NAME

rnd — random number generator

DESCRIPTION

The /dev/random and /dev/urandom devices generate bytes randomly with uniform distribution. Every read from them is independent.

Applications should read from /dev/urandom when they need randomly generated data, e.g. key material for cryptography or seeds for simulations.

Systems should be engineered to judiciously read at least once from /dev/random at boot before running any services that talk to the internet or otherwise require cryptography, in order to avoid generating keys predictably.

/dev/random may block at any time, so programs that read from it must be prepared to handle blocking. Interactive programs that block due to reads from /dev/random can be especially frustrating.

If interrupted by a signal, reads from either /dev/random or /dev/urandom may return short, so programs that handle signals must be prepared to retry reads.

Writing to either /dev/random or /dev/urandom influences subsequent output of both devices, guaranteed to take effect at next open.

If you have a coin in your pocket, you can flip it 256 times and feed the outputs to /dev/random to guarantee your system is in a state that nobody but you and the bored security guard watching the surveillance camera in your office can guess:

% echo tthhhhhthhhththtthhhhthtththttth... > /dev/random

(Sequence generated from a genuine US quarter dollar, guaranteed random.)

SECURITY MODEL

The rnd subsystem provides the following security properties against two different classes of attackers, provided that there is enough entropy from entropy sources not seen by attackers:

An attacker who has seen some outputs and can supply some entropy sources' inputs to the operating system cannot predict past or future unseen outputs.
An attacker who has seen the entire state of the machine cannot predict past outputs.

One ‘output’ means a single read, no matter how short it is.

‘Cannot predict’ means it is conjectured of the cryptography in /dev/random that any computationally bounded attacker who tries to distinguish outputs from uniform random cannot do more than negligibly better than uniform random guessing.

ENTROPY

The operating system contiuously makes observations of hardware devices, such as network packet timings, disk seek delays, and keystrokes. The observations are combined into a seed for a cryptographic pseudorandom number generator (PRNG) which is used to generate the outputs of both /dev/random and /dev/urandom.

An attacker may be able to guess with nonnegligible chance of success what your last keystroke was, but guessing every observation the operating system may have made is more difficult. The difficulty of the best strategy at guessing a random variable is analyzed as the -log_2 of the highest probability of any outcome, measured in bits, and called its min-entropy, or entropy for short in cryptography. For example:

A fair coin toss has one bit of entropy.
A fair (six-sided) die roll has a little over 2.5 bits of entropy.
A string of two independent fair coin tosses has two bits of entropy.
The toss of a pair of fair coins that are glued together has one bit of entropy.
A uniform random distribution with n possibilities has log_2 n bits of entropy.
An utterance from an accounting troll who always says ‘nine’ has zero bits of entropy.

Note that entropy is a property of an observable physical process, not of a particular sample obtained by observing it. There are also kinds of entropy in information theory other than min-entropy, including the more well-known Shannon entropy, but they are not relevant here.

Hardware devices that the operating system monitors for observations are called entropy sources, and the observations are combined into an entropy pool. The rndctl(8) command queries information about entropy sources and the entropy pool, and can control which entropy sources the operating system uses or ignores.

256 bits of entropy is typically considered intractible to guess with classical computers and with current models of the capabilities of quantum computers.

Systems with nonvolatile storage should store a secret from /dev/urandom on disk during installation or shutdown, and feed it back during boot, so that the work the operating system has done to gather entropy -- including the work its operator may have done to flip a coin! -- can be saved from one boot to the next, and so that newly installed systems are not vulnerable to generating cryptographic keys predictably.

The boot loaders in some NetBSD ports support a command to load a seed from disk before the kernel has started. For those that don't, the rndctl(8) command can do it once userland has started, for example by setting “rndctl=YES” in /etc/rc.conf; see rc.conf(5).

LIMITATIONS

Some people worry about recovery from state compromise -- that is, ensuring that even if an attacker sees the entire state of the operating system, then the attacker will be unable to predict any new future outputs as long as the operating system gathers fresh entropy quickly enough.

But if an attacker has seen the entire state of your machine, refreshing entropy is probably the least of your worries, so we do not address that threat model here.

The rnd subsystem does not automatically defend against hardware colluding with an attacker to influence entropy sources based on the state of the operating system.

For example, a PCI device or CPU instruction for random number generation which has no side channel to an attacker other than the /dev/urandom device could be bugged to observe all other entropy sources, and to carefully craft ‘observations’ that cause a certain number of bits of /dev/urandom output to be ciphertext that either is predictable to an attacker or conveys a message to an attacker.

No amount of scrutiny by the system's operator could detect this. The only way to prevent this attack would be for the operator to disable all entropy sources that may be colluding with an attacker. If you're not sure which ones are not, you can always disable all of them and fall back to the coin in your pocket.

IOCTLS

The /dev/random and /dev/urandom devices support a number of ioctls, defined in the <sys/rnd.h> header file, for querying and controlling the entropy pool.

Since timing between hardware events contributes to the entropy pool, statistics about the entropy pool over time may serve as a side channel for the state of the pool, so access to such statistics is restricted to the super-user and should be used with caution.

Several ioctls are concerned with particular entropy sources, described by the following structure:

typedef struct { 
	char		name[16];	/* symbolic name */ 
	uint32_t	total;		/* estimate of entropy provided */ 
	uint32_t	type;		/* RND_TYPE_* value */ 
	uint32_t	flags;		/* RND_FLAG_* mask */ 
} rndsource_t; 
 
#define	RND_TYPE_UNKNOWN 
#define	RND_TYPE_DISK		/* disk device */ 
#define	RND_TYPE_ENV		/* environment sensor (temp, fan, &c.) */ 
#define	RND_TYPE_NET		/* network device */ 
#define	RND_TYPE_POWER		/* power events */ 
#define	RND_TYPE_RNG		/* hardware RNG */ 
#define	RND_TYPE_SKEW		/* clock skew */ 
#define	RND_TYPE_TAPE		/* tape drive */ 
#define	RND_TYPE_TTY		/* tty device */ 
#define	RND_TYPE_VM		/* virtual memory faults */ 
 
#define	RND_TYPE_MAX		/* value of highest-numbered type */ 
 
#define	RND_FLAG_COLLECT_TIME		/* use timings of samples */ 
#define	RND_FLAG_COLLECT_VALUE		/* use values of samples */ 
#define	RND_FLAG_ESTIMATE_TIME		/* estimate entropy of timings */ 
#define	RND_FLAG_ESTIMATE_VALUE		/* estimate entropy of values */ 
#define	RND_FLAG_NO_COLLECT		/* ignore samples from this */ 
#define	RND_FLAG_NO_ESTIMATE		/* do not estimate entropy */

The following ioctls are supported:

IMPLEMENTATION NOTES

(This section describes the current implementation of the rnd subsystem at the time of writing. It may be out-of-date by the time you read it, and nothing in here should be construed as a guarantee about the behaviour of the /dev/random and /dev/urandom devices.)

Samples from entropy sources are fed 32 bits at a time into the entropy pool, which is an array of 4096 bits, or 128 32-bit words, representing 32 linear feedback shift registers each 128 bits long.

When a user process opens /dev/random or /dev/urandom and first reads from it, the kernel draws from the entropy pool to seed a cryptographic pseudorandom number generator, the NIST CTR_DRBG (counter-mode deterministic random bit generator) with AES-128 as the block cipher, and uses that to generate data.

To draw a seed from the entropy pool, the kernel

computes the SHA-1 hash of the entropy pool,
feeds the SHA-1 hash word-by-word back into the entropy pool like an entropy source, and
yields the xor of bytes 0..n with bytes n+0..n+n of the hash, where n is RND_ENTROPY_THRESHOLD (currently 10).

The kernel repeats the process, concatenating the results, until it has filled the seed.

For each entropy source, the kernel estimates based on the previous samples how much entropy the source is providing in each new sample. The kernel maintains a count of the ‘amount of entropy’ or ‘number of bits of entropy’ in the pool. Each sample ‘credits’ to the amount of entropy. Every time the kernel draws a PRNG seed from the entropy pool, it ‘debits’ from the amount of entropy.

Every open from /dev/urandom seeds an independent PRNG which is reseeded at the convenience of the kernel after a billion requests for output. Reads from /dev/urandom never block, even if the kernel estimates its state to be totally predictable.

Every open from /dev/random seeds an independent PRNG which is reseeded after every 16 bytes of output. Reads from /dev/random block if the PRNG needs to be (re)seeded and the kernel's entropy estimate is too low.

It is possible to fool the kernel's entropy estimator, in which case reads from /dev/random may return immediately even if the kernel is in a totally predictable state.

Writes to /dev/random and /dev/urandom devices do not change the kernel's entropy estimate.

FILES

HISTORY

The /dev/random and /dev/urandom devices first appeared in NetBSD 1.3.

AUTHORS

The rnd subsystem was first implemented by Michael Graff <explorer@flame.org>, and was then largely rewritten by Thor Lancelot Simon <tls@NetBSD.org> with later contributions by Taylor R. Campbell <riastradh@NetBSD.org>.

BUGS

There is no way to disable all entropy sources, in this and subsequent boots and no matter what USB devices you plug in against your mother's sage advice, in order to defend against the colluding hardware attack.

The implementation confuses the number of bits in the entropy pool's physical representation, as a set of 32 128-bit LFSRs, with the number of bits of entropy that a system needs in order to be unpredictable, so even if entropy estimates were accurate and high, it takes unreasonably long for /dev/random to stop blocking.

Many people are confused about what /dev/random and /dev/urandom mean. Unfortunately, no amount of software engineering can fix that.

ENTROPY ACCOUNTING

The entropy accounting described here is not grounded in any cryptography theory. It is done because it was always done, and because it gives people a warm fuzzy feeling about information theory.

The folklore is that every n-bit output of /dev/random is not merely indistinguishable from uniform random to a computationally bounded attacker, but information-theoretically is independent and has n bits of entropy even to a computationally unbounded attacker -- that is, an attacker who can recover AES keys, compute SHA-1 preimages, etc. This property is not provided, nor was it ever provided in any implementation of /dev/random known to the author.

This property would require that, after each read, the system discard all measurements from hardware in the entropy pool and begin anew. All work done to make the system unpredictable would be thrown out, and the system would immediately become predictable again. Reverting the system to being predictable every time a process reads from /dev/random would give attackers a tremendous advantage in predicting future outputs, especially if they can fool the entropy estimator, e.g. by sending carefully timed network packets.

If you filled your entropy pool by flipping a coin 256 times, you would have to flip it again 256 times for the next output, and so on. In that case, if you really want information-theoretic guarantees, you might as well take /dev/random out of the picture and use your coin flips verbatim.

On the other hand, every cryptographic protocol in practice, including HTTPS, SSH, PGP, etc., expands short secrets deterministically into long streams of bits, and their security relies on conjectures that a computationally bounded attacker cannot distinguish the long streams from uniform random. If we couldn't do that for /dev/random, it would be hopeless to assume we could for HTTPS, SSH, PGP, etc.

History is littered with examples of broken entropy sources and failed system engineering for random number generators. Nobody has ever reported distinguishing AES ciphertext from uniform random without side channels, nor reported computing SHA-1 preimages faster than brute force. The folklore information-theoretic defence against computationally unbounded attackers replaces system engineering that successfully defends against realistic threat models by imaginary theory that defends only against fantasy threat models.

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