Rand Creates the Same Random Number Over and Over Again

Producing a sequence that cannot be predicted meliorate than by random chance

Dice are an example of a mechanical hardware random number generator. When a cubical dice is rolled, a random number from 1 to 6 is obtained.

Random number generation is a process by which, frequently by means of a random number generator (RNG), a sequence of numbers or symbols that cannot be reasonably predicted better than by random run a risk is generated. This means that the detail issue sequence volition contain some patterns detectable in hindsight but unpredictable to foresight. True random number generators can exist hardware random-number generators (HRNGS) that generate random numbers, wherein each generation is a role of the current value of a concrete surroundings'south attribute that is constantly changing in a manner that is practically impossible to model. This would exist in contrast to so-chosen "random number generations" washed past pseudorandom number generators (PRNGs) that generate numbers that only await random simply are in fact pre-determined—these generations tin be reproduced simply by knowing the state of the PRNG.

Various applications of randomness have led to the development of several dissimilar methods for generating random information. Some of these accept existed since ancient times, among whose ranks are well-known "archetype" examples, including the rolling of dice, coin flipping, the shuffling of playing cards, the use of yarrow stalks (for divination) in the I Ching, as well as countless other techniques. Because of the mechanical nature of these techniques, generating large quantities of sufficiently random numbers (important in statistics) required much work and time. Thus, results would sometimes be collected and distributed as random number tables.

Several computational methods for pseudorandom number generation exist. All fall short of the goal of true randomness, although they may run across, with varying success, some of the statistical tests for randomness intended to measure how unpredictable their results are (that is, to what caste their patterns are discernible). This generally makes them unusable for applications such equally cryptography. Still, advisedly designed cryptographically secure pseudorandom number generators (CSPRNGS) also exist, with special features specifically designed for use in cryptography.

Practical applications and uses [edit]

Random number generators take applications in gambling, statistical sampling, computer simulation, cryptography, completely randomized design, and other areas where producing an unpredictable result is desirable. Generally, in applications having unpredictability as the paramount feature, such every bit in security applications, hardware generators are generally preferred over pseudorandom algorithms, where feasible.

Pseudorandom number generators are very useful in developing Monte Carlo-method simulations, equally debugging is facilitated past the power to run the aforementioned sequence of random numbers once again by starting from the same random seed. They are also used in cryptography – and then long as the seed is secret. Sender and receiver can generate the same set of numbers automatically to apply equally keys.

The generation of pseudorandom numbers is an important and common task in computer programming. While cryptography and certain numerical algorithms require a very high degree of credible randomness, many other operations only need a minor amount of unpredictability. Some simple examples might be presenting a user with a "random quote of the solar day", or determining which mode a reckoner-controlled adversary might motion in a computer game. Weaker forms of randomness are used in hash algorithms and in creating amortized searching and sorting algorithms.

Some applications which appear at first sight to exist suitable for randomization are in fact not quite then simple. For instance, a system that "randomly" selects music tracks for a background music system must only appear random, and may fifty-fifty take ways to control the selection of music: a true random organization would accept no restriction on the aforementioned item appearing ii or three times in succession.

"Truthful" vs. pseudo-random numbers [edit]

There are two principal methods used to generate random numbers. The first method measures some physical phenomenon that is expected to be random and then compensates for possible biases in the measurement process. Case sources include measuring atmospheric noise, thermal noise, and other external electromagnetic and quantum phenomena. For instance, cosmic groundwork radiation or radioactive decay equally measured over short timescales represent sources of natural entropy.

The speed at which entropy can be obtained from natural sources is dependent on the underlying physical phenomena being measured. Thus, sources of naturally occurring "truthful" entropy are said to exist blocking – they are rate-limited until plenty entropy is harvested to meet the demand. On some Unix-similar systems, including most Linux distributions, the pseudo device file /dev/random will cake until sufficient entropy is harvested from the surroundings.^[one] Due to this blocking beliefs, large bulk reads from /dev/random, such every bit filling a hard disk drive with random $.25, can often be slow on systems that apply this type of entropy source.

The second method uses computational algorithms that tin produce long sequences of patently random results, which are in fact completely determined by a shorter initial value, known as a seed value or key. As a result, the entire seemingly random sequence can be reproduced if the seed value is known. This blazon of random number generator is often called a pseudorandom number generator. This type of generator typically does not rely on sources of naturally occurring entropy, though it may be periodically seeded by natural sources. This generator blazon is non-blocking, and then they are not rate-express by an external event, making large bulk reads a possibility.

Some systems take a hybrid arroyo, providing randomness harvested from natural sources when bachelor, and falling back to periodically re-seeded software-based cryptographically secure pseudorandom number generators (CSPRNGs). The fallback occurs when the desired read rate of randomness exceeds the power of the natural harvesting approach to keep up with the demand. This approach avoids the rate-limited blocking behavior of random number generators based on slower and purely ecology methods.

While a pseudorandom number generator based solely on deterministic logic can never be regarded equally a "true" random number source in the purest sense of the give-and-take, in practise they are mostly sufficient even for demanding security-disquisitional applications. Advisedly designed and implemented pseudorandom number generators can be certified for security-critical cryptographic purposes, as is the case with the yarrow algorithm and fortuna. The former is the basis of the /dev/random source of entropy on FreeBSD, AIX, OS X, NetBSD, and others. OpenBSD uses a pseudorandom number algorithm known every bit arc4random.^[2]

Generation methods [edit]

Concrete methods [edit]

The earliest methods for generating random numbers, such as dice, money flipping and roulette wheels, are still used today, mainly in games and gambling as they tend to be as well slow for most applications in statistics and cryptography.

A concrete random number generator can be based on an essentially random diminutive or subatomic physical phenomenon whose unpredictability tin can be traced to the laws of breakthrough mechanics. Sources of entropy include radioactive decay, thermal racket, shot dissonance, avalanche racket in Zener diodes, clock migrate, the timing of actual movements of a hard disk read-write head, and radio noise. Even so, physical phenomena and tools used to measure them generally characteristic asymmetries and systematic biases that make their outcomes not uniformly random. A randomness extractor, such as a cryptographic hash function, can be used to approach a uniform distribution of $.25 from a non-uniformly random source, though at a lower scrap charge per unit.

The appearance of wideband photonic entropy sources, such as optical chaos and amplified spontaneous emission noise, profoundly assistance the development of the concrete random number generator. Amongst them, optical chaos^{[3] [4]} has a high potential to physically produce loftier-speed random numbers due to its loftier bandwidth and large amplitude. A prototype of a high speed, existent-fourth dimension physical random flake generator based on a chaotic laser was congenital in 2013.^[v]

Various imaginative ways of collecting this entropic data have been devised. One technique is to run a hash function confronting a frame of a video stream from an unpredictable source. Lavarand used this technique with images of a number of lava lamps. HotBits measures radioactive decay with Geiger–Muller tubes,^[6] while Random.org uses variations in the amplitude of atmospheric racket recorded with a normal radio.

Demonstration of a simple random number generator based on where and when a button is clicked

Another common entropy source is the behavior of human users of the organization. While people are not considered expert randomness generators upon asking, they generate random beliefs quite well in the context of playing mixed strategy games.^[7] Some security-related reckoner software requires the user to make a lengthy series of mouse movements or keyboard inputs to create sufficient entropy needed to generate random keys or to initialize pseudorandom number generators.^[viii]

Computational methods [edit]

Most computer generated random numbers use PRNGs which are algorithms that tin automatically create long runs of numbers with good random properties simply eventually the sequence repeats (or the retention usage grows without jump). These random numbers are fine in many situations but are non as random as numbers generated from electromagnetic atmospheric racket used as a source of entropy.^[9] The series of values generated by such algorithms is generally adamant by a fixed number called a seed. One of the most common PRNG is the linear congruential generator, which uses the recurrence

${\displaystyle X_{n+one}=(aX_{n}+b)\,{\textrm {mod}}\,m}$

to generate numbers, where a, b and yard are large integers, and ${\displaystyle X_{northward+1}}$ is the next in Ten as a series of pseudorandom numbers. The maximum number of numbers the formula can produce is i less than the modulus, m-ane. The recurrence relation can be extended to matrices to have much longer periods and better statistical properties .^[10] To avoid certain non-random properties of a single linear congruential generator, several such random number generators with slightly unlike values of the multiplier coefficient, a, can be used in parallel, with a "master" random number generator that selects from among the several different generators.^{[ citation needed ]}

A simple pen-and-newspaper method for generating random numbers is the then-called heart square method suggested past John von Neumann. While simple to implement, its output is of poor quality. Information technology has a very short catamenia and severe weaknesses, such as the output sequence almost always converging to zero. A recent innovation is to combine the centre square with a Weyl sequence. This method produces high quality output through a long period.^[11]

Most computer programming languages include functions or library routines that provide random number generators. They are often designed to provide a random byte or give-and-take, or a floating point number uniformly distributed between 0 and 1.

The quality i.e. randomness of such library functions varies widely from completely predictable output, to cryptographically secure. The default random number generator in many languages, including Python, Blood-red, R, IDL and PHP is based on the Mersenne Twister algorithm and is not sufficient for cryptography purposes, every bit is explicitly stated in the language documentation. Such library functions ofttimes have poor statistical properties and some will repeat patterns afterwards only tens of thousands of trials. They are often initialized using a computer'southward real fourth dimension clock every bit the seed, since such a clock generally measures in milliseconds, far beyond the person's precision. These functions may provide plenty randomness for certain tasks (for example video games) merely are unsuitable where high-quality randomness is required, such as in cryptography applications, statistics or numerical analysis.^{[ citation needed ]}

Much higher quality random number sources are available on near operating systems; for instance /dev/random on various BSD flavors, Linux, Mac Bone X, IRIX, and Solaris, or CryptGenRandom for Microsoft Windows. Almost programming languages, including those mentioned above, provide a means to access these college quality sources.

By humans [edit]

Random number generation may also be performed by humans, in the class of collecting diverse inputs from terminate users and using them as a randomization source. However, about studies discover that man subjects take some degree of non-randomness when attempting to produce a random sequence of e.thousand. digits or letters. They may alternate too much between choices when compared to a expert random generator;^[12] thus, this arroyo is not widely used.

Post-processing and statistical checks [edit]

Even given a source of plausible random numbers (perhaps from a quantum mechanically based hardware generator), obtaining numbers which are completely unbiased takes care. In addition, behavior of these generators oft changes with temperature, power supply voltage, the historic period of the device, or other outside interference. And a software bug in a pseudorandom number routine, or a hardware problems in the hardware it runs on, may be similarly difficult to discover.

Generated random numbers are sometimes subjected to statistical tests before use to ensure that the underlying source is all the same working, and then mail-processed to improve their statistical backdrop. An example would be the TRNG9803^[xiii] hardware random number generator, which uses an entropy measurement as a hardware test, and then mail-processes the random sequence with a shift annals stream cipher. It is generally hard to use statistical tests to validate the generated random numbers. Wang and Nicol^[14] proposed a distance-based statistical testing technique that is used to identify the weaknesses of several random generators. Li and Wang^[15] proposed a method of testing random numbers based on laser chaotic entropy sources using Brownian move properties.

Other considerations [edit]

Reshaping the distribution [edit]

Compatible distributions [edit]

Nearly random number generators natively work with integers or private bits, and then an actress footstep is required to arrive at the "approved" uniform distribution between 0 and ane. The implementation is not every bit trivial as dividing the integer by its maximum possible value. Specifically:^{[16] [17]}

1. The integer used in the transformation must provide enough $.25 for the intended precision.
2. The nature of floating-point math itself means in that location exists more precision the closer the number is to null. This extra precision is usually not used due to the sheer number of bits required.
3. Rounding error in division may bias the result. At worst, a supposedly excluded spring may be fatigued countrary to expectations based on real-number math.

The mainstream algorithm, used by OpenJDK, Rust, and Numpy, is described in a proposal for C++'south STL. It does non utilize the extra precision and suffers from bias only in the last bit due to round-to-even.^[18] Other numeric concerns are warranted when shifting this "approved" compatible distribution to a different range.^[nineteen] A proposed method for the Swift programming language claims to employ the total precision everywhere.^[20]

Uniformly distributed integers are commonly used in algorithms such every bit the Fisher–Yates shuffle. Once more, a naive implementation may induce a modulo bias into the consequence, so more involved algorithms must be used. A method that nearly never performs partitioning was described in 2018 by Daniel Lemire,^[21] with the electric current state-of-the-art existence the arithmetic encoding-inspired 2021 "optimal algorithm" by Stephen Canon of Apple Inc.^[22]

Most 0 to 1 RNGs include 0 only exclude i, while others include or exclude both.

Other distributions [edit]

Given a source of uniform random numbers, in that location are a couple of methods to create a new random source that corresponds to a probability density function. One method, called the inversion method, involves integrating up to an expanse greater than or equal to the random number (which should exist generated between 0 and 1 for proper distributions). A 2nd method, chosen the acceptance-rejection method, involves choosing an ten and y value and testing whether the function of ten is greater than the y value. If information technology is, the 10 value is accepted. Otherwise, the x value is rejected and the algorithm tries again.^{[23] [24]}

As an instance for rejection sampling, to generate a pair of statistically independent standard normally distributed random numbers (x, y), one may first generate the polar coordinates (r, θ), where r ²~χ_ii ² and θ~UNIFORM(0,2π) (encounter Box–Muller transform).

Whitening [edit]

The outputs of multiple independent RNGs can be combined (for example, using a bit-wise XOR functioning) to provide a combined RNG at least equally skillful as the all-time RNG used. This is referred to as software whitening.

Computational and hardware random number generators are sometimes combined to reflect the benefits of both kinds. Computational random number generators can typically generate pseudorandom numbers much faster than physical generators, while physical generators tin generate "true randomness."

Depression-discrepancy sequences as an alternative [edit]

Some computations making apply of a random number generator can exist summarized as the computation of a total or average value, such as the computation of integrals by the Monte Carlo method. For such problems, information technology may be possible to detect a more than accurate solution by the use of so-called low-discrepancy sequences, also chosen quasirandom numbers. Such sequences have a definite blueprint that fills in gaps evenly, qualitatively speaking; a truly random sequence may, and usually does, leave larger gaps.

Activities and demonstrations [edit]

The following sites brand available random number samples:

• The SOCR resource pages contain a number of hands-on interactive activities and demonstrations of random number generation using Java applets.
• The Quantum Optics Grouping at the ANU generates random numbers sourced from quantum vacuum. Sample of random numbers are available at their breakthrough random number generator inquiry folio.
• Random.org makes bachelor random numbers that are sourced from the randomness of atmospheric noise.
• The Quantum Random Bit Generator Service at the Ruđer Bošković Institute harvests randomness from the quantum process of photonic emission in semiconductors. They supply a variety of means of fetching the data, including libraries for several programming languages.
• The Group at the Taiyuan University of Technology generates random numbers sourced from a chaotic light amplification by stimulated emission of radiation. Samples of random number are bachelor at their Concrete Random Number Generator Service.

Backdoors [edit]

Since much cryptography depends on a cryptographically secure random number generator for key and cryptographic nonce generation, if a random number generator tin be made predictable, it can be used equally backdoor by an attacker to suspension the encryption.

The NSA is reported to have inserted a backdoor into the NIST certified cryptographically secure pseudorandom number generator Dual EC DRBG. If for case an SSL connection is created using this random number generator, so according to Matthew Green it would let NSA to determine the land of the random number generator, and thereby eventually be able to read all data sent over the SSL connection.^[25] Even though information technology was apparent that Dual_EC_DRBG was a very poor and possibly backdoored pseudorandom number generator long earlier the NSA backdoor was confirmed in 2013, information technology had seen meaning usage in practice until 2013, for example past the prominent security company RSA Security.^[26] There have later on been accusations that RSA Security knowingly inserted a NSA backdoor into its products, maybe every bit part of the Bullrun program. RSA has denied knowingly inserting a backstairs into its products.^[27]

It has also been theorized that hardware RNGs could exist secretly modified to accept less entropy than stated, which would make encryption using the hardware RNG susceptible to attack. One such method which has been published works by modifying the dopant mask of the scrap, which would be undetectable to optical reverse-applied science.^[28] For case, for random number generation in Linux, it is seen as unacceptable to use Intel's RDRAND hardware RNG without mixing in the RDRAND output with other sources of entropy to annul whatever backdoors in the hardware RNG, especially after the revelation of the NSA Bullrun program.^{[29] [xxx]}

In 2010, a U.South. lottery draw was rigged by the information security managing director of the Multi-State Lottery Association (MUSL), who surreptitiously installed backdoor malware on the MUSL's secure RNG computer during routine maintenance.^[31] During the hacks the man won a total amount of $sixteen,500,000 by predicting the numbers correctly a few times in year.

Address infinite layout randomization (ASLR), a mitigation confronting rowhammer and related attacks on the physical hardware of retentiveness fries has been found to exist inadequate every bit of early 2017 past VUSec. The random number algorithm, if based on a shift annals implemented in hardware, is predictable at sufficiently big values of p and can be reverse engineered with enough processing power (Brute Force Hack). This also indirectly means that malware using this method can run on both GPUs and CPUs if coded to do so, even using GPU to suspension ASLR on the CPU itself.^[32]

See also [edit]

• Flipism
• League of entropy
• List of random number generators
• PP (complexity)
• Procedural generation
• Randomized algorithm
• Random password generator
• Random variable, contains a chance-dependent value

References [edit]

1. ^ random(4)  – Linux Developer's Manual – Special Files
2. ^ arc4random(3)  – OpenBSD Library Functions Manual
3. ^ Li, Pu; Wang, Yun-Cai; Zhang, Jian-Zhong (2010-09-xiii). "All-optical fast random number generator". Optics Limited. eighteen (19): 20360–20369. Bibcode:2010OExpr..1820360L. doi:10.1364/OE.xviii.020360. ISSN 1094-4087. PMID 20940928.
4. ^ Li, Pu; Sun, Yuanyuan; Liu, Xianglian; Yi, Xiaogang; Zhang, Jianguo; Guo, Xiaomin; Guo, Yanqiang; Wang, Yuncai (2016-07-15). "Fully photonics-based physical random chip generator". Optics Letters. 41 (14): 3347–3350. Bibcode:2016OptL...41.3347L. doi:10.1364/OL.41.003347. ISSN 1539-4794. PMID 27420532.
5. ^ Wang, Anbang; Li, Pu; Zhang, Jianguo; Zhang, Jianzhong; Li, Lei; Wang, Yuncai (2013-08-26). "4.5 Gbps high-speed real-fourth dimension physical random bit generator". Optics Express. 21 (17): 20452–20462. Bibcode:2013OExpr..2120452W. doi:10.1364/OE.21.020452. ISSN 1094-4087. PMID 24105589. S2CID 10397141.
6. ^ Walker, John. "HotBits: Genuine Random Numbers". Retrieved 2009-06-27 .
7. ^ Halprin, Ran; Naor, Moni. "Games for Extracting Randomness" (PDF). Department of Information science and Applied Mathematics, Weizmann Institute of Scientific discipline. Retrieved 2009-06-27 .
8. ^ TrueCrypt Foundation. "TrueCrypt Beginner's Tutorial, Part 3". Retrieved 2009-06-27 .
9. ^ "RANDOM.ORG - True Random Number Service". www.random.org . Retrieved 2016-01-14 .
10. ^ "High Dimensionality Pseudo Random Number Generators". Retrieved 2018-11-21 .
11. ^ Widynski, Bernard (nineteen May 2020). "Middle Square Weyl Sequence RNG". arXiv:1704.00358 [cs.CR].
12. ^ W. A. Wagenaar (1972). "Generation of random sequences by human being subjects: a critical survey of the literature". Psychological Bulletin. 77 (1): 65–72. CiteSeerXx.ane.ane.211.9085. doi:x.1037/h0032060.
13. ^ Dömstedt, B. (2009). "TRNG9803 True Random Number Generator". Manufacturer: www.TRNG98.se.
14. ^ Wang, Yongge (2014). "Statistical Backdrop of Pseudo Random Sequences and Experiments with PHP and Debian OpenSSL". Computer Security - ESORICS 2014. Lecture Notes in Computer Science. Vol. 8712. Heidelberg: Springer LNCS. pp. 454–471. doi:x.1007/978-three-319-11203-9_26. ISBN978-iii-319-11202-2.
15. ^ Li, Pu; Yi, Xiaogang; Liu, Xianglian; Wang, Yuncai; Wang, Yongge (2016-07-11). "Brownian motion backdrop of optoelectronic random chip generators based on laser anarchy". Eyes Express. 24 (14): 15822–15833. Bibcode:2016OExpr..2415822L. doi:10.1364/OE.24.015822. ISSN 1094-4087. PMID 27410852.
16. ^ Goualard, F. (2020). Generating Random Floating-Point Numbers by Dividing Integers: A Instance Study. ICCS. doi:10.1007/978-3-030-50417-5_2. S2CID 219889587.
17. ^ Campbell, Taylor R. (2014). "Compatible random floats: How to generate a double-precision floating-bespeak number in [0, one] uniformly at random given a compatible random source of bits". Retrieved 4 September 2021.
18. ^ "A new specification for std::generate_canonical". www.open-std.org.
19. ^ Goualard, Frédéric (July 2021). "Drawing random floating-point numbers from an interval". HAL . Retrieved four September 2021.
20. ^ NevinBR. "[stdlib] Floating-bespeak random-number improvements by NevinBR · Pull Asking #33560 · apple/swift". GitHub.
21. ^ Lemire, Daniel (23 February 2019). "Fast Random Integer Generation in an Interval". ACM Transactions on Modeling and Calculator Simulation. 29 (1): 1–12. arXiv:1805.10941. doi:ten.1145/3230636. S2CID 44061046.
22. ^ "An optimal algorithm for bounded random integers by stephentyrone · Pull Asking #39143 · apple/swift". GitHub.
23. ^ The MathWorks. "Common generation methods". Retrieved 2011-10-13 .
24. ^ The Numerical Algorithms Group. "G05 – Random Number Generators" (PDF). NAG Library Manual, Marking 23 . Retrieved 2012-02-09 .
25. ^ matthew Green (2013-09-xviii). "The Many Flaws of Dual_EC_DRBG".
26. ^ Matthew Light-green (2013-09-20). "RSA warns developers non to utilise RSA products".
27. ^ "We don't enable backdoors in our crypto products, RSA tells customers". Ars Technica. 2013-09-20.
28. ^ "Researchers tin can slip an undetectable trojan into Intel's Ivy Bridge CPUs". Ars Technica. 2013-09-xviii.
29. ^ Theodore Ts'o. "I am then glad I resisted pressure level from Intel engineers to let /dev/random rely just on the RDRAND teaching". Google Plus.
30. ^ Theodore Ts'o. "Re: [PATCH] /dev/random: Bereft of entropy on many architectures". LWN.
31. ^ Nestel, M.Fifty. (July vii, 2015). "Inside the Biggest Lottery Scam Ever". The Daily Brute . Retrieved July ten, 2015.
32. ^ "AnC - VUSec". Retrieved thirteen July 2018.

Further reading [edit]

• Donald Knuth (1997). "Chapter 3 – Random Numbers". The Art of Estimator Programming. Vol. ii: Seminumerical algorithms (3 ed.).
• L'Ecuyer, Pierre (2017). "History of Uniform Random Number Generation" (PDF). Proceedings of the 2017 Wintertime Simulation Conference. IEEE Press. pp. 202–230.
• L'Ecuyer, Pierre (2012). "Random Number Generation" (PDF). In J. East. Gentle; W. Haerdle; Y. Mori (eds.). Handbook of Computational Statistics: Concepts and Methods. Handbook of Computational Statistics (second ed.). Springer-Verlag. pp. 35–71. doi:10.1007/978-three-642-21551-3_3. hdl:10419/22195. ISBN978-3-642-21550-6.
• Kroese, D. P.; Taimre, T.; Botev, Z.I. (2011). "Chapter i – Uniform Random Number Generation". Handbook of Monte Carlo Methods. New York: John Wiley & Sons. p. 772. ISBN978-0-470-17793-8.
• Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007). "Chapter seven. Random Numbers". Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York: Cambridge University Press. ISBN978-0-521-88068-eight.
• NIST SP800-90A, B, C series on random number generation
• M. Tomassini, M. Sipper, and M. Perrenoud (October 2000). "On the generation of loftier-quality random numbers by two-dimensional cellular automata". IEEE Transactions on Computers. 49 (10): 1146–1151. doi:10.1109/12.888056. {{cite journal}}: CS1 maint: uses authors parameter (link)

External links [edit]

• RANDOM.ORG True Random Number Service
• Quantum random number generator at ANU
• Random and Pseudorandom on In Our Fourth dimension at the BBC
• jRand a Coffee-based framework for the generation of simulation sequences, including pseudorandom sequences of numbers
• Random number generators in NAG Fortran Library
• Randomness Beacon at NIST, broadcasting full-entropy bit-strings in blocks of 512 bits every 60 seconds. Designed to provide unpredictability, autonomy, and consistency.
• A organization call for random numbers: getrandom(), a LWN.cyberspace commodity describing a dedicated Linux organisation call
• Statistical Backdrop of Pseudo Random Sequences and Experiments with PHP and Debian OpenSSL
• Random Sequence Generator based on Avalanche Noise

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Source: https://en.wikipedia.org/wiki/Random_number_generation

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