# Random Number Generator

## What is a Random Number Generator?

A **random number generator (RNG)** is a device that generates a sequence of numbers or symbols that cannot be reasonably predicted better than by a random chance. Random number generators can be true hardware random-number generators (HRNG), which generate genuinely random numbers, or pseudo-random number generators (PRNG), which generate numbers that look random, but are actually deterministic, and can be reproduced if the state of the PRNG is known.

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Various applications of randomness have led to the development of several different methods for generating random data, of which some have existed since ancient times, among whose ranks are well-known "classic" 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/or time. Thus, results would sometimes be collected and distributed as random number tables.

Several computational methods for pseudo-random number generation exist. All fall short of the goal of true randomness, although they may meet, with varying success, some of the statistical tests for randomness intended to measure how unpredictable their results are (that is, to what degree their patterns are discernible). This generally makes them unusable for applications such as cryptography. However, carefully designed cryptographically secure pseudo-random number generators (CSPRNG) also exist, with special features specifically designed for use in cryptography.

Practical applications and uses Random number generators have 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, such as in security applications, hardware generators are generally preferred over pseudo-random algorithms, where feasible. 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. They are also used in cryptography – so long as the seed is secret. Sender and receiver can generate the same set of numbers automatically to use as keys.

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. Some simple examples might be presenting a user with a "Random Quote of the Day", or determining which way a computer-controlled adversary might move 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 be suitable for randomization are in fact not quite so simple. For instance, a system that "randomly" selects music tracks for a background music system must only appear random, and may even have ways to control the selection of music: a true random system would have no restriction on the same item appearing two or three times in succession.

### Generation Methods

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

A physical random number generator can be based on an essentially random atomic or subatomic physical phenomenon whose unpredictability can be traced to the laws of quantum mechanics. Sources of entropy include radioactive decay, thermal noise, shot noise, avalanche noise in Zener diodes, clock drift, the timing of actual movements of a hard disk read/write head, and radio noise. However, physical phenomena and tools used to measure them generally feature 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 bits from a non-uniformly random source, though at a lower bit rate.

The appearance of wideband photonic entropy sources, such as optical chaos and amplified spontaneous emission noise, greatly aid the development of the physical random number generator. Among them, optical chaos has a high potential to physically produce high-speed random numbers due to its high bandwidth and large amplitude. A prototype of a high speed, real-time physical random bit generator based on a chaotic laser was built in 2013.

Various imaginative ways of collecting this entropic information have been devised. One technique is to run a hash function against 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, while Random.org uses variations in the amplitude of atmospheric noise recorded with a normal radio.

Another common entropy source is the behavior of human users of the system. While people are not considered good randomness generators upon request, they generate random behavior quite well in the context of playing mixed strategy games. Some security-related computer 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.

A PRNG suitable for cryptographic applications is called a cryptographically secure PRNG (CSPRNG). A requirement for a CSPRNG is that an adversary not knowing the seed has only negligible advantage in distinguishing the generator's output sequence from a random sequence. In other words, while a PRNG is only required to pass certain statistical tests, a CSPRNG must pass all statistical tests that are restricted to polynomial time in the size of the seed. Though a proof of this property is beyond the current state of the art of computational complexity theory, strong evidence may be provided by reducing the CSPRNG to a problem that is assumed to be hard, such as integer factorization. In general, years of review may be required before an algorithm can be certified as a CSPRNG.

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