-1|arxiv=hep-lat/9309020}}
19. ^{{Cite journal|last=Matthews|first=Robert A. J.|date=1992|title=Maximally periodic reciprocals|url=https://www.researchgate.net/publication/266728416|journal=Bull. Inst. Math. Appl.|volume=28|pages=147–148|via=}}
20. ^{{Cite journal|last=Marsaglia|first=George|last2=Zaman|first2=Arif|date=1993|title=The KISS generator|url=|journal=Technical Report, Department of Statistics, Florida State University, Tallahassee, FL, USA|volume=|issue=|doi=|pmid=|access-date=|via=}}
21. ^Post by George Marsaglia on the newsgroup sci.stat.math dated 1 August 2018 with title '[https://groups.google.com/forum/#!searchin/sci.stat.math/Yet$20another$20rng%7Csort:date/sci.stat.math/p7aLW3TsJys/QGb1kti6kN0J Yet another RNG]'.
22. ^{{Cite journal|last=Koç|first=Cemal|date=1995|title=Recurring-with-Carry Sequences|journal=Journal of Applied Probability|volume= 32|issue=4|pages=966–971|jstor=3215210|doi=10.2307/3215210}}
23. ^{{Cite journal|last=Couture|first=Raymond|last2=L'Ecuyer|first2=Pierre|date=1997|title=Distribution properties of multiply-with-carry random number generators|url=http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00827-2/S0025-5718-97-00827-2.pdf|journal=Mathematics of Computation|volume=66 Number. 218|pages=591–607|via=}}
24. ^{{Cite journal|last=Matsumoto|first=M.|last2=Nishimura|first2=T.|date=1998|title=MersenneTwister: A623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator|url=|journal=ACM Trans. On Modeling and Computer Simulation|volume=8|issue=1|pages=3–30|via=|doi=10.1145/272991.272995|citeseerx=10.1.1.215.1141}}
25. ^{{cite journal| first=George | last=Marsaglia | authorlink=George Marsaglia| title=Xorshift RNGs| journal=Journal of Statistical Software| volume=8 | issue=14| date=July 2003| doi=10.18637/jss.v008.i14}}
26. ^{{Cite journal| ref = harv| doi = 10.1145/1132973.1132974| title = Improved long-period generators based on linear recurrences modulo 2| journal = ACM Transactions on Mathematical Software| volume = 32| number = 1| pages = 1–16| date = March 2006| last1 = Panneton | first1 = François O. | last2 = l'Ecuyer | first2 = Pierre | last3 = Matsumoto | first3 = Pierre | url = http://www.iro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf| citeseerx = 10.1.1.73.5499}}
27. ^{{Cite web|url=http://burtleburtle.net/bob/rand/smallprng.html|title=A small noncryptographic PRNG|last=Jenkins|first=Bob|date=2009|website=|archive-url=|archive-date=|dead-url=|access-date=}}
28. ^1 2 {{Cite conference|title = Parallel random numbers: as easy as 1, 2, 3|last = Salmon|first = John|date = 2011|book-title = Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, Article No. 16|doi = 10.1145/2063384.2063405|last2 = Moraes|first2 = Mark|last3 = Dror|first3 = Ron|last4 = Shaw|first4 = David}}
29. ^{{Cite journal|last=Steele|first=Guy L. Jr.|last2=Lea|first2=Doug|last3=Flood|first3=Christine H.|date=2014|title=Fast splittable pseudorandom number generators|url=http://gee.cs.oswego.edu/dl/papers/oopsla14.pdf|journal=OOPSLA '14 Proceedings of the 2014 ACM International Conference on Object Oriented Programming Systems Languages & Applications|volume=|pages=|via=}}
30. ^{{Cite journal|last=O'Neill|first=Melissa E.|date=2014|title=PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation|url=http://www.pcg-random.org/pdf/hmc-cs-2014-0905.pdf|journal=Technical Report|volume=|pages=|via=}}
31. ^{{Cite journal|last=Cookman|first=Richard|date=2016|title=random cycle bit generator (rcb_generator)|url=https://github.com/ceorron/cycle-bit-random-number-generator|journal=Technical Report|volume=|pages=|via=}}
32. ^{{cite arXiv |last=Blackman |first=David |last2=Vigna|first2=Sebastiano|eprint=1805.01407 |title= Scrambled Linear Pseudorandom Generators|class=cs.DS |year=2018 }}
33. ^{{Citation |title=Real time demonstration of high bitrate quantum random number generation with coherent laser light |author1=Thomas Symul |author2=Syed M. Assad |author3=Ping Koy Lam |journal=Applied Physics Letters |volume=98 |issue=23 |page=231103|date=2011-06-07 |doi=10.1063/1.3597793 |arxiv=1107.4438}}

External links

  • SP800-90 series on Random Number Generation, NIST
  • [https://www.gnu.org/software/gsl/manual/html_node/Random-Number-Generation.html Random Number Generation in the GNU Scientific Library Reference Manual]
  • Random Number Generation Routines in the NAG Numerical Library
  • Chris Lomont's overview of PRNGs, including a good implementation of the WELL512 algorithm
  • Source code to read data from a TrueRNG V2 hardware TRNG
  • An alternative C libray to get sequences of pseudo-random numbers
{{DEFAULTSORT:Random number generators}}

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