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Introduction to Randomness and Random Numbers

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Explain why your school work is important. Describe the ways you help out at home. A good deal of research has gone into pseudo-random number theory, and modern algorithms for generating pseudo-random numbers are so good that the numbers look exactly like they were really random.

Because PRNGs generate random numbers by using mathematical formulae or precalculated lists, using one corresponds to someone rolling a die many times and writing down the results. Whenever you ask for a die roll, you get the next on the list.

Effectively, the numbers appear random, but they are really predetermined. PRNGs are efficient , meaning they can produce many numbers in a short time, and deterministic , meaning that a given sequence of numbers can be reproduced at a later date if the starting point in the sequence is known.

Efficiency is a nice characteristic if your application needs many numbers, and determinism is handy if you need to replay the same sequence of numbers again at a later stage. PRNGs are typically also periodic , which means that the sequence will eventually repeat itself. While periodicity is hardly ever a desirable characteristic, modern PRNGs have a period that is so long that it can be ignored for most practical purposes.

These characteristics make PRNGs suitable for applications where many numbers are required and where it is useful that the same sequence can be replayed easily. Popular examples of such applications are simulation and modeling applications. PRNGs are not suitable for applications where it is important that the numbers are really unpredictable, such as data encryption and gambling. It should be noted that even though good PRNG algorithms exist, they aren't always used, and it's easy to get nasty surprises.

Take the example of the popular web programming language PHP. However, if you use PHP for Microsoft Windows, you will probably find that your random numbers aren't quite up to scratch as shown in this visual analysis from Another example dates back to when one researcher reported that the PRNG on MacOS was not good enough for scientific simulation of virus infections.

The bottom line is that even if a PRNG will serve your application's needs, you still need to be careful about which one you use. You can imagine this as a die connected to a computer, but typically people use a physical phenomenon that is easier to connect to a computer than a die is. The physical phenomenon can be very simple, like the little variations in somebody's mouse movements or in the amount of time between keystrokes. In practice, however, you have to be careful about which source you choose.

For example, it can be tricky to use keystrokes in this fashion, because keystrokes are often buffered by the computer's operating system, meaning that several keystrokes are collected before they are sent to the program waiting for them. To a program waiting for the keystrokes, it will seem as though the keys were pressed almost simultaneously, and there may not be a lot of randomness there after all. However, there are many other ways to get true randomness into your computer.

A really good physical phenomenon to use is a radioactive source. The points in time at which a radioactive source decays are completely unpredictable, and they can quite easily be detected and fed into a computer, avoiding any buffering mechanisms in the operating system.

The HotBits service at Fourmilab in Switzerland is an excellent example of a random number generator that uses this technique. Another suitable physical phenomenon is atmospheric noise, which is quite easy to pick up with a normal radio.

You could also use background noise from an office or laboratory, but you'll have to watch out for patterns. The fan from your computer might contribute to the background noise, and since the fan is a rotating device, chances are the noise it produces won't be as random as atmospheric noise. Thunderstorms generate atmospheric noise. As long as you are careful, the possibilities are endless. Undoubtedly the visually coolest approach was the lavarand generator , which was built by Silicon Graphics and used snapshots of lava lamps to generate true random numbers.

Unfortunately, lavarand is no longer operational, but one of its inventors is carrying on the work without the lava lamps at the LavaRnd web site. ORG, but also from web page hits received by the EntropyPool's own web server. Regardless of which physical phenomenon is used, the process of generating true random numbers involves identifying little, unpredictable changes in the data.

ORG uses little variations in the amplitude of atmospheric noise. They are also nondeterministic , meaning that a given sequence of numbers cannot be reproduced, although the same sequence may of course occur several times by chance. TRNGs have no period. These characteristics make TRNGs suitable for roughly the set of applications that PRNGs are unsuitable for, such as data encryption, games and gambling.

Conversely, the poor efficiency and nondeterministic nature of TRNGs make them less suitable for simulation and modeling applications, which often require more data than it's feasible to generate with a TRNG. The following table contains a summary of which applications are best served by which type of generator:.

One characteristic that builders of TRNGs sometimes discuss is whether the physical phenomenon used is a quantum phenomenon or a phenomenon with chaotic behaviour. There is some disagreement about whether quantum phenomena are better or not, and oddly enough it all comes down to our beliefs about how the universe works. The key question is whether the universe is deterministic or not, i.

Determinism is a difficult subject that has been the subject of quite a lot of philosophical inquiry, and the problem is far from as clear cut as you might think.

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Introduction to Randomness and Random Numbers. by Dr Mads Haahr. is a true random number service that generates randomness via atmospheric noise. This page explains why it's hard (and interesting) to get a computer to generate proper random numbers. comprehensive analysis of’s numbers as her nal year project. As part of the project, Louise identi ed and implemented a series of ve tests particularly suitable for true random numbers and compared the quality of the numbers generated at with those generated by Silicon Graphics’lavarandgenerator.

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