<s>
A	O
counter-based	O
random	O
number	O
generation	O
(	O
CBRNG	O
,	O
also	O
known	O
as	O
a	O
counter-based	O
pseudo-random	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
,	O
or	O
CBPRNG	O
)	O
is	O
a	O
kind	O
of	O
pseudorandom	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
that	O
uses	O
only	O
an	O
integer	O
counter	O
as	O
its	O
internal	O
state	O
.	O
</s>
<s>
We	O
can	O
think	O
of	O
a	O
pseudorandom	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
(	O
PRNG	O
)	O
as	O
a	O
function	O
that	O
transforms	O
a	O
series	O
of	O
bits	O
known	O
as	O
the	O
state	O
into	O
a	O
new	O
state	O
and	O
a	O
random	O
number	O
.	O
</s>
<s>
In	O
some	O
PRNGs	O
,	O
such	O
as	O
the	O
Mersenne	B-Algorithm
Twister	I-Algorithm
,	O
the	O
state	O
is	O
large	O
,	O
more	O
than	O
2048	O
bytes	O
.	O
</s>
<s>
In	O
other	O
PRNGs	O
,	O
such	O
as	O
xorshift	B-Algorithm
,	O
and	O
are	O
one	O
and	O
the	O
same	O
(	O
and	O
so	O
the	O
state	O
is	O
small	O
,	O
just	O
4	O
,	O
8	O
,	O
or	O
16	O
bytes	O
,	O
depending	O
on	O
the	O
size	O
of	O
the	O
numbers	O
being	O
generated	O
)	O
.	O
</s>
<s>
Such	O
algorithms	O
are	O
inherently	O
sequential	O
and	O
not	O
amenable	O
to	O
running	O
on	O
parallel	O
machines	O
like	O
multi-core	B-Architecture
CPUs	I-Architecture
and	O
GPUs	B-Architecture
.	O
</s>
<s>
In	O
contrast	O
,	O
a	O
counter-based	B-Algorithm
random	I-Algorithm
number	I-Algorithm
generator	I-Algorithm
(	O
CBRNG	O
)	O
is	O
a	O
PRNG	O
where	O
the	O
state	O
"	O
evolves	O
"	O
in	O
a	O
particularly	O
simple	O
manner	O
:	O
.	O
</s>
<s>
This	O
property	O
make	O
it	O
easy	O
to	O
run	O
a	O
CBRNG	O
on	O
a	O
multiple	O
CPU	O
threads	O
or	O
a	O
GPU	B-Architecture
.	O
</s>
<s>
For	O
example	O
,	O
to	O
generate	O
random	O
numbers	O
on	O
a	O
GPU	B-Architecture
,	O
you	O
might	O
spawn	O
threads	O
and	O
have	O
the	O
th	O
thread	O
calculate	O
.	O
</s>
<s>
This	O
yields	O
a	O
strong	O
,	O
cryptographically-secure	B-Algorithm
source	I-Algorithm
of	I-Algorithm
randomness	I-Algorithm
.	O
</s>
<s>
But	O
cryptographically-secure	B-Algorithm
pseudorandom	I-Algorithm
number	I-Algorithm
generators	I-Algorithm
tend	O
to	O
be	O
slow	O
compared	O
to	O
insecure	O
PRNGs	O
,	O
and	O
in	O
practice	O
many	O
uses	O
of	O
random	O
numbers	O
do	O
n't	O
require	O
this	O
degree	O
of	O
security	O
.	O
</s>
<s>
at	O
D	B-Application
.	I-Application
E	I-Application
.	I-Application
Shaw	I-Application
Research	I-Application
introduced	O
two	O
CBRNGs	O
based	O
on	O
reduced-strength	O
versions	O
of	O
block	O
ciphers	O
.	O
</s>
<s>
Threefry	O
uses	O
a	O
reduced-strength	O
version	O
of	O
the	O
Threefish	B-Algorithm
block	O
cipher	O
.	O
</s>
<s>
ARS	O
uses	O
a	O
reduced-strength	O
version	O
of	O
the	O
AES	B-Algorithm
block	O
cipher	O
.	O
</s>
<s>
(	O
"	O
ARS	O
"	O
is	O
a	O
pun	O
on	O
"	O
AES	B-Algorithm
"	O
;	O
"	O
AES	B-Algorithm
"	O
stands	O
for	O
"	O
advanced	B-Algorithm
encryption	I-Algorithm
standard	I-Algorithm
"	O
,	O
and	O
"	O
ARS	O
"	O
stands	O
for	O
"	O
advanced	O
randomization	O
system	O
"	O
)	O
.	O
</s>
<s>
ARS	O
is	O
used	O
in	O
recent	O
versions	O
of	O
Intel	O
's	O
Math	B-Language
Kernel	I-Language
Library	I-Language
and	O
gets	O
good	O
performance	O
by	O
using	O
instructions	O
from	O
the	O
AES-NI	O
instruction	O
set	O
,	O
which	O
specifically	O
accelerate	O
AES	B-Algorithm
encryption	I-Algorithm
.	O
</s>
<s>
As	O
of	O
2020	O
,	O
Philox	O
is	O
popular	O
on	O
CPUs	O
and	O
GPUs	B-Architecture
.	O
</s>
<s>
On	O
GPUs	B-Architecture
,	O
nVidia	O
's	O
library	O
and	O
TensorFlow	B-Language
provide	O
implementations	O
of	O
Philox	O
.	O
</s>
<s>
On	O
CPUs	O
,	O
Intel	O
's	O
MKL	B-Language
provides	O
an	O
implementation	O
.	O
</s>
