Free Serial Number Generator
Malena Bower
A random number is a number chosen from a pool of limited or unlimited numbers that has no discernible pattern for prediction. The pool of numbers is almost always independent from each other. However, the pool of numbers may follow a specific distribution. For example, the height of the students in a school tends to follow a normal distribution around the median height. If the height of a student is picked at random, the picked number has a higher chance to be closer to the median height than being classified as very tall or very short. The random number generators above assume that the numbers generated are independent of each other, and will be evenly spread across the whole range of possible values.
A random number generator, like the ones above, is a device that can generate one or many random numbers within a defined scope. Random number generators can be hardware based or pseudo-random number generators. Hardware based random-number generators can involve the use of a dice, a coin for flipping, or many other devices.
A pseudo-random number generator is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. Computer based random number generators are almost always pseudo-random number generators. Yet, the numbers generated by pseudo-random number generators are not truly random. Likewise, our generators above are also pseudo-random number generators. The random numbers generated are sufficient for most applications yet they should not be used for cryptographic purposes. True random numbers are based on physical phenomena such as atmospheric noise, thermal noise, and other quantum phenomena. Methods that generate true random numbers also involve compensating for potential biases caused by the measurement process.
A pseudo-random number generator (PRNG) is typically programmed using a randomizing math function to select a "random" number within a set range. These random number generators are pseudo-random because the computer program or algorithm may have unintended selection bias. In other words, randomness from a computer program is not necessarily an organic, truly random event.
A true random number generator (TRNG) relies on randomness from a physical event that is external to the computer and its operating system. Examples of such events are blips in atmospheric noise, or points at which a radioactive material decays. A true random number generator receives information from these types of unpredictable events to produce a truly random number.
Part of what I do is study typical behavior of large combinatorial structures by looking at pseudorandom instances. But many commercially available pseudorandom number generators have known defects, which makes me wonder whether I should just use the digits (or bits) of $\pi$.
A colleague of mine says he "read somewhere" that the digits of $\pi$ don't make a good random number generator. Perhaps he's thinking of the article "A study on the randomness of the digits of $\pi$" by Shu-Ju Tu and Ephraim Fischbach. Does anyone know this article? Some of the press it got (see e.g. ) made it sound like $\pi$ wasn't such a good source of randomness, but the abstract for the article itself (see ) suggests the opposite.
If you are worried about the quality of random digits that you're getting, then you may want to use cryptographic random number generators. For example, finding a pattern in the Blum-Blum-Shub random number generator would probably yield a new algorithm for factoring large integers! Cryptographic random number generators will run more slowly than the "commercial" random number generators you're talking about but you can certainly find some that will generate digits faster than algorithms for computing $\pi$ will.
In a technical sense, no. A good pseudorandom number generator would be one that you can plug into any randomized algorithm and expect to see the same behavior that you would from an actual random number generator. One way of making a technical definition out of this is to say that the pseudorandom number generator cannot be distinguished from truly random (with probability bounded away from 1/2) by any polynomial time test.
For the same reason, no fully deterministic sequence can be a good random sequence. Instead, to fit this definition, you need to use a pseudorandom number generator that takes some number n of truly random bits as an input seed and generates from them a longer sequence (polynomial in n) of pseudorandom bits that cannot be distinguished from random by a polynomial time algorithm.
I'd say no if you are using the random numbers to generate cryptographic keys, then you immediately open yourself to attacks, because the attacker can probably mimic your random number generator, and thus you add one weak link into the chain.
But are the digits "as good as random"? The short answer is that, as far as anyone can tell, the answer seems to be empirically yes (See Marsaglia's On the Randomness of Pi and Other Decimal Expansions). That is, there are no known ways in which the digits of $\pi$ behave systematically unlike a random number.
Cryptographic PRNG's are the gold standard since if you have a practical way to detect the slightest non-randomness in the output, that is considered a break against the generator, and a significant research result (in cryptanalysis) if the PRNG was considered any good (say if it was based on AES, the Advanced Encryption Standard, in some sensible way). It's easy to make them deterministic: for any key K, just take the encryptions E(0), E(1), E(2), ... where E is the encryption function.
One other thing: std::random_device is not your friend -- it can throw at any time for all kinds of stupid reasons. Make sure to wrap it up in a try..catch block. Or, and I recommend this, use a platform specific way to get a true random number. (On Windows, use the Crypto API. On everything else, use /dev/urandom/.)
Various applications of randomness have led to the development of different methods for generating random data. Some of these have existed since ancient times, including well-known examples like 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 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 pseudorandom number generators (CSPRNGS) also exist, with special features specifically designed for use in cryptography.
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 feature, such as in security applications, hardware generators are generally preferred over pseudorandom algorithms, where feasible.
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 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.
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. Example sources include measuring atmospheric noise, thermal noise, and other external electromagnetic and quantum phenomena. For example, cosmic background radiation or radioactive decay as measured over short timescales represent sources of natural entropy (as a measure of unpredictability or surprise of the number generation process).
The second method uses computational algorithms that can produce long sequences of apparently 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 type 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 type is non-blocking, so they are not rate-limited by an external event, making large bulk reads a possibility.
Some systems take a hybrid approach, providing randomness harvested from natural sources when available, 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 ability 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 environmental 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.
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