What are typical means by which a random number can be generated in an embedded system?

Question

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?

Answer 1

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.}