Our RNGs

There are many kinds of RNGs, with different trade-offs. Rand provides some convenient generators in the rngs module. Often you can just use thread_rng, a function which automatically initializes an RNG in thread-local memory and returns a reference to it. It is fast, good quality, and (to the best of our knowledge) cryptographically secure.

Contents of this documentation:

1. The generators
2. Performance and size
3. Quality and cycle length
4. Security
5. Extra features
6. Further reading

The generators

Basic pseudo-random number generators (PRNGs)

The goal of "standard" non-cryptographic PRNGs is usually to find a good balance between simplicity, quality, memory usage and performance. Non-cryptographic generators pre-date cryptographic ones and are in some ways obsoleted by them, however non-cryptographic generators do have some advantages: a small state size, fast initialisation, simplicity, lower energy usage for embedded CPUs. (However, not all non-crypto PRNGs provide these benefits, e.g. the Mersenne Twister has a very large state despite being easy to predict).

These algorithms are very important to Monte Carlo simulations, and also suitable for several other problems such as randomized algorithms and games, where predictability is not an issue. (Note however that for gambling games predictability may be an issue and a cryptographic PRNG is recommended.)

The Rand project provides several non-cryptographic PRNGs. A sub-set of these are summarised below. You may wish to refer to the pcg-random and xoshiro websites.

Here, performance is measured roughly for u64 outputs on a 3.4GHz Haswell CPU (note that this will vary significantly by application; in general cryptographic RNGs do better with byte sequence output). Quality ratings are based on theory and observable defects, roughly as follows:

• ★☆☆☆☆ = suitable for simple applications but with significant flaws
• ★★☆☆☆ = good performance in most tests, some issues
• ★★★☆☆ = good performance and theory, no major issues
• ★★★★★ = cryptographic quality

Cryptographically secure pseudo-random number generators (CSPRNGs)

CSPRNGs have much higher requirements than basic PRNGs. The primary consideration is security. Performance and simplicity are also important, but in general CSPRNGs are more complex and slower than regular PRNGs. Quality is no longer a concern, as it is a requirement for a CSPRNG that the output is basically indistinguishable from true randomness since any bias or correlation makes the output more predictable.

There is a close relationship between CSPRNGs and cryptographic ciphers. Any block cipher can be turned into a CSPRNG by encrypting a counter. Stream ciphers are basically a CSPRNG and a combining operation, usually XOR. This means that we can easily use any stream cipher as a CSPRNG.

This library provides the following CSPRNGs. We can make no guarantees of any security claims. This table omits the "quality" column from the previous table since CSPRNGs may not have observable defects.

It should be noted that the ISAAC generators are only included for historical reasons: they have been with the Rust language since the very beginning. They have good quality output and no attacks are known, but have received little attention from cryptography experts.

Notes on generators

Performance

First it has to be said most PRNGs are very fast, and will rarely be a performance bottleneck.

Performance of basic PRNGs is a bit of a subtle thing. It depends a lot on the CPU architecture (32 vs. 64 bits), inlining, and also on the number of available registers. This often causes the performance to be affected by surrounding code due to inlining and other usage of registers.

When choosing a PRNG for performance it is important to benchmark your own application due to interactions between PRNGs and surrounding code and dependence on the CPU architecture as well as the impact of the size of data requested. Because of all this, we do not include performance numbers here but merely a qualitative rating.

CSPRNGs are a little different in that they typically generate a block of output in a cache, and pull outputs from the cache. This allows them to have good amortised performance, and reduces or completely removes the influence of surrounding code on the CSPRNG performance.

Worst-case performance

Simple PRNGs typically produce each random value on demand. In contrast, CSPRNGs usually produce a whole block at once, then read from this cache until it is exhausted, giving them much less consistent performance when drawing small quantities of random data.

Memory usage

Simple PRNGs often use very little memory, commonly only a few words, where a word is usually either u32 or u64. This is not true for all non-cryptographic PRNGs however, for example the historically popular Mersenne Twister MT19937 algorithm requires 2.5 kB of state.

CSPRNGs typically require more memory; since the seed size is recommended to be at least 192 bits and some more may be required for the algorithm, 256 bits would be approximately the minimum secure size. In practice, CSPRNGs tend to use quite a bit more, ChaChaRng is relatively small with 136 bytes of state.

Initialization time

The time required to initialize new generators varies significantly. Many simple PRNGs and even some cryptographic ones (including ChaChaRng) only need to copy the seed value and some constants into their state, and thus can be constructed very quickly. In contrast, CSPRNGs with large state require an expensive key-expansion.

Quality

Many basic PRNGs are not much more than a couple of bitwise and arithmetic operations. Their simplicity gives good performance, but also means there are small regularities hidden in the generated random number stream.

How much do those hidden regularities matter? That is hard to say, and depends on how the RNG gets used. If there happen to be correlations between the random numbers and the algorithm they are used in, the results can be wrong or misleading.

A random number generator can be considered good if it gives the correct results in as many applications as possible. The quality of PRNG algorithms can be evaluated to some extent analytically, to determine the cycle length and to rule out some correlations. Then there are empirical test suites designed to test how well a PRNG performs on a wide range of possible uses, the latest and most complete of which are TestU01 and PractRand.

CSPRNGs tend to be more complex, and have an explicit requirement to be unpredictable. This implies there must be no obvious correlations between output values.

Quality stars:

PRNGs with 3 stars or more should be good enough for most non-crypto applications. 1 or 2 stars may be good enough for typical apps and games, but do not work well with all algorithms.

Period

The period or cycle length of a PRNG is the number of values that can be generated after which it starts repeating the same random number stream. Many PRNGs have a fixed-size period, while for others ("chaotic RNGs") the cycle length may depend on the seed and short cycles may exist.

Note that a long period does not imply high quality (e.g. a counter through u128 values provides a decently long period). Conversely, a short period may be a problem, especially when multiple RNGs are used simultaneously. In general, we recommend a period of at least 2¹²⁸. (Alternatively, a PRNG with shorter period of at least 2⁶⁴ and support for multiple streams may be sufficient. Note however that in the case of PCG, its streams are closely correlated.)

Avoid reusing values! On today's hardware, a fast RNG with a cycle length of only 2⁶⁴ can be used sequentially for centuries before cycling. However, when multiple RNGs are used in parallel (each with a unique seed), there is a significant chance of overlap between the sequences generated. For a generator with a large period P, n independent generators, and a sequence of length L generated by each generator, the chance of any overlap between sequences can be approximated by Ln² / P when nL / P is close to zero. For more on this topic, please see these remarks by the Xoshiro authors.

Collisions and the birthday paradox! For a generator with outputs of equal size to its state, it is recommended not to use more than √P outputs. A generalisation for kw-bit state and w-bit generators is to ensure kL² < P. This requirement stems from the generalised birthday problem, asking how many unbiased samples from a set of size d = 2^w can be taken before the probability of a repeat is at least half. Note that for kL² > P a generator with kw-dimensional equidistribution cannot generate the expected number of repeated samples, however generators without this property are also not guaranteed to generate the expected number of repeats.

Security

Predictability

From the context of any PRNG, one can ask the question given some previous output from the PRNG, is it possible to predict the next output value? This is an important property in any situation where there might be an adversary.

Regular PRNGs tend to be predictable, although with varying difficulty. In some cases prediction is trivial, for example plain Xorshift outputs part of its state without mutation, and prediction is as simple as seeding a new Xorshift generator from four u32 outputs. Other generators, like PCG and truncated Xorshift* are harder to predict, but not outside the realm of common mathematics and a desktop PC.

The basic security that CSPRNGs must provide is the infeasibility to predict output. This requirement is formalized as the next-bit test; this is roughly stated as: given the first k bits of a random sequence, the sequence satisfies the next-bit test if there is no algorithm able to predict the next bit using reasonable computing power.

A further security that some CSPRNGs provide is forward secrecy: in the event that the CSPRNGs state is revealed at some point, it must be infeasible to reconstruct previous states or output. Note that many CSPRNGs do not have forward secrecy in their usual formulations.

Verifying security claims of an algorithm is a hard problem, and we are not able to provide any guarantees of the security of algorithms used or recommended by this project. We refer you to the NIST institute and ECRYPT network for recommendations.

State and seeding

It is worth noting that a CSPRNG's security relies absolutely on being seeded with a secure random key. Should the key be known or guessable, all output of the CSPRNG is easy to guess. This implies that the seed should come from a trusted source; usually either the OS or another CSPRNG. For this purpose, we recommend using the getrandom crate which interfaces the OS's secure random interface. SeedableRng::from_entropy is a wrapper around getrandom for convenience. Alternatively, using a user-space CSPRNG such as ThreadRng for seeding should be sufficient.

Further, it should be obvious that the internal state of a CSPRNG must be kept secret. With that in mind, our implementations do not provide direct access to most of their internal state, and Debug implementations do not print any internal state. This does not fully protect CSPRNG state; code within the same process may read this memory (and we allow cloning and serialisation of CSPRNGs for convenience). Further, a running process may be forked by the operating system, which may leave both processes with a copy of the same generator.

Not a crypto library

It should be emphasised that this is not a cryptography library; although Rand does take some measures to provide secure random numbers, it does not necessarily take all recommended measures. Further, cryptographic processes such as encryption and authentication are complex and must be implemented very carefully to avoid flaws and resist known attacks. It is therefore recommended to use specialized libraries where possible, for example openssl, ring and the RustCrypto libraries.

Extra features

Some PRNGs may provide extra features, like:

• Support for multiple streams, which can help with parallel tasks.
• The ability to jump or seek around in the random number stream; with a large period this can be used as an alternative to streams.

Further reading

There is quite a lot that can be said about PRNGs. The PCG paper is very approachable and explains more concepts.

Another good paper about RNG quality is "Good random number generators are (not so) easy to find" by P. Hellekalek.