Hi,
It is well-known that it is impossible to map e.g. a 32-bit random
number with a uniform distribution over its full range of values onto a
range with fewer different values while maintaining a uniform
distribution, except when the target range contains a whole power of 2
number of different values.
Prior to 7.1.0, mt_rand()'s mapping onto the target range was done with
some floating-point math, so there was no modulo division exposed in
code, yet the problem above is fundamental and indeed it applied, e.g.:
<?php
// PHP pre-7.1.0 modulo bias demo
mt_srand(1234567890);
$total = 100000;
$max = 0x66666666;
$halves[0] = $halves[1] = 0;
for ($i = 0; $i < $total; $i++) {
$halves[(mt_rand(0, $max - 1) >> 1) & 1]++;
}
printf("%.1f%% vs. %.1f%%\n", 100. * $halves[0] / $total, 100. * $halves[1] / $total);
?>
Output for 7.1.0 - 7.2.0beta2
49.9% vs. 50.1%
Output for 5.2.1 - 5.6.30, hhvm-3.10.1 - 3.21.0, 7.0.0 - 7.0.20
40.0% vs. 60.0%
Output for 4.3.0 - 5.2.0
39.8% vs. 60.2%
PHP 7.1.0 moved to explicit integer modulo division yet tried to avoid
the modulo bias by generating multiple original 32-bit or 64-bit random
numbers in cases where the modulo bias would occur. Unfortunately,
because of an implementation bug it failed, e.g.:
<?php
// PHP 7.1.0 to 7.2.0beta2 modulo bias bug found during work on http://www.openwall.com/php_mt_seed/
mt_srand(1234567890);
$total = 100000;
$max = 0x66666666;
$halves[0] = $halves[1] = 0;
for ($i = 0; $i < $total; $i++) {
$halves[mt_rand(0, $max - 1) / ($max / 2)]++;
}
printf("%.1f%% vs. %.1f%%\n", 100. * $halves[0] / $total, 100. * $halves[1] / $total);
?>
Output for 7.1.0 - 7.2.0beta2
60.0% vs. 40.0%
Output for 4.3.0 - 5.6.30, hhvm-3.10.1 - 3.21.0, 7.0.0 - 7.0.20
50.0% vs. 50.0%
(Even higher bias can be seen in both cases by changing the 0x66666666
to 0xaaaaaaaa.)
I first found the bug through code review while working on adding PHP
7.1.0+ support to php_mt_seed. The above 3v4l was only to confirm it.
As I said in the Twitter thread (certainly not a proper place):
https://twitter.com/solardiz/status/897617315008839686
"The bug is unconditional use of 64-bit ZEND_ULONG_MAX in the bias
avoidance, even when the intermediate result is 32-bit (up to UINT32_MAX)."
Leigh confirmed this understanding, tweeting:
"Yep, happens when (max - min) is less than UINT32_MAX. A check on
(umax > UINT32_MAX) and setting the limit fixes it."
This sounds like almost the correct fix to me. The code is:
PHPAPI zend_long php_mt_rand_range(zend_long min, zend_long max)
{
zend_ulong umax = max - min;
zend_ulong limit;
zend_ulong result;
result = php_mt_rand();
#if ZEND_ULONG_MAX > UINT32_MAX
if (umax > UINT32_MAX) {
result = (result << 32) | php_mt_rand();
}
#endif
/* Special case where no modulus is required */
if (UNEXPECTED(umax == ZEND_ULONG_MAX)) {
return (zend_long)result;
}
/* Increment the max so the range is inclusive of max */
umax++;
/* Powers of two are not biased */
if (EXPECTED((umax & (umax - 1)) != 0)) {
/* Ceiling under which ZEND_LONG_MAX % max == 0 */
limit = ZEND_ULONG_MAX - (ZEND_ULONG_MAX % umax) - 1;
/* Discard numbers over the limit to avoid modulo bias */
while (UNEXPECTED(result > limit)) {
#if ZEND_ULONG_MAX > UINT32_MAX
if (umax > UINT32_MAX) {
result = (result << 32) | php_mt_rand();
}
else {
result = php_mt_rand();
}
#else
result = php_mt_rand();
#endif
}
}
return (zend_long)((result % umax) + min);
}
and what Leigh means is something like:
/* Ceiling under which *_MAX % max == 0 */
if (umax > UINT32_MAX)
limit = ZEND_ULONG_MAX - (ZEND_ULONG_MAX % umax) - 1;
else
limit = UINT32_MAX - (UINT32_MAX % umax) - 1;
Strictly speaking, the check should be the same as the one earlier in
the function, which decided how "result" was obtained with one or two
calls to php_mt_rand(). The above proposed check isn't exactly the same
because of the "umax++" inbetween. The special case of "umax" being
exactly UINT32_MAX prior to the increment needs more thought. Probably
the check in the first instance of:
if (umax > UINT32_MAX) {
result = (result << 32) | php_mt_rand();
}
is buggy and should actually be:
if (umax >= UINT32_MAX) {
result = (result << 32) | php_mt_rand();
}
whereas further code should continue with "umax > UINT32_MAX" because of
the increment.
Also, why even bother to support ranges beyond 32-bit? Sounds like a
misfeature to me, considering it won't(?) be universally available on
all PHP builds anyway (not on 32-bit ones, right?) and thus shouldn't(?)
be relied upon by applications (although it might become reasonable for
application developers not to care about 32-bit soon). I also see few
use cases for it, even if it were universally available.
The main bug reported in this message (wrongly using ZEND_ULONG_MAX for
computing "limit" when "result" is 32-bit) also means that PHP 7.1.0 to
7.2.0beta2 probably produce partially different sequences of mt_rand()
outputs between 32- and 64-bit builds for the same seed, for most ranges
that fit within 32 bits. Specifically, 32-bit builds probably correctly
avoid the modulo bias. (However, I didn't confirm this with a test.
Unfortunately, 3v4l.org appears to be 64-bit only.) Possibility of bugs
like this is yet another reason not to have introduced the little-needed
64-bit build specific functionality. OTOH, this was also a (missed)
opportunity to detect this bug with more testing (requiring same
behavior of 32- and 64-bit builds for 32-bit inputs).
Alexander
Also, why even bother to support ranges beyond 32-bit? Sounds like a
misfeature to me, considering it won't(?) be universally available on
all PHP builds anyway (not on 32-bit ones, right?) and thus shouldn't(?)
be relied upon by applications (although it might become reasonable for
application developers not to care about 32-bit soon). I also see few
use cases for it, even if it were universally available.
It was possible (on 64 bit builds) to specify min and max such that the
size of the output required from mt_rand was the full 64 bit range.
Prior to 7.1 this full output was created by stretching a single 32 bit
output up to the required range using floating point arithmetic, which
caused other biases in the output.
Unfortunately when fixing this bias, a new bias was introduced. I took
known working code from the CSPRNG and didn't account for the variable
length of the sample.
My proposed fix would be to add a "limit_max" variable, initialise it to
UINT32_MAX, and in the first range check where we decide to add an extra
output or not, set it to ZEND_ULONG_MAX. Then the statement creating the
ceiling value can use limit_max instead of the constant value.
Also, why even bother to support ranges beyond 32-bit? Sounds like a
misfeature to me, considering it won't(?) be universally available on
all PHP builds anyway (not on 32-bit ones, right?) and thus shouldn't(?)
be relied upon by applications (although it might become reasonable for
application developers not to care about 32-bit soon). I also see few
use cases for it, even if it were universally available.It was possible (on 64 bit builds) to specify min and max such that the
size of the output required from mt_rand was the full 64 bit range.Prior to 7.1 this full output was created by stretching a single 32 bit
output up to the required range using floating point arithmetic, which
caused other biases in the output.Unfortunately when fixing this bias, a new bias was introduced. I took
known working code from the CSPRNG and didn't account for the variable
length of the sample.My proposed fix would be to add a "limit_max" variable, initialise it to
UINT32_MAX, and in the first range check where we decide to add an extra
output or not, set it to ZEND_ULONG_MAX. Then the statement creating the
ceiling value can use limit_max instead of the constant value.
I'd suggest to split the 32-bit and 64-bit code codepaths entirely, as the
interleaved #ifs are somewhat hard to follow. Something like
https://gist.github.com/nikic/64e7ec58ebb6121d350fb80927a65082 (not
thoroughly tested).
Nikita
I'd suggest to split the 32-bit and 64-bit code codepaths entirely, as the
interleaved #ifs are somewhat hard to follow. Something like
https://gist.github.com/nikic/64e7ec58ebb6121d350fb80927a65082 (not
thoroughly tested).
This looks good to me - especially how you reduced the nesting of if's
by special-casing the "Powers of two are not biased" return. With this
change, you can as well drop the "Special case where no modulus is
required", as it'd happen to be handled the same by your new return.
OTOH, that optimization might require an extra comment on its own.
Here's what this might look like (totally untested):
https://gist.github.com/solardiz/5e3d313bbee2c1ce6e200e433b750bef
Alexander
I'd suggest to split the 32-bit and 64-bit code codepaths entirely, as the
interleaved #ifs are somewhat hard to follow. Something like
https://gist.github.com/nikic/64e7ec58ebb6121d350fb80927a65082 (not
thoroughly tested).This looks good to me - especially how you reduced the nesting of if's
by special-casing the "Powers of two are not biased" return. With this
change, you can as well drop the "Special case where no modulus is
required", as it'd happen to be handled the same by your new return.
OTOH, that optimization might require an extra comment on its own.Here's what this might look like (totally untested):
https://gist.github.com/solardiz/5e3d313bbee2c1ce6e200e433b750bef
One difference I didn't notice at first: the currently committed code
does only one php_mt_rand() call per loop iteration when it's skipping
"numbers over the limit", even in the 64-bit case (thus, it replaces 32
bits of the value at a time). Your 64-bit version (and my revision of
it) does two calls per iteration (replacing the whole number).
Arguably, the currently committed code is smarter and more efficient in
that respect, whereas yours is cleaner. Regardless, it's an extra
change that will affect the generated random numbers in some cases where
we could avoid making that change (it's not fixing any bug).
I think it's preferable not to unnecessarily change what numbers are
generated.
Alexander
I'd suggest to split the 32-bit and 64-bit code codepaths entirely, as
the
interleaved #ifs are somewhat hard to follow. Something like
https://gist.github.com/nikic/64e7ec58ebb6121d350fb80927a65082 (not
thoroughly tested).This looks good to me - especially how you reduced the nesting of if's
by special-casing the "Powers of two are not biased" return. With this
change, you can as well drop the "Special case where no modulus is
required", as it'd happen to be handled the same by your new return.
OTOH, that optimization might require an extra comment on its own.Here's what this might look like (totally untested):
https://gist.github.com/solardiz/5e3d313bbee2c1ce6e200e433b750bef
One difference I didn't notice at first: the currently committed code
does only one php_mt_rand() call per loop iteration when it's skipping
"numbers over the limit", even in the 64-bit case (thus, it replaces 32
bits of the value at a time). Your 64-bit version (and my revision of
it) does two calls per iteration (replacing the whole number).Arguably, the currently committed code is smarter and more efficient in
that respect, whereas yours is cleaner. Regardless, it's an extra
change that will affect the generated random numbers in some cases where
we could avoid making that change (it's not fixing any bug).I think it's preferable not to unnecessarily change what numbers are
generated.Alexander
Good point. However, I think that this optimization is not actually
correct. For example, let's take umax = 0x1_0000_0001, which is the
smallest value for which this codepath is taken. In this case limit would
be 0xffff_ffff_ffff_fffe, so we only resample if the value is exactly
0xffff_ffff_ffff_ffff. So if the resampling codepath is taken in this case,
and we only generate one new 32-bit value, the top word of the result will
be fixed to 0xffff_ffff. (A very small bias in this case, but there's
probably more significant cases.)
Nikita
One difference I didn't notice at first: the currently committed code
does only one php_mt_rand() call per loop iteration when it's skipping
"numbers over the limit", even in the 64-bit case (thus, it replaces 32
bits of the value at a time). Your 64-bit version (and my revision of
it) does two calls per iteration (replacing the whole number).Arguably, the currently committed code is smarter and more efficient in
that respect, whereas yours is cleaner. Regardless, it's an extra
change that will affect the generated random numbers in some cases where
we could avoid making that change (it's not fixing any bug).I think it's preferable not to unnecessarily change what numbers are
generated.
Good point. However, I think that this optimization is not actually
correct. For example, let's take umax = 0x1_0000_0001, which is the
smallest value for which this codepath is taken. In this case limit would
be 0xffff_ffff_ffff_fffe, so we only resample if the value is exactly
0xffff_ffff_ffff_ffff. So if the resampling codepath is taken in this case,
and we only generate one new 32-bit value, the top word of the result will
be fixed to 0xffff_ffff. (A very small bias in this case, but there's
probably more significant cases.)
Great point. More generally, we can't reuse the same random number for
decision-making (to skip it) and as part of the next (not so) random
number, without introducing bias. So we shouldn't, and we should in
fact move away from the old "smarter" behavior as a bug fix. Thank you!
Alexander
One difference I didn't notice at first: the currently committed code
does only one php_mt_rand() call per loop iteration when it's skipping
"numbers over the limit", even in the 64-bit case (thus, it replaces 32
bits of the value at a time). Your 64-bit version (and my revision of
it) does two calls per iteration (replacing the whole number).Arguably, the currently committed code is smarter and more efficient in
that respect, whereas yours is cleaner. Regardless, it's an extra
change that will affect the generated random numbers in some cases where
we could avoid making that change (it's not fixing any bug).I think it's preferable not to unnecessarily change what numbers are
generated.Good point. However, I think that this optimization is not actually
correct. For example, let's take umax = 0x1_0000_0001, which is the
smallest value for which this codepath is taken. In this case limit would
be 0xffff_ffff_ffff_fffe, so we only resample if the value is exactly
0xffff_ffff_ffff_ffff. So if the resampling codepath is taken in this case,
and we only generate one new 32-bit value, the top word of the result will
be fixed to 0xffff_ffff. (A very small bias in this case, but there's
probably more significant cases.)Great point. More generally, we can't reuse the same random number for
decision-making (to skip it) and as part of the next (not so) random
number, without introducing bias. So we shouldn't, and we should in
fact move away from the old "smarter" behavior as a bug fix. Thank you!
So I guess both the bug I reported and this one Nikita found are going
to get fixed soon? For 7.2.0 maybe?
Meanwhile, I released php_mt_seed 4.0 yesterday with support for latest
PHP's mt_rand(), as well as with support for PHP 5.2.0 and below (as it
happens, all the way to 3.0.7, although that's overkill). Near the end
of its documentation, I included a lengthy section entitled "PHP version
curiosities", which I include below in this e-mail in case any of this
is useful for PHP's own documentation. It starts from PHP 3.0.6, but
then actually spends half of the text on PHP 7.1.0+. Here we go:
While php_mt_seed supports 3 major revisions of PHP's mt_rand()
algorithm and that sort of covers PHP 3.0.7 through 7.1.0+ (up to the
latest as of this writing and probably beyond), the reality is somewhat
trickier than that. From older versions to newer:
As a mere historical curiosity, php_mt_seed is in fact able to crack
seeds of PHP 3.0.6, which is the very first version that introduced
mt_rand(), but only as long as no range was passed into mt_rand(). That
version had broken support for ranges, and indeed there's no point in
supporting that short-lived breakage in php_mt_seed now. With this
detail, php_mt_seed has some support for all mt_rand() capable versions
of PHP released so far.
Then there's PHP 3.0.7 through 5.2.0, where Mersenne Twister's state
initialization is with multiples of 69069. This enables our stateless
implementation to quickly jump to the state array element needed to
compute the first mt_rand() output by using a precomputed value for
69069 raised to the power 396 (mod 2**32), which is MT's M-1. Another
curiosity of those versions, which we take advantage of too, is that
they treat adjacent even and odd seeds the same, so the effective seed
space is 31-bit.
PHP 3.0.6 to 4.1.2 used a default seed of 4357 (and thus also 4356) if
mt_srand() was not called. PHP 4.2.0 changed that to automatic seeding
using system time and PHP process ID (still predictable and now also
leaky, but no longer a constant), but there was "Bug #25007 rand &
mt_rand seed RNG every call" until 4.3.3, which presumably affected how
cracked seeds could (not) be used.
PHP 5.2.1 changed MT state initialization to MT authors' new recommended
algorithm, which is no longer linear so we have to compute the first 397
state elements (out of 624) even though in the simplest case we only
need (and only store) the first and last one of those (or we could use a
time-memory trade-off, which we currently don't).
PHP 5.2.1 also introduced a bug into its implementation of MT (use of a
wrong variable, whereas pre-5.2.1 code was correct in that respect).
This bug lets us skip a few operations for every other seed, which we
do, although this optimization is so minor that we could as well not
bother. PHP 7.1.0 fixed this bug (reverting to pre-5.2.1 code in that
respect, so we use the same logic for pre-5.2.1 and 7.1.0+ there).
In PHP versions from 3.0.7 to 7.0.x, if mt_rand() was called with its
optional output range specified, a 31-bit (0 to 2147483647) MT PRNG
output was scaled to that range using floating-point math. This meant
that if a range wider than 31-bit was requested on a 64-bit build of
PHP, some values would never occur. This also meant that even for most
ranges smaller than 31-bit a bias was introduced (some output values
became more likely than others), as compared to MT's raw output (which
was relatively unbiased).
PHP 7.1.0 tried to fix those biases by dropping the floating-point math
and instead mapping the raw 32-bit MT PRNG outputs to the target range
using integer modulo division. To avoid inherent bias when the target
range isn't a whole power of 2 of possible integer values, a loop was
introduced to skip raw 32-bit PRNG outputs (until a suitable one is
seen) that would result in such bias. A bug in that code was found and
reported due to work on php_mt_seed. As it turned out, the loop only
works right in 32-bit builds of PHP, and is ineffective on 64-bit
(except with 64-bit ranges, see below). Luckily, this actually makes
things simpler for php_mt_seed, and currently php_mt_seed fully supports
the behavior of 64-bit builds only (for ranges up to 0 to 2147483646).
There's currently no intent to add to php_mt_seed the complication of
bias-avoidance of 32-bit builds of PHP 7.1.0+, as well as of 64-bit
builds of future versions where the bug will presumably get fixed. What
this means in practice is that for 32-bit builds of PHP and future
versions of PHP, php_mt_seed may occasionally find wrong and miss
correct seeds for mt_rand() invoked with a range, but the probability of
this happening is very low except for very wide ranges that are not a
whole power of 2 of possible integer values. For example, mt_rand(0,
- or mt_rand(111, 222) are very unlikely to trigger the problem,
mt_rand(0, 255) can't trigger the problem, whereas mt_rand(1000000000,
2000000000) is somewhat likely to trigger it. Such likely problematic
ranges are probably rarely used and are of little relevance to uses of
php_mt_seed. Also, supporting this buggy vs. correct behavior would
require treating 32- and 64-bit builds of PHP separately and reporting
on them differently.
PHP 7.1.0 also tried to introduce proper support for 64-bit ranges in
64-bit builds. It generates two raw 32-bit PRNG outputs to derive one
mt_rand() output when the target range spans more than a 32-bit space.
Unfortunately, the implementation is buggy in a way where it'd introduce
biases into such mt_rand() outputs. The bug will presumably get fixed
as well, but regardless there's currently no intent to support wider
than 31-bit ranges in php_mt_seed. This is obscure functionality
(arguably, originally an accidental misfeature, which the PHP developers
didn't really have to make official) that is only available on 64-bit
builds of PHP. Currently, php_mt_seed does not allow specifying larger
than 31-bit integers on its command line (it will report an error when a
larger value is specified).
Prior to PHP 7.1.0, mt_rand(0, 2147483647) was equivalent to mt_rand()
without a range, and php_mt_seed still assumes so. This assumption is
no longer valid for PHP 7.1.0+, which means that when searching for
seeds for PHP 7.1.0+ for mt_rand() called with a range specified, you
can specify at most a range one smaller than that, thus "0 2147483646"
being the maximum that php_mt_seed supports for those versions. This
minor limitation shouldn't matter in practice, except that you might
need to be aware you can continue to specify a range of "0 2147483647"
to indicate that no range was passed into mt_rand().
PHP 7.1.0 also aliased rand() to mt_rand() and srand() to mt_srand().
This means that on one hand you can use php_mt_seed to crack rand()
seeds for PHP 7.1.0+ (since those are also mt_rand() seeds), but on the
other hand this cross-seeding and cross-consumption of random numbers
can affect which attacks work or don't work, and exactly how, against
specific applications that make use of both sets of PHP functions.
PHP 7.1.0 also introduced MT_RAND_PHP as optional second parameter to
mt_srand(). When specified, it correctly enables behavior identical to
that of PHP versions 5.2.1 to 7.0.x. Thus, seeds that php_mt_seed
reports as valid for 5.2.1 to 7.0.x are always also valid for 7.1.0+
with MT_RAND_PHP, and conversely seeds that php_mt_seed reports as valid
for 7.1.0+ are often invalid for 7.1.0+ with MT_RAND_PHP (except when
the same seeds are also valid for 5.2.1 to 7.0.x, which is common).
Alexander
On Thu, Aug 17, 2017 at 12:02 AM, Solar Designer solar@openwall.com
wrote:One difference I didn't notice at first: the currently committed code
does only one php_mt_rand() call per loop iteration when it's
skipping
"numbers over the limit", even in the 64-bit case (thus, it replaces
32
bits of the value at a time). Your 64-bit version (and my revision
of
it) does two calls per iteration (replacing the whole number).Arguably, the currently committed code is smarter and more efficient
in
that respect, whereas yours is cleaner. Regardless, it's an extra
change that will affect the generated random numbers in some cases
where
we could avoid making that change (it's not fixing any bug).I think it's preferable not to unnecessarily change what numbers are
generated.Good point. However, I think that this optimization is not actually
correct. For example, let's take umax = 0x1_0000_0001, which is the
smallest value for which this codepath is taken. In this case limit
would
be 0xffff_ffff_ffff_fffe, so we only resample if the value is exactly
0xffff_ffff_ffff_ffff. So if the resampling codepath is taken in this
case,
and we only generate one new 32-bit value, the top word of the result
will
be fixed to 0xffff_ffff. (A very small bias in this case, but there's
probably more significant cases.)Great point. More generally, we can't reuse the same random number for
decision-making (to skip it) and as part of the next (not so) random
number, without introducing bias. So we shouldn't, and we should in
fact move away from the old "smarter" behavior as a bug fix. Thank you!So I guess both the bug I reported and this one Nikita found are going
to get fixed soon? For 7.2.0 maybe?Meanwhile, I released php_mt_seed 4.0 yesterday with support for latest
PHP'smt_rand(), as well as with support for PHP 5.2.0 and below (as it
happens, all the way to 3.0.7, although that's overkill). Near the end
of its documentation, I included a lengthy section entitled "PHP version
curiosities", which I include below in this e-mail in case any of this
is useful for PHP's own documentation. It starts from PHP 3.0.6, but
then actually spends half of the text on PHP 7.1.0+. Here we go:
While php_mt_seed supports 3 major revisions of PHP's
mt_rand()
algorithm and that sort of covers PHP 3.0.7 through 7.1.0+ (up to the
latest as of this writing and probably beyond), the reality is somewhat
trickier than that. From older versions to newer:As a mere historical curiosity, php_mt_seed is in fact able to crack
seeds of PHP 3.0.6, which is the very first version that introduced
mt_rand(), but only as long as no range was passed intomt_rand(). That
version had broken support for ranges, and indeed there's no point in
supporting that short-lived breakage in php_mt_seed now. With this
detail, php_mt_seed has some support for allmt_rand()capable versions
of PHP released so far.Then there's PHP 3.0.7 through 5.2.0, where Mersenne Twister's state
initialization is with multiples of 69069. This enables our stateless
implementation to quickly jump to the state array element needed to
compute the firstmt_rand()output by using a precomputed value for
69069 raised to the power 396 (mod 2**32), which is MT's M-1. Another
curiosity of those versions, which we take advantage of too, is that
they treat adjacent even and odd seeds the same, so the effective seed
space is 31-bit.PHP 3.0.6 to 4.1.2 used a default seed of 4357 (and thus also 4356) if
mt_srand()was not called. PHP 4.2.0 changed that to automatic seeding
using system time and PHP process ID (still predictable and now also
leaky, but no longer a constant), but there was "Bug #25007 rand &
mt_rand seed RNG every call" until 4.3.3, which presumably affected how
cracked seeds could (not) be used.PHP 5.2.1 changed MT state initialization to MT authors' new recommended
algorithm, which is no longer linear so we have to compute the first 397
state elements (out of 624) even though in the simplest case we only
need (and only store) the first and last one of those (or we could use a
time-memory trade-off, which we currently don't).PHP 5.2.1 also introduced a bug into its implementation of MT (use of a
wrong variable, whereas pre-5.2.1 code was correct in that respect).
This bug lets us skip a few operations for every other seed, which we
do, although this optimization is so minor that we could as well not
bother. PHP 7.1.0 fixed this bug (reverting to pre-5.2.1 code in that
respect, so we use the same logic for pre-5.2.1 and 7.1.0+ there).In PHP versions from 3.0.7 to 7.0.x, if
mt_rand()was called with its
optional output range specified, a 31-bit (0 to 2147483647
<%28214%29%20748-3647>) MT PRNG
output was scaled to that range using floating-point math. This meant
that if a range wider than 31-bit was requested on a 64-bit build of
PHP, some values would never occur. This also meant that even for most
ranges smaller than 31-bit a bias was introduced (some output values
became more likely than others), as compared to MT's raw output (which
was relatively unbiased).PHP 7.1.0 tried to fix those biases by dropping the floating-point math
and instead mapping the raw 32-bit MT PRNG outputs to the target range
using integer modulo division. To avoid inherent bias when the target
range isn't a whole power of 2 of possible integer values, a loop was
introduced to skip raw 32-bit PRNG outputs (until a suitable one is
seen) that would result in such bias. A bug in that code was found and
reported due to work on php_mt_seed. As it turned out, the loop only
works right in 32-bit builds of PHP, and is ineffective on 64-bit
(except with 64-bit ranges, see below). Luckily, this actually makes
things simpler for php_mt_seed, and currently php_mt_seed fully supports
the behavior of 64-bit builds only (for ranges up to 0 to 2147483646
<%28214%29%20748-3646>).There's currently no intent to add to php_mt_seed the complication of
bias-avoidance of 32-bit builds of PHP 7.1.0+, as well as of 64-bit
builds of future versions where the bug will presumably get fixed. What
this means in practice is that for 32-bit builds of PHP and future
versions of PHP, php_mt_seed may occasionally find wrong and miss
correct seeds formt_rand()invoked with a range, but the probability of
this happening is very low except for very wide ranges that are not a
whole power of 2 of possible integer values. For example, mt_rand(0,
- or mt_rand(111, 222) are very unlikely to trigger the problem,
mt_rand(0, 255) can't trigger the problem, whereas mt_rand(1000000000,
2000000000) is somewhat likely to trigger it. Such likely problematic
ranges are probably rarely used and are of little relevance to uses of
php_mt_seed. Also, supporting this buggy vs. correct behavior would
require treating 32- and 64-bit builds of PHP separately and reporting
on them differently.PHP 7.1.0 also tried to introduce proper support for 64-bit ranges in
64-bit builds. It generates two raw 32-bit PRNG outputs to derive one
mt_rand()output when the target range spans more than a 32-bit space.
Unfortunately, the implementation is buggy in a way where it'd introduce
biases into suchmt_rand()outputs. The bug will presumably get fixed
as well, but regardless there's currently no intent to support wider
than 31-bit ranges in php_mt_seed. This is obscure functionality
(arguably, originally an accidental misfeature, which the PHP developers
didn't really have to make official) that is only available on 64-bit
builds of PHP. Currently, php_mt_seed does not allow specifying larger
than 31-bit integers on its command line (it will report an error when a
larger value is specified).Prior to PHP 7.1.0, mt_rand(0, 2147483647 <%28214%29%20748-3647>) was
equivalent tomt_rand()
without a range, and php_mt_seed still assumes so. This assumption is
no longer valid for PHP 7.1.0+, which means that when searching for
seeds for PHP 7.1.0+ formt_rand()called with a range specified, you
can specify at most a range one smaller than that, thus "0 2147483646
<%28214%29%20748-3646>"
being the maximum that php_mt_seed supports for those versions. This
minor limitation shouldn't matter in practice, except that you might
need to be aware you can continue to specify a range of "0 2147483647
<%28214%29%20748-3647>"
to indicate that no range was passed intomt_rand().PHP 7.1.0 also aliased
rand()tomt_rand()andsrand()tomt_srand().
This means that on one hand you can use php_mt_seed to crackrand()
seeds for PHP 7.1.0+ (since those are alsomt_rand()seeds), but on the
other hand this cross-seeding and cross-consumption of random numbers
can affect which attacks work or don't work, and exactly how, against
specific applications that make use of both sets of PHP functions.PHP 7.1.0 also introduced
MT_RAND_PHPas optional second parameter to
mt_srand(). When specified, it correctly enables behavior identical to
that of PHP versions 5.2.1 to 7.0.x. Thus, seeds that php_mt_seed
reports as valid for 5.2.1 to 7.0.x are always also valid for 7.1.0+
with MT_RAND_PHP, and conversely seeds that php_mt_seed reports as valid
for 7.1.0+ are often invalid for 7.1.0+ withMT_RAND_PHP(except when
the same seeds are also valid for 5.2.1 to 7.0.x, which is common).Alexander
Sorry for the long delay. I've just applied
https://github.com/php/php-src/commit/fd07302024bc47082b13b32217147fd39d1e9e61
to the 7.2 branch.
Davey, Joe, do we want to take action here for 7.1? It's a pretty severe
bias, but fixing it is going to change seed sequences. I think at this
point we're too far in the 7.1 cycle to apply this kind of change.
Nikita
Sorry for the long delay. I've just applied
https://github.com/php/php-src/commit/fd07302024bc47082b13b32217147fd39d1e9e61
to the 7.2 branch.
Thank you!
Maybe you'd add similar tests for 64-bit ranges? Right now,
rand_range64()'s bias avoidance is left untested. Need to come up with
numbers that would demonstrate the bias if the bias-avoiding loop
failed.
Also, the comment (by me, in the test) that says "7.1.0 to 7.2.0beta2"
should now say "7.1.0 to 7.2.0beta3" since beta3 was released with the
bug still intact.
Alexander