<s>
A	O
pseudorandom	B-Algorithm
sequence	I-Algorithm
of	O
numbers	O
is	O
one	O
that	O
appears	O
to	O
be	O
statistically	O
random	O
,	O
despite	O
having	O
been	O
produced	O
by	O
a	O
completely	O
deterministic	O
and	O
repeatable	O
process	O
.	O
</s>
<s>
The	O
generation	O
of	O
random	O
numbers	O
has	O
many	O
uses	O
,	O
such	O
as	O
for	O
random	O
sampling	O
,	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
,	O
board	O
games	O
,	O
or	O
gambling	O
.	O
</s>
<s>
In	O
many	O
applications	O
,	O
the	O
deterministic	O
process	O
is	O
a	O
computer	O
algorithm	O
called	O
a	O
pseudorandom	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
,	O
which	O
must	O
first	O
be	O
provided	O
with	O
a	O
number	O
called	O
a	O
random	B-Algorithm
seed	I-Algorithm
.	O
</s>
<s>
In	O
some	O
cases	O
where	O
it	O
is	O
important	O
for	O
the	O
sequence	O
to	O
be	O
demonstrably	O
unpredictable	O
,	O
physical	O
sources	O
of	O
random	O
numbers	O
have	O
been	O
used	O
,	O
such	O
as	O
radioactive	O
decay	O
,	O
atmospheric	O
electromagnetic	O
noise	O
harvested	O
from	O
a	O
radio	O
tuned	O
between	O
stations	O
,	O
or	O
intermixed	O
timings	O
of	O
keystrokes	B-Application
.	O
</s>
<s>
The	O
time	O
investment	O
needed	O
to	O
obtain	O
these	O
numbers	O
leads	O
to	O
a	O
compromise	O
:	O
using	O
some	O
of	O
these	O
physics	O
readings	O
as	O
a	O
seed	O
for	O
a	O
pseudorandom	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
.	O
</s>
<s>
Before	O
modern	O
computing	O
,	O
researchers	O
requiring	O
random	O
numbers	O
would	O
either	O
generate	O
them	O
through	O
various	O
means	O
(	O
dice	B-Language
,	O
cards	O
,	O
roulette	O
wheels	O
,	O
etc	O
.	O
)	O
</s>
<s>
In	O
theoretical	O
computer	O
science	O
,	O
a	O
distribution	O
is	O
pseudorandom	B-Error_Name
against	O
a	O
class	O
of	O
adversaries	O
if	O
no	O
adversary	O
from	O
the	O
class	O
can	O
distinguish	O
it	O
from	O
the	O
uniform	O
distribution	O
with	O
significant	O
advantage	O
.	O
</s>
<s>
This	O
notion	O
of	O
pseudorandomness	B-Error_Name
is	O
studied	O
in	O
computational	O
complexity	O
theory	O
and	O
has	O
applications	O
to	O
cryptography	O
.	O
</s>
<s>
A	O
distribution	O
D	O
over	O
S	O
is	O
ε-pseudorandom	O
against	O
F	O
if	O
for	O
every	O
f	O
in	O
F	O
,	O
the	O
statistical	O
distance	O
between	O
the	O
distributions	O
and	O
,	O
where	O
is	O
sampled	O
from	O
D	O
,	O
and	O
,	O
where	O
and	O
is	O
sampled	O
from	O
the	O
uniform	O
distribution	O
on	O
S	O
,	O
is	O
at	O
most	O
ε	O
.	O
</s>
<s>
In	O
typical	O
applications	O
,	O
the	O
class	O
F	O
describes	O
a	O
model	O
of	O
computation	O
with	O
bounded	O
resources	O
and	O
one	O
is	O
interested	O
in	O
designing	O
distributions	O
D	O
with	O
certain	O
properties	O
that	O
are	O
pseudorandom	B-Error_Name
against	O
F	O
.	O
The	O
distribution	O
D	O
is	O
often	O
specified	O
as	O
the	O
output	O
of	O
a	O
pseudorandom	B-Error_Name
generator	O
.	O
</s>
