C++11 comes with a set of PRNG's.
In what situation should one choose one over another? What are their advantages, disadvantages etc.
I think the Mersenne twister std::mt19937 engine is just fine as the "default" PRNG.
You can just use std::random_device to get a non-deterministic seed for mt19937.
There is a very interesting talk from GoingNative 2013 by Stephan T. Lavavej:
rand() Considered Harmful
You can download the slides as well from that web site. In particular, slide #23 clearly compares mt19937 vs. random_device:
mt19937 is:
Fast (499 MB/s = 6.5 cycles/byte for me)
Extremely high quality, but not cryptographically secure
Seedable (with more than 32 bits if you want)
Reproducible (Standard-mandated algorithm)
random_device is:
Possibly slow (1.93 MB/s = 1683 cycles/byte for me)
Strongly platform-dependent (GCC 4.8 can use IVB RDRAND)
Possibly crypto-secure (check documentation, true for VC)
Non-seedable, non-reproducible
The trade-off is speed, memory foot-print and period of PRNG.
Linear Congruential Generators: fast, low memory, small period
Lagged Fibonacci(Subtract with Carry): fast, large memory, large period
Mersenne Twister: slow, very large memory, very large period
Related
I need to generate cryptographically secure random data in c++11 and I'm worried that using random_device for all the data would severely limit the performance (See slide 23 of Stephan T. Lavavej's "rand() Considered Harmful" where he says that when he tested it (on his system), random_device was 1.93 MB/s and mt19937 was 499 MB/s) as this code will be running on mobile devices (Android via JNI and iOS) which are probably slower than the numbers above.
In addition I'm aware that mt19937 is not cryptographically secure, from wikipedia: "observing a sufficient number of iterations (624 in the case of MT19937, since this is the size of the state vector from which future iterations are produced) allows one to predict all future iterations".
Taking all of the above information into account, can I generate cryptographically secure random data by generating a new random seed from random_device every 624 iterations of mt19937? Or (possibly) better yet, every X iterations where X is a random number (from random_device or mt19937 seeded by random_device) between 1 and 624?
Don't do this. Seriously, just don't. This isn't just asking for trouble--it's more like asking and begging for trouble by going into the most crime-ridden part of the most dangerous city you can find, carrying lots of valuables.
Instead of trying to re-seed MT 19937 often enough to cover up how insecure it is, I'd advise generating your random numbers by running AES in counter mode. This requires that you get one (but only one) good random number of the right size to use as your initial "seed" for your generator.
You use that as the key for AES, and simply use it to encrypt sequential numbers to get a stream of output that looks random, but is easy to reproduce.
This has many advantages. First, it uses an algorithm that's actually been studied heavily, and is generally believed to be quite secure. Second, it means you only need to distribute one (fairly small) random number as the "key" for the system as a whole. Third, it probably gives better throughput. Both Intel's and (seemingly) independent tests show a range of throughput that starts out competitive with what you're quoting for MT 19937 at the low end, and up to around 4-5 times faster at the top end. Given the way you're using it, I'd expect to see you get results close to (and possibly even exceeding1) the top end of the range they show.
Bottom line: AES in counter mode is obviously a better solution to the problem at hand. The very best you can hope for is that MT 19937 ends up close to as fast and close to as secure. In reality, it'll probably disappoint both those hopes, and end up both slower and substantially less secure.
1. How would it exceed those results? Those are undoubtedly based on encrypting bulk data--i.e., reading a block of data from RAM, encrypting it, and writing the result back to RAM. In your case, you don't need to read the result from RAM--you just have to generate consecutive numbers in the CPU, encrypt them, and write out the results.
The short answer is, no you cannot. The requirements for a cryptographically secure RNG are very stringent, and if you have to ask this question here, then you are not sufficiently aware of those requirements. As Jerry says, AES-CTR is one option, if you need repeatability. Another option, which does not allow repeatability, would be to look for an implementation of Yarrow or Fortuna for your system. In general it is much better to find a CSRNG in a library than to roll your own. Library writers are sufficiently aware of the requirements for a good CSRNG.
I've been working on a physics simulations requiring the generation of a large amount of random numbers (at least 10^13 if you want an idea). I've been using the C++11 implementation of the Mersenne twister. I've also read that GPU implementation of this same algorithm are now a part of Cuda libraries and that GPU can be extremely efficient at this task; but I couldn't find explicit numbers or a benchmark comparison. For example compared to an 8 cores i7, are Nvidia cards of the last generations more performant in generating random numbers? If yes, how much and in which price range?
I'm thinking that my simulation could gain from having a GPU generating a huge pile of random numbers and the CPU doing the rest.
Some comparisons can be found here:
https://developer.nvidia.com/cuRAND
If you have a new enough Intel CPU (IvyBridge or newer), you can use the RDRAND instruction.
This can be used via the _rdrand16_step(), _rdrand32_step() and _rdrand64_step() intrinsic functions.
Available via VS2012/13, Intel compiler and gcc.
The generated random number is originally seeded on a real random number. Designed for NIST SP 800-90A compliance, its randomness is very high.
Some numbers for reference:
On an IvyBridge dual core laptop with HT (2.3GHz), 2^32 (4 Gigs) random 32bit numbers took 5.7 seconds for single thread and 1.7 seconds with OpenMP.
I'm coding a physics simulation heavily using random numbers, I just profiled my code for the first time so I may be in wrong in reading the output but I see this line coming first:
% cumulative self self total
time seconds seconds calls ms/call ms/call name
90.09 21.88 21.88 265536 0.08 0.08 std::mersenne_twister_engine<unsigned long, 32ul, 624ul, 397ul, 31ul, 2567483615ul, 11ul, 4294967295ul, 7ul, 2636928640ul, 15ul, 4022730752ul, 18ul, 1812433253ul>::operator()()
It seems to mean that generating number generator takes 90% of the time.
I had already written a previous post asking if not constructing the random probability distributions at each loop could save me time but after trying and timing it didn't help (Is defining a probability distribution costly? ). Are there common options for optimizing random number generation?
Thank you in advance, my simulations (in its current state) runs for days so reducing on 90% of this computation time would be a significant progress.
There is always a trade-off between the efficiency, i.e. speed and size (number of bytes of the state), on the one hand and "randomness" of any RNG on the other. The Mersenne twister has quite good randomness (provided you use a high-entropy seed, such as provided by std::random_device), but slow and has large state. std::minstd_rand or std::knuth_b (linear congruential) are faster and ranlux48 (Fibbonacci) yet faster, but are less random (pass fewer test for randomness, i.e. have some non-random spectral properties). Just experiment and test if you're happy with the randomness provided (i.e. have no unsuspected correlations in the random data).
edit: 1 All these RNG are not truly random, of course, and are also not random enough for cryptography. If you need that, use std::random_device, but don't complain about speed. 2 In parallel (which you should consider), use thread_local RNGs, each initialised with another seed.
If your code spends most of its time generating random numbers, you may want to take some time to choose the best algorithm for your application and implement it yourself. The Mersenne Twister is a pretty fast algorithm, and has good randomness, but you can always trade off some quality of the random numbers generated for more speed. It will depend on what your simulation requires and on the type of numbers you are generating (ints or floats). If you absolutely need good randomness, Mersenne Twister is probably already one of your best options. Otherwise, you may want to implement a simple linear congruential generator in your code.
Another thing to watch out for is if your code is parallel, you should be using a reentrant version of the random number generator and make sure that different threads use their own internal state variables for their generators. Otherwise, mutexes to avoid overwriting internal state variables of the generator will slow down your code a lot. Many library generators are not reentrant, mind you. If your code is not parallel, you should probably parallelize it and use a separate thread to populate a list of random numbers for your simulation to consume. Another option is to use the GPU to generate random numbers in parallel.
Here are some links comparing the performance of diferent generators:
http://www.boost.org/doc/libs/1_38_0/libs/random/random-performance.html
https://www.gnu.org/software/gsl/manual/html_node/Random-Number-Generator-Performance.html
Use a dedicated random number library.
I would suggest WELL512 (link contains the paper and source code).
Marsaglia's KISS RNG is fast and is fine for simulation work. I am assuming that you don't need cryptographic quality.
If the randomness requirements allow it, you can use the RDTSC instruction to get random numbers, e.g. int from0to9 = rdtsc() % 10.
I have a class that contains two sources of randomness.
std::random_device rd;
std::mt19937 random_engine;
I seed the std::mt19937 with a call to std::random_device. If I want to generate a number and I don't care about repeatability, should I call rd() or random_engine()?
In my particular case, I'm sure both would work just fine, because this is going to be called in some networking code where performance is not at a premium, and the results are not especially sensitive. However, I am interested in some "rules of thumb" on when to use hardware entropy and when to use pseudo-random numbers.
Currently, I am only using std::random_device to seed my std::mt19937 engine, and any random number generation I need for my program, I use the std::mt19937 engine.
edit: Here's an explanation for exactly what I am using this particular example for:
This is for a game playing program. This particular game allows the user to customize their 'team' prior to beginning a round against an opponent. Part of setting up a battle involves sending a team to the server. My program has several teams and uses the random number to determine which team to load. Each new battle makes a call to std::random_device to seed the pseudo-random number generator. I log the initial state of the battle, which includes this team that I'm randomly selecting and the initial seed.
The particular random number I'm asking about in this question is for the random team selection (where it is beneficial to not have the opponent know ahead of time what team I'm using, but not mission-critical), but what I'm really looking for is a rule of thumb. Is it fine to always use std::random_device if I don't need repeatability of my numbers, or is there a real risk of using up entropy faster than it can be collected?
The standard practice, as far as I am aware, is to seed the random number generator with a number that is not calculated by the computer (but comes from some external, unpredictable source). That should be the case with your rd() function. From then on, you call the pseudo-random number generator(PRNG) for each and every pseudo-random number that you need.
If you are worried about the numbers not being random enough, then you should pick a different PRNG. Entropy is a scarce and precious resource and should be treated as such. Although, you may not be needing that many random numbers right now, you may in the future; or other applications could need them. You want that entropy to be available whenever an application asks for it.
It sounds like, for your application, that the mersenne twister will suit your needs just fine. No one who plays your game will ever feel like the teams that are loaded aren't random.
If you are not using it for encryption it is fine and well to repeatedly use mt19937 which is seeded by random_engine.
For the rest of this answer, I assume you are using the random numbers for encryption in your networking code. In short, mt19937 is not suitable for that use.
http://en.wikipedia.org/wiki/Mersenne_twister#Disadvantages
There is a potential risk that you will leak information (perhaps indirectly) over time so that an attacker could start to predict the random numbers. At least in theory, but this is what it's about. From Wikipedia
...since this figure is the size of the state vector from
which future iterates are produced) allows one to predict all future iterates.
A simple means of preventing random number generation information to leak to the user is to use one-way hash functions, but there's much more to it. You should use a random number generator designed for that purpose:
http://en.wikipedia.org/wiki/Cryptographically_secure_pseudorandom_number_generator
Various examples (with code) are found here http://xlinux.nist.gov/dads/HTML/pseudorandomNumberGen.html
If you need randomness for a simulation or a game, then that you're doing is fine. Call the random device just once, and do everything else with a randomly seeded pseudo-RNG. As a bonus, you should store the seed value in a log file so you can later replay the pseudo-random sequence:
auto const seed = std::random_device()();
// save "seed" to log file
std::mt19937 random_engine(seed);
(For multiple threads, use the PRNG in the main thread to generate seeds for further PRNGs in the spawned threads.)
If you need a lot of true randomness for cryptographic purposes, then a PRNG is never a good idea, though, since a long sequence of output contains a lot less randomness than true randomness, i.e. you can predict all of it from a small subset. If you need true randomness, you should collect it from some unpredictable source (e.g. heat sensors, user keyboard/mouse activity, etc.). Unix's /dev/random may be such a "true randomness" source, but it may not fill up very quickly.
You may want to have a look at http://channel9.msdn.com/Events/GoingNative/2013/rand-Considered-Harmful that explains why you should use uniform_int_distribution, and the relatives strengths of random_device / mt19937.
In this video, Stephan T. Lavavej specifically states that on visual C++, random_device can be used for cryptographic purposes.
The answer is platform dependent. I seem to remember that with Visual C++ 2010, std::random_device is just mt19937 seeded in some undocumented way.
Of course you realize that any ad hoc encryption scheme based on a random number generator is likely to be very weak.
Assuming this is not for cryptographic purposes, the most important thing to remember about random number generation is to think of how you want the distribution of the random numbers to be and what is the range you are expecting.
Usually standard random number generators within libraries are designed to give out uniform distribution. So the numbers will range between 0 and some RAND_MAX ( say on 32 bit machine it is 2^31 -1 )
Now here is the thing to remember with pseudo random number generators. Most of them are designed to generate random numbers and not random bits. The difference is subtle. If you need numbers between 0 and 8 most programmers will say rand()%8
This is bad because the algorithm was for randomizing 32 bits. But you are using only the bottom 3 bits. No good. This will not give you a uniform distribution (assuming that is what you are looking for)
You should use 8 * (rand() + 1) / (RAND_MAX) which will now give you a uniformly random number between 0 and 8.
Now with hardware random number generators you may have random bits being produced. If that is indeed the case, then you have each bit independently being generated. Then it is more like a set of identical independent random bits. The modeling here would have to be a bit different. Keep that in mind, especially in simulations the distribution becomes important.
I'm using kubuntu with kernel 2.6.38-12-generic
I want to read 16 random numbers from /dev/random at the start of my program.
However, it blocks after a relatively short time.
How long does it take for the /dev/random buffer to fill? why is it taking so long to fill.
I'm using this as a uuid generator with other sources of randomness added to seed
my mersenne twister. It's critical that I don't get duplicates or a duplicate seed.
If I change to /dev/urandom it works ok. Any view on using /dev/random over /dev/urandom.
You really should never use /dev/random. There are no known circumstances where the advantages of /dev/random over /dev/urandom matter, and the disadvantages are pretty obvious.
The difference is that /dev/urandom provides 'merely' cryptographically-secure random numbers while /dev/random provides truly random numbers (at least, that is what we believe). But there is no known situation where this difference matters and no known test that can distinguish "true" randomness from merely cryptographically-secure randomness.
I usually joke that /dev/urandom provides water and /dev/random provides holy water.
The man page of man 4 random answers the question:
When read, the /dev/random device will only return random bytes
within the estimated number of bits of noise in the entropy pool.
/dev/random should be suitable for uses that need very high quality
randomness such as one-time pad or key generation. When the
entropy pool is empty, reads from /dev/random will block until
additional environmental noise is gathered.
I'm so surprised people prefer asking than reading the man pages! You don't even need Internet to read the man pages of your system.
BTW, as I commented, the entropy pool is fed by physical phenomena (depends of the hardware), like e.g. mouse movements, key presses, ethernet packets, etc. Some few processors have a hardware random noise generator (e.g. the RDRAND machine instruction), and you can buy random USB devices (see also this list), etc.... Hence reading from /dev/random could be expansive (or even blocking). You'll use it for high quality randomness (e.g. required by cryptographic keys) or, at initialization, for seeding your PRNG. You should expect /dev/random to have a relatively small bandwidth (e.g. a few kilobytes or at most a megabyte per second at most) and it could have a lot of latency (dozens of milliseconds, or even more). Details are of course computer specific.
Read also Thomas Hühn's Myths about /dev/urandom
Reading from /dev/random is non-determinstic, because all it does is fetch the requested number of bits from the random pool. It will block until it can read the requested number of bits.
/dev/urandom, however, is the kernel's PRNG, and can supply a near-infinite stream of pseudo-random numbers.