True random number generation

问题:

How is exactly that we talk about "true random" numbers when we are actually measuring something. I mean, isn't measuring almost the opposite of randomness.

Som articles says that, for example, throwing a dice is "true random". Of course it isn't Pseudo-random, but is it even random?? If you could have a machine that throw dices from de exactly same position and always in the same direction with the exact same force always: woudn't it always turn out the same number? (I thing it does).

Please, can someone help me understand "true random" numbers??

回答1:

Quantum effects are the source of this "True Randomness". E.g. the Heisenberg Uncertanity Principle says that your dice thrower can't exactly define both impulse and location of its throwing arm. (Reading up on pop-sci quantum physics can be scary - the predictability and stability of our world seems to be no more than a great feat of statistics.)

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[edit] Since it came up in the comments: There are other, less "obscure" processes "looking random", e.g. wear and air turbulence for a die roll. However, all these things could be argued to be beyond our knowledge but fundamentally deterministic (assuming an objective reality.) Quantum processes are truly random at least under the widely accepted Copenhagen interpretation. [/edit]

There are - as mentioned in other replies - appliances that turn quantum effects into observable random number generators. There are algorithms to "extract" the randomness of any stream of data. There are test algorithms to check if a stream of data "behaves" like a random stream.

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OTOH you can argue rather successfully that "random" is a man-made concept, i.e. something that isn't integral part of the objective world, but our limit of understanding (though the uncertainty principle is considered to be not just an observer effect).

When someone asks for any random number generator, the counter question should be: for what application? In the context of this discussion: who do you need to fool? Pseudo vs. True are just generation mechanisms, not fundamental opposites.

In that sense, chaotic beahvior is often "random enough" for most purposes, and can be created with few degrees of freedom already.

回答2:

Randomness is essentially a measure of how much we don't know. The universe may or may not be truly deterministic, it doesn't matter - we don't know (and have no foreseeable way of knowing) what the exact time between 2 cosmic ray impacts will be. For pseudorandom numbers, we do, in principle, have a way of knowing, because we can recreate the initial conditions and get the same output again.

回答3:

I think that when some talks about "true random" numbers in IT this is always from measuring/observing something that is thought to be random in contrast to the pseudo-random algorithms that will always return the very same pattern (given the same starting point or after wrapping around after a certain length). For example, I've heard about devices that measure the electric noise produced by some components like transistors. This is indeed "more" random than a deterministic algorithm.

To increase the "randomness" I know that for example Linux tries to incorporate various external events into its random number generator, for example mouse movements, key presses (AFAIK even duration of key presses), timings from the HD, etc. pp. That is, they try to improve the deterministic algorithm by adding indeterministic sources to it.

回答4:

For true randomness you'll need to observe physical events. Try this.

回答5:

True random numbers are those impossible to predict even when you have all the information you can currently collect. For example, the decay of radioactive atoms, wind direction and velocity at different places in the world or even the noise generated by a webcam (this list is in decreasing degrees of impossibility to predict.) There is no guarantee that what's random now will be random a thousand years from now.

Pseudo random numbers are totally possible to predict with the right information, either exploting flaws or knowing the seeds.

To get as close as possible to true random numbers in a computer, you'd need some special hardware.

The crucial difference is that we currently don't know how to predict stuff considered random, but we do currently know how to predict pseudo random numbers.

See this question for all the information you could possibly want about this.

回答6:

I suppose, theoretically, a precise machine could be built that could skew the results of a die throw. In practice, though, there is always some level of variation that can't be predicted. That's where the randomness comes from. Certainly when a person throws a die, there is so much variation in each throw that the result is "truly random".

Computers can generate "true random" numbers by making use of random phenomena like quantum mechanical effects, or electro-magnetic noise.

回答7:

On computer (Quartz) you can't generate true random because 2+2 is always 4. Then your random can be only pseudo random better or not better depends on how good this is hashed.

回答8:

True randomization is a problem when you are working with logic, logic isn't random (at least not if it's working correctly..) That's the reason to why some cryptographic programs ask you to move your mouse in a random pattern since it's hard to reverse engineer you ;)

Anyway, as @DarkDust said, and @mdrg mentioned, you have to rely on physical observations, an example would be to hook up a radition meter and observe when some radioactive materia falls apart. Or measure the wind speed outside. Or measure the noise in some transistor. With some mathematical transformation it's impossible (apart from brute force..) to reverse engineer that random number then.

回答9:

Randomness is really important for a large set of problem solving techniques in AI, economics, physics etc. The need to impose a probability distribution over a set of possible outcomes drives the need for better and better random number generation.

That said, true randomness is probably a debatable concept. Deterministically speaking it shouldn't happen - a la your dice tossing example. I think this is kind of a sensitive argument for philosophers. In reality we can take 'random' measurement with a geiger counter and some radioactive material. In an ideal setting this gives us a pretty good result made by measurement.

From a human perspective the randomness of our number generators only needs to achieve a certain probability of being random given a priori knowledge of the desired complexity of the outcome the random numbers are going to be required for.

If you think about using Bayes principle given the degree of true randomness measured by some arbitrary notion about how good your random numbers are (In the form of a probability distribution) then you can say something about 'trueness' of man-made random number generation. In fact the 'trueness' will approach zero as the period of a truely random number generator is infinite. This only matters when you get that far but we can't - so 'truely random' is a pretty useless distinction for computer scientists who know how to design a nice pseudo-random (everything is pseudo-random relative to some scale) number generator.

回答10:

Experiments have shown that coin tossing by a human is not random - it appears that there is roughly a 51% chance that the face upwards when the coin is tossed will show when it lands.

Any physical event that is based on very large numbers is likely to generate true random numbers - examples are white noise or the last few digits of the number of transactions in a day on a major stock market.

Measurement is not the opposite of randomness. Measuring randomness can only be done on very large numbers of the random event, and is statistical in nature. What measuring randomness does is look for patterns in the event at different levels - single events, runs of two events, runs of three events etc. A pseudo random generator will generate patterns, if only the full cycle of the generator, but the better generators show fewer patterns.

回答11:

From Japan, we are producing modules and PC-boards for True random number generator with the self check function. I think, you can study what is the true random from our "theory" web pagem since how to check the random number randomness is equal to understanding the true randomness.
Please visit our web site, www.letech-rng.jp, and you can see, we joined Monte-Carlo conference 2010, and presented this theory. And also, you can download our paper at the conference, if you like.

回答12:

Any number produced by applying classical physics cannot be truly random, because the parameters can be known and outcomes can be influenced by outside interference. The throw of the dice for example is not random. However, since influencing or determining the result of the throw would be very complicated, most people would call this a "true" random result. For all intents and purposes, it can be considered random. But strictly speaking, it is not truly random. Even the weather is not random. It can (theoretically) be influenced and predicting it is immensely complicated. In theory, you can know all parameters that influence it. In practice, you can't, but that's not good enough for true randomness, where actual theoretical impossibility of prediction or influence is a must.

The only true source of randomness, where the result is not predictable even when all involved parameters are known and outside interference cannot influence the result in any predictable manner, is the observation of certain quantum events. It has been mathematically proven that quantum behavior is unpredictable. Radioactive decay, for example. Random number generators based on radioactive decay do actually exist. An easier source of true randomness is the observation of photons reflecting off of a semi-transparent mirror. Such RNGs also exist. A search for "quantum random number generators" should give some quite interesting reads.

回答13:

I have created a random pad using microphone audio input of the room noise combined with a pseudorandom. This is the only possible way I could think of (adding some kind of an analog, unpredicted, signal) to create true randomness.