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.
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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.
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/.)
Could any expert in pseudo-random number generators give some detailed explanations so that I can convince my friend? I would be happy to see answers explaining further detail in some pseudo-random number generator algorithm.
Each of these is deterministic. A random number generator is an algorithm that has some internal state. Applying the algorithm once yields a new internal state and an output number. Seeding the generator means setting up an internal state; it's not always the case that the seed interface allows setting up every possible internal state. As a good rule of thumb, always assume that the default library random() routine operates at only the weakest level, level 1.
To answer your specific question, the algorithm in the question (1) cannot increase the randomness and (2) might decrease it. The expectation of randomness, thus, is strictly lower than seeding it once at the beginning. The reason comes from the possible existence of short iterative cycles. An iterative cycle for a function F is a pair of integers n and k where F^(n) (k) = k, where the exponent is the number of times F is applied. For example, F^(3) (x) = F(F(F(x))). If there's a short iterative cycle, the random numbers will repeat more often than they would otherwise. In the code presented, the iteration function is to seed the generator and then take the first output.
To answer a question you didn't quite ask, but which is relevant to getting an understanding of this, seeding with a millisecond counter makes your generator fail the test of level 3, unguessability. That's because the number of possible milliseconds is cryptographically small, which is a number known to be subject to exhaustive search. As of this writing, 2^50 should be considered cryptographically small. (For what counts as cryptographically large in any year, please find a reputable expert.) Now the number of milliseconds in a century is approximately 2^(41.5), so don't rely on that form of seeding for security purposes.
I am taking a college course that requires us to use Labview but doesn't explain it much. On a test today I was thrown when it asked for us to "create a random number generator that creates values between 20 and 40, use that to get 3 values then average them." It was more complicated than that with multiple steps after that, but I got stuck on the random number generator part.
We are using Labview 2019 on campus but I'm using 2020 at home. I know there is a random number generator range VI, but not in 2019. So my main question is how to get it to stop after 3 number and average them. I attached what I have so far, but I don't know where to go from here. I know there are probably very easy ways to do this but we have to do the most tedious basic way. If we use advanced things or ways of doing it we get penalized.
The first thing that you will need to do is to generate those 3 numbers, it can be generated within a for loop. Since for loops are more suitable to work as arrays or specific iterations, (in your case 3) you can make it to run 3 times, inside the for loop putting the dice random number generator, on the output you'll need to have indexing tunnels for work as an array, and save the value for each iteration. After that there's a VI for get the mean value of an array, but if you want to program it for yourself, again using for loops you can achieve that, but now you'll need to get the sum of that values and then divide the number of values that you have been adding in this case the array size: you can save this image and paste it in your labview enviroment:
Edit: And I just noticed you have the random number generator being multiplied by 20. That would give me a max value of 20, I need a number between 20 and 40, without using the random number range VI. Only thing I can think of is to "filter" out the number somehow. Which is why I made it go thru a logic test 20>x
Thank you so much! That's exactly what I was looking for! It's so simple now. The way you did the range on the random number generator makes so much sense now. I have to view it as a percentage, now a true number. Genius. And for the shift register, does it only output they data after the loop has ran? I understand how its storing the data by just adding to itself. So then when the loop is done, then it outputs to the divider circuit? I'm kinda trying to understand the order of operations in Labview. I'm familiar with Python how it runs the code one line at a time instead of compiling all at once. Love python, took Java the next semester then proceeded to drop it and change majors. Lol.
But there is a RANDOM() function, that gives you a random float number and you can workaround a lot of stuff with it. While I was able to randomize a 1-letter-3-numbers solution, I was not able to get 3-letters-3-numbers, here is how and why: 2351a5e196
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