I have to build an One Time Pad system and for that, I have to build my own TRNG. I want to know how to make record atmospheric noise and use that to generate random numbers. I've tried so far to record a .wav file and read it in Java, but the values don't seem very...random. Any suggestions? I know about Random.org, but I can't really use their generators, I have to build my own, so what I want is some insight into how the folks at Random.org have built their numbers generator, with atmospheric noise as a source of 'randomness'.
Non Real-time solution
What you can do is record the audio surrounding the room before in and save a temporary WAV file. If you know how the WAV file works which is based on the RIFF specification. Then strip the WAV header which is 44 bytes in length. Then read the audio bytes and do the proper conversions depending on whether you want to generate WORDS, DWORDS, or BYTES, it is up to you. Then you should have some random values to work with. Then use those random values accordingly.
Real-time solution
Since I do not know whether you want to program this in Java or some other language. In addition, I do not know the intended platform; so I cannot recommend you any realtime audio processing libraries.
For C# you can use NAudio and you can record the audio in realtime and recieve the audio bytes. Then you can convert the audio bytes into either a DWORD, QWORD, WORD, etc. You should be able to have some random values. Remember to stop recording and to release unmanaged resources when generating random numbers has ceased.
Good Resources On The WAV File Specification
Link to the specification (Easy to understand)
The answer is unknown and probably intentionally so. Although hard to be sure, the site seems to be a combination of charity and for-profit work. Each radio source only produces a few Kbps of random data. How he describes it in many links, I don't see evidence of a CSRNG. It doesn't matter. For OTP purposes, if it's not truly random, it's a glorified stream cipher. (I think that's what Bruce and others have always said.)
I find it hard to recall when a good CSRNG was broken. I'd recommend you use something like ISAAC or a properly implemented block/stream cipher. Perfect Paper Passwords does this. Use a Fortuna construction with the internals of Fortuna using the above ciphers/algorithms to produce the majority of the random data. The Fortuna system can regularly have data injected into it by a TRNG. The very best TRNG on a budget is random.org plus locally generated stuff. The best cheap, hardware solution is a VIA Artigo board with VIA Padlock (TRNG + acceleration for SHA-1, SHA256, AES, & RSA) for $300. They have libraries to help you use things, too. (There's even a pseudo-TRNG that uses processor timing under network load.)
Remember, the crypto is usually the strongest link in the chain. System security exists on many levels: processor, firmware, peripheral firmware (esp DMA), kernel mode code, OS, trusted middleware or OS functions, application. Security as a whole includes users, policy, physical security, EMSEC, etc. Anyone worrying way too much about RNG's is usually wasting effort. Just use an accepted solution or something I mentioned above. Then, focus on the rest. Especially, how people and systems interact. Configuration, patching, choice of OS, policies. Most problems happen there.
I recall an article on random.org that I can't seem to find now. I all remember is that they used the lsb of the noise they were measuring. The MSBs will certainly not be random. Then then generated a string of 1s and 0's based on the lsb. Don't do something silly like a simple binary conversion, that won't work. You maybe have to sample the noise in binary, to make the distribution of the lsb have a more uniform sampling.
The trick they used to ensure an even distribution was to not use this string of 1's and 0's as the random numbers. Instead they would parse the string, 2 bits at a time. Every time the bits matched (ie 00 or 11) they added a 1 to their random string. Every times the bits flipped (ie 01 or 10) they added a 0 to their random string.
If you make your own TRNG, make sure you verify it!
It is hardly possible to get real random numbers out of software. Even the static in your wav file is likely to be influenced by periodic EMI generated by your computer and is therefore not purely random.
Can you use special hardware or are you forced to stick to pure software? Why won't pseudo random numbers satisfy your needs? They will do fine on a relatively small number of random samples. Because you want to use the random numbers in an OTP, I guess you won't be using it in a big scale.
Can you provide a little more detail?
The atmospheric noise approach to generating random numbers is complex because the atmosphere is filled with non-random signals, all of which pollute the entropy you seek. There is an easier way.
Chances are good your CPU already contains a true random number generator, assuming you have an Intel Ivy Bridge-based Core/Xeon processor, which became available in April, 2012. (The new Haswell architecture also has this feature).
Intel's random generator exploits the random effects of thermal noise inside an unstable digital circuit. Thermal noise is just random atomic vibrations, which is pretty much the same underlying physical phenomenon that Random.org uses when it samples atmospheric noise. The sampled random bits go through a sophisticated conditioning and testing process to eliminate pollution from non-random signals. I highly recommend this excellent article on IEEE Spectrum which describes the process in detail.
Intel added a new x86 instruction called RDRAND that allows programs to directly retrieve these random numbers. Although Java does not yet support direct access to RDRAND, it's possible using JNI. This is the approach I took with the drnglib project. For example:
DigitalRandom random = new DigitalRandom();
System.out.println(random.nextInt());
The nextInt() method is implemented as a JNI native call that invokes RDRAND. The performance is pretty good considering the quality of randomness. Using eight threads, I've generated ~760 MB/sec of random data.
True random number generators (TRNGs) are usually from natural sources like seismic signals, non-stationary bio-signals, etc. The two issues faced by these generators are:
1) The data points are non-uniformly distributed
2) It takes very long time to generate large sequence of numbers (specially when the requirement is in millions).
However, the most important advantage on their part is their unpredictable nature. To overcome their issues and to retain its advantage, it is better to fuse the output of TRNG to seed a pseudo-random number generator. For this, you may try using the amplitude values of atmospheric noise at random time points and use it to seed a PRNG.
This will help you to get large numbers of uniformly distributed values. As the seed is unpredictable, the output of PRNG too becomes unpredictable.
Related
What are typical means by which a random number can be generated in an embedded system? Can you offer advantages and disadvantages for each method, and/or some factors that might make you choose one method over another?
First, you have to ask a fundamental question: do you need unpredictable random numbers?
For example, cryptography requires unpredictable random numbers. That is, nobody must be able to guess what the next random number will be. This precludes any method that seeds a random number generator from common parameters such as the time: you need a proper source of entropy.
Some applications can live with a non-cryptographic-quality random number generator. For example, if you need to communicate over Ethernet, you need a random number generator for the exponential back-off; statistic randomness is enough for this¹.
Unpredictable RNG
You need an unpredictable RNG whenever an adversary might try to guess your random numbers and do something bad based on that guess. For example, if you're going to generate a cryptographic key, or use many other kinds of cryptographic algorithms, you need an unpredictable RNG.
An unpredictable RNG is made of two parts: an entropy source, and a pseudo-random number generator.
Entropy sources
An entropy source kickstarts the unpredictability. Entropy needs to come from an unpredictable source or a blend of unpredictable sources. The sources don't need to be fully unpredictable, they need to not be fully predictable. Entropy quantifies the amount of unpredictability. Estimating entropy is difficult; look for research papers or evaluations from security professionals.
There are three approaches to generating entropy.
Your device may include some non-deterministic hardware. Some devices include a dedicated hardware RNG based on physical phenomena such as unstable oscillators, thermal noise, etc. Some devices have sensors which capture somewhat unpredictable values, such as the low-order bits of light or sound sensors.
Beware that hardware RNG often have precise usage conditions. Most methods require some time after power-up before their output is truly random. Often environmental factors such as extreme temperatures can affect the randomness. Read the RNG's usage notes very carefully. For cryptographic applications, it is generally recommended to make statistical tests the HRNG's output and refuse to operate if these tests fail.
Never use a hardware RNG directly. The output is rarely fully unpredictable — e.g. each bit may have a 60% probability of being 1, or the probability of two consecutive bits being equal may be only 48%. Use the hardware RNG to seed a PRNG as explained below.
You can preload a random seed during manufacturing and use that afterwards. Entropy doesn't wear off when you use it²: if you have enough entropy to begin with, you'll have enough entropy during the lifetime of your device. The danger with keeping entropy around is that it must remain confidential: if the entropy pool accidentally leaks, it's toast.
If your device has a connection to a trusted third party (e.g. a server of yours, or a master node in a sensor network), it can download entropy from that (over a secure channel).
Pseudo-random number generator
A PRNG, also called deterministic random bit generator (DRBG), is a deterministic algorithm that generates a sequence of random numbers by transforming an internal state. The state must be seeded with sufficient entropy, after which the PRNG can run practically forever. Cryptographic-quality PRNG algorithms are based on cryptographic primitives; always use a vetted algorithm (preferably some well-audited third-party code if available).
The PRNG needs to be seeded with entropy. You can choose to inject entropy once during manufacturing, or at each boot, or periodically, or any combination.
Entropy after a reboot
You need to take care that the device doesn't boot twice in the same RNG state: otherwise an observer can repeat the same sequence of RNG calls after a reset and will know the RNG output the second time round. This is an issue for factory-injected entropy (which by definition is always the same) as well as for entropy derived from sensors (which takes time to accumulate).
If possible, save the RNG state to persistent storage. When the device boots, read the RNG state, apply some transformation to it (e.g. by generating one random word), and save the modified state. After this is done, you can start returning random numbers to applications and system services. That way, the device will boot with a different RNG state each time.
If this is not possible, you ned to be very careful. If your device has factory-injected entropy plus a reliable clock, you can mix the clock value into the RNG state to achieve unicity; however, beware that if your device loses power and the clock restarts from some fixed origin (blinking twelve), you'll be in a repeatable state.
Predictable RNG state after a reset or at the first boot is a common problem with embedded devices (and with servers). For example, a study of RSA public keys showed that many had been generated with insufficient entropy, resulting in many devices generating the same key³.
Statistical RNG
If you can't achieve a cryptographic quality, you can fall back to a less good RNG. You need to be aware that some applications (including a lot of cryptography) will be impossible.
Any RNG relies on a two-part structure: a unique seed (i.e. an entropy source) and a deterministic algorithm based on that seed.
If you can't gather enough entropy, at least gather as much as possible. In particular, make sure that no two devices start from the same state (this can usually be achieved by mixing the serial number into the RNG seed). If at all possible, arrange for the seed not to repeat after a reset.
The only excuse not to use a cryptographic DRBG is if your device doesn't have enough computing power. In that case, you can fall back to faster algorithm that allow observers to guess some numbers based on the RNG's past or future output. The Mersenne twister is a popular choice, but there have been improvements since its invention.
¹ Even this is debatable: with non-crypto-quality random backoff, another device could cause a denial of service by aligning its retransmission time with yours. But there are other ways to cause a DoS, by transmitting more often.
² Technically, it does, but only at an astronomical scale.
³ Or at least with one factor in common, which is just as bad.
One way to do it would be to create a Pseudo Random Bit Sequence, just a train of zeros and ones, and read the bottom bits as a number.
PRBS can be generated by tapping bits off a shift register, doing some logic on them, and using that logic to produce the next bit shifted in. Seed the shift register with any non zero number. There's a math that tells you which bits you need to tap off of to generate a maximum length sequence (i.e., 2^N-1 numbers for an N-bit shift register). There are tables out there for 2-tap, 3-tap, and 4-tap implementations. You can find them if you search on "maximal length shift register sequences" or "linear feedback shift register.
from: http://www.markharvey.info/fpga/lfsr/
HOROWITZ AND HILL gave a great part of a chapter on this. Most of the math surrounds the nature of the PRBS and not the number you generate with the bit sequence. There are some papers out there on the best ways to get a number out of the bit sequence and improving correlation by playing around with masking the bits you use to generate the random number, e.g., Horan and Guinee, Correlation Analysis of Random Number Sequences based on Pseudo Random Binary Sequence Generation, In the Proc. of IEEE ISOC ITW2005 on Coding and Complexity; editor M.J. Dinneen; co-chairs U. Speidel and D. Taylor; pages 82-85
An advantage would be that this can be achieved simply by bitshifting and simple bit logic operations. A one-liner would do it. Another advantage is that the math is pretty well understood. A disadvantage is that this is only pseudorandom, not random. Also, I don't know much about random numbers, and there might be better ways to do this that I simply don't know about.
How much energy you expend on this would depend on how random you need the number to be. If I were running a gambling site, and needed random numbers to generate deals, I wouldn't depend on Pseudo Random Bit Sequences. In those cases, I would probably look into analog noise techniques, maybe Johnson Noise around a big honking resistor or some junction noise on a PN junction, amplify that and sample it. The advantages of that are that if you get it right, you have a pretty good random number. The disadvantages are that sometimes you want a pseudorandom number where you can exactly reproduce a sequence by storing a seed. Also, this uses hardware, which someone must pay for, instead of a line or two of code, which is cheap. It also uses A/D conversion, which is yet another peripheral to use. Lastly, if you do it wrong -- say make a mistake where 60Hz ends up overwhelming your white noise-- you can get a pretty lousy random number.
What are typical means by which a random number can be generated in an embedded system?
Giles indirectly stated this: it depends on the use.
If you are using the generator to drive a simulation, then all you need is a uniform distribution and a linear congruential generator (LCG) will work fine.
If you need a secure generator, then its a trickier problem. I'm side-stepping what it means to be secure, but from 10,000 feet think "wrap it in a cryptographic transformation", like a SHA-1/HMAC or SHA-512/HMAC. There are others ways, like sampling random events, but they may not be viable.
When you need secure random numbers, some low resource devices are notoriously difficult to work with. See, for example, Mining Your Ps and Qs: Detection of Widespread Weak Keys in Network Devices and Traffic sensor flaw that could allow driver tracking fixed. And a caveat for Linux 3.0 kernel users: the kernel removed a couple of entropy sources, so entropy depletion and starvation might have gotten worse. See Appropriate sources of entropy on LWN.
If you have a secure generator, then your problem becomes getting your hands on a good seed (or seeds over time). One of the better methods I have seen for environments that are constrained is Hedging. Hedging was proposed for Virtual Machines where a program could produce the same sequence after a VM reset.
The idea for hedging is to extract the randomness provided by your peer, and use it to keep you secure generator fit. For example, in the case of TLS, there is a client_random and a server_random. If the device is a server, then it would stir in the client_random. If the device is a client, then it would stir in server_random.
You can find the two papers of interest that address hedging at:
When Good Randomness Goes Bad: Virtual Machine Reset
Vulnerabilities and Hedging Deployed Cryptography
When Virtual is Harder than Real: Resource Allocation Challenges in
Virtual Machine Based IT Environments
Using client_random and a server_random is consistent with Peter Guttman's view on the subject: "mix every entropy source you can get your hands on into your PRNG, including less-than-perfect ones". Gutmann is the author of Engineering Security.
Hedging only solves part of the problem. You will still need to solve other problems, like how to bootstrap the entropy pool, how to regenerate system key pairs when the pool is in a bad state, and how persist the entropy across reboots when there's no filesystem.
Although it may not be the most complex or sound method, it can be fun to use external stimuli as your seed for random number generation. Consider using analogue input from a photodiode, or a thermistor. Even random noise from a floating pin could potentially yield some interesting results.
My application would like to get a random number, preferably with entropy if available, but does not need cryptographic quality, and would like to do ensure that the call does not block if the system entropy pool is depleted (e.g. on a server in a farm).
I am aware of CryptGenRandom, but its behaviour with respect to blocking under adverse entropy conditions is not specified.
On Unix, /dev/urandom supports this use case. Is there equivalent functionality available on Windows? I would prefer to avoid using a non-system RNG simply to get non-blocking semantics.
For a toy application, you could use the standard library function rand(), but the implementation on Windows is of notoriously poor quality. For cryptographically secure random numbers, you can use the rand_s() standard library function.
A better bet is simply to include a suitable pseudo-random number generator in your program. The Mersenne Twister is a good choice IMO, particularly as there are plenty of available implementations (including in the C++11 standard library and in Boost).
If I need non-blocking behaviour on random numbers, I generally pre-generate n numbers and store them in an in memory variable: ie if I know I will need 30 random numbers per second, takes 3 seconds to compute them (including blocks), then I will pre-generate 300 while the main code is loading, store them in an array or vector and use them at need; whilst using them I generate another one on a separate thread every time I use one up, replacing the utilised random number with the newly generated one and moving on to the next one in the list, that way when I hit the limit (in this case 300) I know when I can simply start again at the start of my array/vector/list and all the random numbers are fresh and will be non-blocking (as they are pre-generated).
This means you can use any random number generator you like and not worry about blocking behaviour, however it has the expense of utilising more ram, negligible however for the sort of coding I need random numbers for.
Hope this helps, as I couldn't fit this all into a comment:)
You could wait for one good seed full of entropy and follow GMasucci advice to pre-generate a long list of random numbers.
Unless your system is already compromised it seems that a good seed it's good enough to generate a series of non-related numbers as discussed in http://www.2uo.de/myths-about-urandom/
From the discussion I get that a continuous feed of ("true"/"fresh") random numbers it's only needed if your system state (your sources of entropy are known and the attacker knows their current state) it is compromised at some point. After feeding your block cypher more randomness, the predictability of its output will get lower.
Source of seeds? Two or more pieces of trusted software that are less likely to be already compromised. I try to blur out the predictability of the functions that use time functions as seed: local rand_function() + some variable delay + mysql's rand().
From there, a list of pseudo-random numbers generated by some good library.
What are the addresses of some websites that offers random numbers from physical sources? I'm looking both for free services and services that cost money.
I have been using http://www.random.org/, and i like it. Generates random numbers from atmospheric noise, and also is capable of generate:
coin flips
dice rolling
card shuffling
among others, take a look at it.
HotBits:
Genuine random numbers, generated by radioactive decay.
HotBits are generated by timing successive pairs of radioactive decays detected by a Geiger-Müller tube interfaced to a computer.
Once the random bytes are delivered to you, they are immediately discarded—the same data will never be sent to any other user and no records are kept of the data at this or any other site.
Secure Server HotBits Request
Sounds like the Quantum Random Bit Generator may be of use ? It relies on photonic emission in semiconductors and the detection thereof by photoelectric effect.
They supply command line and library/API access via various different platforms/frameworks.
www.Random.org
Apparently they use Atmospheric noise to generate they're numbers though I'm not sure if they've published their algorithms.
Many Linux systems have a /dev/random device built in. That provides random numbers from physical sources.
The random number generator gathers
environmental noise from device
drivers and other sources into an
entropy pool
See http://en.wikipedia.org/wiki/Urandom
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Given the extremely high requirements for unpredictability to prevent casinos from going bankrupt, what random number generation algorithm and seeding scheme is typically used in devices like slot machines, video poker machines, etc.?
EDIT: Related questions:
Do stateless random number generators exist?
True random number generator
Alternative Entropy Sources
There are many things that the gaming sites have to consider when choosing/implementing an RNG. Without due dilligence, it can go spectacularly wrong.
To get a licence to operate a gaming site in a particular jurisdiction usually requires that the RNG has been certified by an independent third-party. The third-party testers will analyse the source code and run statistical tests (e.g. Diehard) to ensure that the RNG behaves randomly. Reputable poker sites will usually include details of the certification that their RNG has undergone (for example: PokerStars's RNG page).
I've been involved in a few gaming projects, and for one of them I had to design and implement the RNG part, so I had to investigate all of these issues. Most poker sites will use some hardware device for entropy, but they won't rely on just hardware. Usually it will be used in conjunction with a pseudo-RNG (PRNG). There are two main reasons for this. Firstly, the hardware is slow, it can only extract a certain number of bits of entropy in a given time period from whatever physical process it is monitoring. Secondly, hardware fails in unpredictable ways that software PRNGs do not.
Fortuna is the state of the art in terms of cryptographically strong PRNGs. It can be fed entropy from one or more external sources (e.g. a hardware RNG) and is resilient in the face of attempted exploits or RNG hardware failure. It's a decent choice for gaming sites, though some might argue it is overkill.
Pokerroom.com used to just use Java's SecureRandom (they probably still do, but I couldn't find details on their site). This is mostly good enough, but it does suffer from the degrees of freedom problem.
Most stock RNG implementations (e.g. Mersenne Twister) do not have sufficient degrees of freedom to be able to generate every possible shuffle of a 52-card deck from a given initial state (this is something I tried to explain in a previous blog post).
EDIT: I've answered mostly in relation to online poker rooms and casinos, but the same considerations apply to physical video poker and video slots machines in real world casinos.
For a casino gaming applications, I think the seeding of the algorithm is the most important part to make sure all games "booted" up don't run through the same sequence or some small set of predictable sequences. That is, the source of entropy leading to the seed for the starting position is the critical thing. Beyond that, any good quality random number generator where each bit position as has a ~50/50 probability of being 1/0 and the period is relatively long would be sufficient. For example, something like the Mersenne twister PRNG has such properties.
Using cryptographically secure random generators only becomes important when the actual output of the random generator can be viewed directly. For example, if you were monitoring each number actually generated by the number generator - after viewing many numbers in the sequence - with a non-cryptographic generator information about that sequence can lead to establishing information about all the internal state of the generator. At this point, if you know what the algorithm looks like, you would be able to predict future numbers and that would be bad. The cryptographic generator prevents that reverse engineering back to the internal state so that predicting future numbers becomes "impossible".
However, in the case of a casino game, you would (or should) have no visibility to the actual numbers being generated under the hood. Each time a random number is generated - say a 32-bit number - that number will be used then, for example, mod 52 for a deck shuffling algorithm....no where in that process do you have any idea what numbers were being generated by the algorithm to shuffle that deck. That is, most of the bits of "randomness" is just being thrown out and even the ones being used you have no visibility to. Therefore, no way to reverse engineer the state.
Getting back to a true source of entropy to seed the whole process, that is the hard part. See the Wikipedia entry on entropy for some starting points on techniques.
As an aside, if you did want cryptographically sequence random numbers from a "regular" algorithm, a simple approach is to take a few random numbers in sequence, concatenate them together and then run something like MD5 or SHA-1 on them and the result is just as random and also cryptographically secure. That is, you just made your own "secure" random number generator.
We've been using the Protego R210-USB TRNG (and the non-usb version before that) as random seed generators in casino applications, with java.security.SecureRandom
on top. We had The Swedish National Laboratory of Forensic Science perform a separate audit of the R210, and it passed without a flaw.
You probably need a cryptographically secure pseudo-random generator. There are a lot of variants. Google "Blum-Blum-Shub", for example.
The security properties of these pseudo-random generators will generally be that, even when the attacker can observe polynomially many outputs from such generators, it won't be feasible to guess the next output with a probability much better than random guessing. Also, it is not feasible to distinguish the output of such generators from truly random bits. The security holds even when all the algorithms and parameters are known by the attacker (except for the secret seed).
The security of the generators is often measured with respect to a security parameter. In the case of BBS, it is the size of the modulus. This is no different from other crypto stuff. For example, RSA is secure only when the key is long enough.
Note that, the output of such generators may not be uniform (in fact, can be far away from uniform in statistical sense). But since no one can distinguish the two distributions without infinite computing power, these generators will suffice in most applications that require truly random bits.
Bear in mind, however, that these cryptographically secure pseudo-random generators are usually slow. So if speed is indeed a concern, less rigorous approaches may be more relevant, such as using hash functions, as suggested by Jeff.
Casino slot machines generate random numbers continuously at very high speed and use the most recent result(s) when the user pulls the lever (or hits the button) to spin the reels.
Even a simplistic generator can be used. Even if you knew the algorithm used, you cannot observe where in the sequence it is because nearly all the results are discarded. If somehow you did know where it was in the sequence, you'd have to have millisecond or better timing to take advantage of it.
Modern "mechanical reel" machines use PRNGs and drive the reels with stepper motors to simulate the old style spin-and-brake.
http://en.wikipedia.org/wiki/Slot_machine#Random_number_generators
http://entertainment.howstuffworks.com/slot-machine3.htm
Casinos shouldn't be using Pseudo-random number generators, they should be using hardware ones: http://en.wikipedia.org/wiki/Hardware_random_number_generator
I suppose anything goes for apps and offshore gambling nowadays, but all these other answers are incomplete, at least for Nevada Gaming Control Board licensed machines, which I believe the question is originally about.
The technical specifications for RNGs licensed in Nevada for gaming purposes are laid out in Regulation 14.040(2).
As of May 24, 2012, here is a summary of the rules a RNG must follow:
Static seeds cannot be used. You have to seed the RNG using a millisecond time source or other true entropy source which has no external readout anywhere on the machine. (This helps to reduce the incidence of "magic number" attacks)
The RNG must continue generating numbers in its sequence at least 100 times per second when the game is not being played. (This helps to avoid timing attacks)
RNG outputs cannot be reused; they must be used exactly once if at all and then thrown away.
Multi-system cabinets must use a separate RNG and separate seed for each game.
Games that use RNGs for helping to choose numbers on behalf of the player (such as Lotto Quick Pick) must use a separate RNG for that process.
Games must not roll RNGs until they are actually needed in a game. (i.e. you need to wait until the player chooses to deal or spin before generating RNGs)
The RNG must pass a 95% confidence chi-squared test based on 10,000 trials as apart of a system test. It must display a warning if this test fails, and it must disable play if it fails twice in a row.
It must remember, and be able to report on, the last 10 test results as described in 7.
Every possible game outcome must be generatable by the RNG. As a pessimal example, linear congruential generators don't actually generate every possible output in their range, so they're not very useful for gaming.
Additionally, your machine design has to be submitted to the gaming commission and it has to be approved, which is expensive and takes lots of time. There are a few third-party companies that specialize in auditing your new RNG to make sure it's random. Gaming Laboratories publishes an even stricter set of standards than Nevada does. They go into much greater detail about the limitations of hardware RNGs, and Nevada in particular likes to see core RNGs that it's previously approved. This can all get very expensive, which is why many developers prefer to license an existing previously-approved RNG for new game projects.
Here is a fun list of random number generator attacks to keep you up late at night.
For super-nerds only: the source for most USB hardware RNGs is typically an avalanche diode. However, the thermal noise produced by this type of diode is not quantum-random, and it is possible to influence the randomness of an avalanche diode by significantly lowering the temperature.
As a final note, someone above recommended just using a Mersenne Twister for random number generation. This is a Bad Idea unless you are taking additional entropy from some other source. The plain vanilla Mersenne Twister is highly inappropriate for gaming and cryptographic applications, as described by its creator.
If you want to do it properly you have to get physical - ERNIE the UK national savings number picker uses a shot noise in Neon tubes.
I for sure have seen a german gambling machine that was not allowed to be ran commercially after a given date, so I suppose it was a PNRG with a looong one time pad seed list.
Most poker sites use hardware random number generators. They will also modify the output to remove any scaling bias and often use 'pots' of numbers which can be 'stirred' using entropic events (user activity, serer i/o events etc). Quite often the resultant numbers just index pre-generated decks (starting off as a sorted list of cards).
It'd be nice to be able, for some purposes, to bypass any sort of algorithmically generated random numbers in favor of natural input---say, dice rolls. Cryptographic key generation, for instance, strikes me as a situation where little enough random data is needed, and the requirement that the data be truly random is high enough, that this might be a feasible and desirable thing to do.
So what I'd like to know, before I go and get my hands dirty, is this: does any software exist for building an entropy pool directly from random digit input? Note that it's not quite enough to simply convert things from radix r to radix 2; since, for instance, 3 and 2 are relatively prime, it's not entirely straightforward to turn a radix-3 (or radix-6) number into binary digits while holding onto maximal entropy in the original input.
The device /dev/random does exactly this on Linux -- maybe it would be worth looking at the source?
EDIT:
As joeytwiddle says, if sufficient randomness is unavailable, /dev/random will block, waiting for entropy to "build up" by monitoring external devices (e.g. mouse, disk drives). This may or may not be what you want. If you'd prefer never to wait and are satisfied with possibly-lower-quality randomness, use /dev/urandom instead -- it's a non-blocking pseudorandom number generator that injects randomness from /dev/random whenever it is available, making it more random than a plain deterministic PRNG. (See man /dev/urandom for further details.)
This paper suggests various approaches with implementation ideas for both UN*X and Windows.
I'm not sure what you're asking for. "Entropy pool" is just a word for "some random numbers", so you could certainly use dice rolls; simply use them as the seen to a pseudorandom number generator that has the characteristics you want.
You can get physically generated random numbers online from, eg, Lavarnd or Hotbits.
Note that the amount of entropy in the pool doesn't necessarily have to be an integer. This should mostly deal with your prime-factors-other-than-2 issue.
Even if you end up using an implementation that does require integer estimates, you need quite a few dice rolls to generate a crypto key. So you could just demand them in bunches. If the user gives you the results of 10 d6 rolls, and you estimate the entropy as 25 bits, you've only lost 0.08 bits per dice roll. Remember to round down ;-)
Btw, I would treat asking the user for TRNG data, rather than drawing it from hardware sources as /dev/random does, to be a fun toy rather than an improvement. It's difficult enough for experts to generate random numbers - you don't want to leave general users at the mercy of their own amateurism. "The generation of random numbers is too important to be left to chance" --Robert Coveyou.
By another way, the authors of BSD argue that since entropy estimation for practical sources on PC hardware isn't all that well understood (being a physics problem, not a math problem), using a PRNG isn't actually that bad an option, provided that it is well-reseeded according to Schneier / Kelsey / Ferguson's Yarrow design. Your dice idea does at least have the advantage over typical sources of entropy for /dev/random, that as long as the user can be trusted to find fair dice and roll them properly, you can confidently put a lower bound the entropy. It has the disadvantage that an observer with a good pair of binoculars and/or a means of eavesdropping on their keyboard (e.g. by its E/M emissions) can break the whole scheme, so really it all depends on your threat model.