.\"	$NetBSD: rnd.4,v 1.24.14.1 2019/12/08 13:16:53 martin Exp $
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.\" Copyright (c) 2014 The NetBSD Foundation, Inc.
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.\" This code is derived from software contributed to The NetBSD Foundation
.\" by Taylor R. Campbell.
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.Dd September 3, 2019
.Dt RND 4
.Os
.Sh NAME
.Nm rnd
.Nd random number generator
.Sh DESCRIPTION
The
.Pa /dev/random
and
.Pa /dev/urandom
devices generate bytes randomly with uniform distribution.
Every read from them is independent.
.Bl -tag -width /dev/urandom
.It Pa /dev/urandom
Never blocks.
.It Pa /dev/random
Sometimes blocks.
Will block early at boot if the system's state is known to be
predictable.
.El
.Pp
Applications should read from
.Pa /dev/urandom
when they need randomly generated data, e.g. key material for
cryptography or seeds for simulations.
.Pp
Systems should be engineered to judiciously read at least once from
.Pa /dev/random
at boot before running any services that talk to the internet or
otherwise require cryptography, in order to avoid generating keys
predictably.
.Pp
.Pa /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
.Pa /dev/random
can be especially frustrating.
.Pp
If interrupted by a signal, reads from either
.Pa /dev/random
or
.Pa /dev/urandom
may return short, so programs that handle signals must be prepared to
retry reads.
.Pp
Writing to either
.Pa /dev/random
or
.Pa /dev/urandom
influences subsequent output of both devices, guaranteed to take
effect at next open.
.Pp
If you have a coin in your pocket, you can flip it 256 times and feed
the outputs to
.Pa /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:
.Bd -literal -offset abcd
% echo tthhhhhthhhththtthhhhthtththttth... > /dev/random
.Ed
.Pp
(Sequence generated from a genuine US quarter dollar, guaranteed
random.)
.Sh SECURITY MODEL
The
.Nm
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:
.Bl -bullet -offset abcd
.It
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.
.It
An attacker who has seen the entire state of the machine cannot predict
past outputs.
.El
.Pp
One
.Sq output
means a single read, no matter how short it is.
.Pp
.Sq Cannot predict
means it is conjectured of the cryptography in
.Fa /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.
.Sh ENTROPY
The operating system continuously 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
.Pa /dev/random
and
.Pa /dev/urandom .
.Pp
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
.Em min-entropy ,
or
.Em entropy
for short in cryptography.
For example:
.Bl -bullet -offset abcd -compact
.It
A fair coin toss has one bit of entropy.
.It
A fair (six-sided) die roll has a little over 2.5 bits of entropy.
.It
A string of two independent fair coin tosses has two bits of entropy.
.It
The toss of a pair of fair coins that are glued together has one bit of
entropy.
.It
A uniform random distribution with
.Fa n
possibilities has log_2
.Fa n
bits of entropy.
.It
An utterance from an accounting troll who always says
.Sq nine
has zero bits of entropy.
.El
.Pp
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.
.Pp
Hardware devices that the operating system monitors for observations
are called
.Em "entropy sources" ,
and the observations are combined into an
.Em "entropy pool" .
The
.Xr rndctl 8
command queries information about entropy sources and the entropy pool,
and can control which entropy sources the operating system uses or
ignores.
.Pp
256 bits of entropy is typically considered intractable to guess with
classical computers and with current models of the capabilities of
quantum computers.
.Pp
Systems with nonvolatile storage should store a secret from
.Pa /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 \(em
including the work its operator may have done to flip a coin! \(em can be
saved from one boot to the next, and so that newly installed systems
are not vulnerable to generating cryptographic keys predictably.
.Pp
The boot loaders in some
.Nx
ports support a command to load a seed from disk before the
kernel has started.
For those that don't, the
.Xr rndctl 8
command can do it once userland has started, for example by setting
.Dq Va random_seed=YES
in
.Pa /etc/rc.conf ,
which is enabled by default; see
.Xr rc.conf 5 .
.Sh LIMITATIONS
Some people worry about recovery from state compromise \(em 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.
.Pp
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.
.Pp
The
.Nm
subsystem does
.Em not
automatically defend against hardware colluding with an attacker to
influence entropy sources based on the state of the operating system.
.Pp
For example, a PCI device or CPU instruction for random number
generation which has no side channel to an attacker other than the
.Pa /dev/urandom
device could be bugged to observe all other entropy sources, and to
carefully craft
.Sq observations
that cause a certain number of bits of
.Pa /dev/urandom
output to be ciphertext that either is predictable to an attacker or
conveys a message to an attacker.
.Pp
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.
.Sh IOCTLS
The
.Pa /dev/random
and
.Pa /dev/urandom
devices support a number of ioctls, defined in the
.In sys/rndio.h
header file, for querying and controlling the entropy pool.
.Pp
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.
.Pp
Several ioctls are concerned with particular entropy sources, described
by the following structure:
.Bd -literal
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 */
.Ed
.Pp
The following ioctls are supported:
.Bl -tag -width abcd
.It Dv RNDGETENTCNT Pq Vt uint32_t
Return the number of bits of entropy the system is estimated to have.
.It Dv RNDGETSRCNUM Pq Vt rndstat_t
.Bd -literal
typedef struct {
	uint32_t	start;
	uint32_t	count;
	rndsource_t	source[RND_MAXSTATCOUNT];
} rndstat_t;
.Ed
.Pp
Fill the
.Fa sources
array with information about up to
.Fa count
entropy sources, starting at
.Fa start .
The actual number of sources described is returned in
.Fa count .
At most
.Dv RND_MAXSTATCOUNT
sources may be requested at once.
.It Dv RNDGETSRCNAME Pq Vt rndstat_name_t
.Bd -literal
typedef struct {
	char		name[16];
	rndsource_t	source;
} rndstat_name_t;
.Ed
.Pp
Fill
.Fa source
with information about the entropy source named
.Fa name ,
or fail with
.Dv ENOENT
if there is none.
.It Dv RNDCTL Pq Vt rndctl_t
.Bd -literal
typedef struct {
	char		name[16];
	uint32_t	type;
	uint32_t	flags;
	uint32_t	mask;
} rndctl_t;
.Ed
.Pp
For each entropy source of the type
.Fa type ,
or if
.Fa type
is
.Li 0xff
then for the entropy source named
.Fa name ,
replace the flags in
.Fa mask
by
.Fa flags .
.It Dv RNDADDDATA Pq Vt rnddata_t
.Bd -literal
typedef struct {
	uint32_t	len;
	uint32_t	entropy;
	unsigned char	data[RND_SAVEWORDS * sizeof(uint32_t)];
} rnddata_t;
.Ed
.Pp
Feed
.Fa len
bytes of data to the entropy pool.
The sample is expected to have been drawn with at least
.Fa entropy
bits of entropy.
.Pp
This ioctl can be used only once per boot.
It is intended for a system that saves entropy to disk on shutdown and
restores it on boot, so that the system can immediately be
unpredictable without having to wait to gather entropy.
.Pp
This ioctl is the only way for userland to directly change the system's
entropy estimate.
.It Dv RNDGETPOOLSTAT Pq Vt rndpoolstat_t
.Bd -literal
typedef struct {
	uint32_t poolsize;	/* size of each LFSR in pool */
	uint32_t threshold;	/* no. bytes of pool hash returned */
	uint32_t maxentropy;	/* total size of pool in bits */
	uint32_t added;		/* no. bits of entropy ever added */
	uint32_t curentropy;	/* current entropy `balance' */
	uint32_t discarded;	/* no. bits dropped when pool full */
	uint32_t generated;	/* no. bits yielded by pool while
				   curentropy is zero */
} rndpoolstat_t;
.Ed
.Pp
Return various statistics about entropy.
.El
.Sh IMPLEMENTATION NOTES
(This section describes the current implementation of the
.Nm
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
.Pa /dev/random
and
.Pa /dev/urandom
devices.)
.Pp
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.
.\" XXX Finish this description so it is implementable.
.Pp
When a user process opens
.Pa /dev/random
or
.Pa /dev/urandom
and first reads from it, the kernel draws from the entropy pool to seed
a cryptographic pseudorandom number generator, the NIST Hash_DRBG
(hash-based deterministic random bit generator) with SHA-256 as the
hash function, and uses that to generate data.
.Pp
To draw a seed from the entropy pool, the kernel
.Bl -bullet -offset abcd -compact
.It
computes the SHA-1 hash of the entropy pool,
.It
feeds the SHA-1 hash word-by-word back into the entropy pool like an
entropy source, and
.It
yields the xor of bytes
.Pf 0.. Fa n
with bytes
.Fa n Ns +0.. Ns Fa n Ns Pf + Fa n
of the hash, where
.Fa n
is
.Dv RND_ENTROPY_THRESHOLD
(currently 10).
.El
The kernel repeats the process, concatenating the results, until it has
filled the seed.
.Pp
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
.Sq amount of entropy
or
.Sq number of bits of entropy
in the pool.
Each sample
.Sq credits
to the amount of entropy.
Every time the kernel draws a PRNG seed from the entropy pool, it
.Sq debits
from the amount of entropy.
.Pp
Every open from
.Pa /dev/urandom
seeds an independent PRNG which is reseeded at the convenience of the
kernel after a billion requests for output.
Reads from
.Pa /dev/urandom
never block, even if the kernel estimates its state to be totally
predictable.
.Pp
Every open from
.Pa /dev/random
seeds an independent PRNG which is reseeded after every 16 bytes of
output.
Reads from
.Pa /dev/random
block if the PRNG needs to be (re)seeded and the kernel's entropy
estimate is too low.
.Pp
It is possible to fool the kernel's entropy estimator, in which case
reads from
.Pa /dev/random
may return immediately even if the kernel is in a totally predictable
state.
.Pp
Writes to
.Pa /dev/random
and
.Pa /dev/urandom
devices do not change the kernel's entropy estimate.
.Sh FILES
.Bl -tag -width /dev/urandom -compact
.It Pa /dev/random
Uniform random byte source.
May block.
.It Pa /dev/urandom
Uniform random byte source.
Never blocks.
.El
.Sh SEE ALSO
.Xr arc4random 3 ,
.Xr rndctl 8 ,
.Xr cprng 9
.Rs
.%A Elaine Barker
.%A John Kelsey
.%T Recommendation for Random Number Generation Using Deterministic Random Bit Generators
.%D June 2015
.%I National Institute of Standards and Technology
.%O NIST Special Publication 800-90A, Revision 1
.%U https://csrc.nist.gov/publications/detail/sp/800-90a/rev-1/final
.Re
.Rs
.%A Daniel J. Bernstein
.%T Entropy Attacks!
.%D 2014-02-05
.%U http://blog.cr.yp.to/20140205-entropy.html
.Re
.Rs
.%A Nadia Heninger
.%A Zakir Durumeric
.%A Eric Wustrow
.%A J. Alex Halderman
.%T Mining Your Ps and Qs: Detection of Widespread Weak Keys in Network Devices
.%B Proceedings of the 21st USENIX Security Symposium
.%I USENIX
.%D August 2012
.%P 205-220
.%U https://www.usenix.org/conference/usenixsecurity12/technical-sessions/presentation/heninger
.%U https://factorable.net/
.Re
.Sh HISTORY
The
.Pa /dev/random
and
.Pa /dev/urandom
devices first appeared in
.Nx 1.3 .
.Sh AUTHORS
The
.Nm
subsystem was first implemented by
.An Michael Graff Aq Mt explorer@flame.org ,
and was then largely rewritten by
.An Thor Lancelot Simon Aq Mt tls@NetBSD.org
with later contributions by
.An Taylor R. Campbell Aq Mt riastradh@NetBSD.org .
.Sh 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.
.Pp
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
.Pa /dev/random
to stop blocking.
.Pp
Many people are confused about what
.Pa /dev/random
and
.Pa /dev/urandom
mean.
Unfortunately, no amount of software engineering can fix that.
.Sh ENTROPY ACCOUNTING
The entropy accounting described here is not grounded in any
cryptography theory.
.Sq Entropy estimation
doesn't mean much: the kernel hypothesizes an extremely simple-minded
parametric model for all entropy sources which bears little relation to
any physical processes, implicitly fits parameters from data, and
accounts for the entropy of the fitted model.
.Pp
Past versions of the
.Nm
subsystem were concerned with
.Sq information-theoretic
security, under the premise that the number of bits of entropy out must
not exceed the number of bits of entropy in \(em never mind that its
.Sq entropy estimation
is essentially meaningless without a model for the physical processes
the system is observing.
.Pp
But 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
.Fa /dev/random ,
it would be hopeless to assume we could for HTTPS, SSH, PGP, etc.
.Pp
History is littered with examples of broken entropy sources and failed
system engineering for random number generators.
Nobody has ever reported distinguishing SHA-256 hashes with secret
inputs from uniform random, nor reported computing SHA-1 preimages
faster than brute force.