<s>
Modern	O
cryptographic	B-Protocol
protocols	I-Protocol
often	O
require	O
frequent	O
generation	O
of	O
random	O
quantities	O
.	O
</s>
<s>
Cryptographic	O
attacks	O
that	O
subvert	O
or	O
exploit	O
weaknesses	O
in	O
this	O
process	O
are	O
known	O
as	O
random	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
attacks	I-Algorithm
.	O
</s>
<s>
Nevertheless	O
,	O
in	O
the	O
specific	O
case	O
of	O
playing	O
mixed	O
strategy	O
games	O
,	O
use	O
of	O
human	O
gameplay	O
entropy	B-Algorithm
for	O
randomness	O
generation	O
was	O
studied	O
by	O
Ran	O
Halprin	O
and	O
Moni	O
Naor	O
.	O
</s>
<s>
Just	O
as	O
with	O
other	O
components	O
of	O
a	O
cryptosystem	O
,	O
a	O
software	B-Algorithm
random	I-Algorithm
number	I-Algorithm
generator	I-Algorithm
should	O
be	O
designed	O
to	O
resist	O
certain	O
attacks	O
.	O
</s>
<s>
Input-based	O
attacks	O
modify	O
the	O
input	O
to	O
the	O
RNG	O
to	O
attack	O
it	O
,	O
for	O
example	O
by	O
"	O
flushing	O
"	O
existing	O
entropy	B-Algorithm
out	O
of	O
the	O
system	O
and	O
put	O
it	O
into	O
a	O
known	O
state	O
.	O
</s>
<s>
This	O
can	O
happen	O
when	O
a	O
generator	O
starts	O
up	O
and	O
has	O
little	O
or	O
no	O
entropy	B-Algorithm
(	O
especially	O
if	O
the	O
computer	O
has	O
just	O
been	O
booted	O
and	O
followed	O
a	O
very	O
standard	O
sequence	O
of	O
operations	O
)	O
,	O
so	O
an	O
attacker	O
may	O
be	O
able	O
to	O
obtain	O
an	O
initial	O
guess	O
at	O
the	O
state	O
.	O
</s>
<s>
A	O
number	O
of	O
attacks	O
on	O
hardware	O
random	O
number	O
generators	O
are	O
possible	O
,	O
including	O
trying	O
to	O
capture	O
radio-frequency	O
emissions	O
from	O
the	O
computer	O
(	O
obtaining	O
hard	O
drive	O
interrupt	O
times	O
from	O
motor	O
noise	O
,	O
for	O
example	O
)	O
,	O
or	O
trying	O
to	O
feed	O
controlled	O
signals	O
into	O
a	O
supposedly	O
random	O
source	O
(	O
such	O
as	O
turning	O
off	O
the	O
lights	O
in	O
a	O
lava	O
lamp	O
or	O
feeding	O
a	O
strong	O
,	O
known	O
signal	O
into	O
a	O
sound	B-Device
card	I-Device
)	O
.	O
</s>
<s>
Subverted	O
random	O
numbers	O
can	O
be	O
created	O
using	O
a	O
cryptographically	B-Algorithm
secure	I-Algorithm
pseudorandom	I-Algorithm
number	I-Algorithm
generator	I-Algorithm
with	O
a	O
seed	B-Algorithm
value	I-Algorithm
known	O
to	O
the	O
attacker	O
but	O
concealed	O
in	O
the	O
software	O
.	O
</s>
<s>
CPU	B-General_Concept
chips	O
with	O
built-in	O
hardware	O
random	O
number	O
generators	O
can	O
be	O
replaced	O
by	O
compatible	O
chips	O
with	O
a	O
subverted	O
RNG	O
in	O
the	O
chips	O
 '	O
firmware	O
.	O
</s>
<s>
Mix	O
(	O
with	O
,	O
for	O
example	O
,	O
xor	B-Application
)	O
hardware	O
generated	O
random	O
numbers	O
with	O
the	O
output	O
of	O
a	O
good	O
quality	O
stream	B-Algorithm
cipher	I-Algorithm
,	O
as	O
close	O
to	O
the	O
point	O
of	O
use	O
as	O
possible	O
.	O
</s>
<s>
The	O
stream	B-Algorithm
cipher	I-Algorithm
key	O
or	O
seed	O
should	O
be	O
changeable	O
in	O
a	O
way	O
that	O
can	O
be	O
audited	O
and	O
derived	O
from	O
a	O
trustworthy	O
source	O
,	O
e.g.	O
</s>
<s>
The	O
Fortuna	B-Algorithm
random	O
number	O
generator	O
is	O
an	O
example	O
of	O
an	O
algorithm	O
which	O
uses	O
this	O
mechanism	O
.	O
</s>
<s>
From	O
this	O
perspective	O
,	O
sound	B-Device
cards	I-Device
and	O
webcams	B-Protocol
may	O
be	O
a	O
better	O
source	O
of	O
randomness	O
than	O
hardware	O
made	O
for	O
that	O
purpose	O
.	O
</s>
<s>
Early	O
versions	O
of	O
Netscape	O
's	O
Secure	B-Protocol
Sockets	I-Protocol
Layer	I-Protocol
(	O
SSL	O
)	O
encryption	B-Protocol
protocol	I-Protocol
used	O
pseudo-random	O
quantities	O
derived	O
from	O
a	O
PRNG	O
seeded	O
with	O
three	O
variable	O
values	O
:	O
the	O
time	O
of	O
day	O
,	O
the	O
process	O
ID	O
,	O
and	O
the	O
parent	O
process	O
ID	O
.	O
</s>
<s>
These	O
quantities	O
are	O
often	O
relatively	O
predictable	O
,	O
and	O
so	O
have	O
little	O
entropy	B-Algorithm
and	O
are	O
less	O
than	O
random	O
,	O
and	O
so	O
that	O
version	O
of	O
SSL	O
was	O
found	O
to	O
be	O
insecure	O
as	O
a	O
result	O
.	O
</s>
<s>
The	O
problem	O
in	O
the	O
running	O
code	O
was	O
discovered	O
in	O
1995	O
by	O
Ian	O
Goldberg	O
and	O
David	O
Wagner	O
,	O
who	O
had	O
to	O
reverse	O
engineer	O
the	O
object	B-Language
code	I-Language
because	O
Netscape	O
refused	O
to	O
reveal	O
the	O
details	O
of	O
its	O
random	O
number	O
generation	O
(	O
security	O
through	O
obscurity	O
)	O
.	O
</s>
<s>
That	O
RNG	O
was	O
fixed	O
in	O
later	O
releases	O
(	O
version	O
2	O
and	O
higher	O
)	O
by	O
more	O
robust	O
(	O
i.e.	O
,	O
more	O
random	O
and	O
so	O
higher	O
entropy	B-Algorithm
from	O
an	O
attacker	O
's	O
perspective	O
)	O
seeding	O
.	O
</s>
<s>
Microsoft	O
uses	O
an	O
unpublished	O
algorithm	O
to	O
generate	O
random	O
values	O
for	O
its	O
Windows	B-Application
operating	I-Application
system	I-Application
.	O
</s>
<s>
These	O
random	O
quantities	O
are	O
made	O
available	O
to	O
users	O
via	O
the	O
CryptGenRandom	B-Algorithm
utility	O
.	O
</s>
<s>
from	O
the	O
Hebrew	O
University	O
of	O
Jerusalem	O
and	O
University	O
of	O
Haifa	O
published	O
a	O
paper	O
titled	O
Cryptanalysis	O
of	O
the	O
Random	O
Number	O
Generator	O
of	O
the	O
Windows	B-Application
Operating	I-Application
System	I-Application
.	O
</s>
<s>
had	O
inserted	O
a	O
back	O
door	O
into	O
a	O
2006	O
standard	O
adopted	O
by	O
T	O
...	O
called	O
the	O
Dual	O
EC	O
DRBG	B-Algorithm
standard	O
"	O
,	O
thereby	O
revealing	O
that	O
the	O
NSA	O
carried	O
out	O
a	O
malware	O
attack	O
against	O
the	O
American	O
people	O
.	O
</s>
<s>
In	O
December	O
2013	O
,	O
Reuters	O
reported	O
that	O
documents	O
released	O
by	O
Edward	O
Snowden	O
indicated	O
that	O
the	O
NSA	O
had	O
paid	O
RSA	B-Architecture
Security	O
$10	O
million	O
to	O
make	O
Dual_EC_DRBG	O
the	O
default	O
in	O
their	O
encryption	O
software	O
,	O
and	O
raised	O
further	O
concerns	O
that	O
the	O
algorithm	O
might	O
contain	O
a	O
backdoor	O
for	O
the	O
NSA	O
.	O
</s>
<s>
Due	O
to	O
these	O
concerns	O
,	O
in	O
2014	O
,	O
NIST	O
withdrew	O
Dual	O
EC	O
DRBG	B-Algorithm
from	O
its	O
draft	O
guidance	O
on	O
random	O
number	O
generators	O
,	O
recommending	O
"	O
current	O
users	O
of	O
Dual_EC_DRBG	O
transition	O
to	O
one	O
of	O
the	O
three	O
remaining	O
approved	O
algorithms	O
as	O
quickly	O
as	O
possible.	O
"	O
</s>
<s>
Crypto-1	B-Algorithm
is	O
a	O
cryptosystem	O
developed	O
by	O
NXP	O
for	O
use	O
on	O
MIFARE	O
chips	O
.	O
</s>
<s>
Upon	O
reverse	O
engineering	O
of	O
the	O
chip	O
,	O
researchers	O
from	O
the	O
University	O
of	O
Virginia	O
and	O
the	O
Chaos	O
Computer	O
Club	O
found	O
an	O
attack	O
on	O
Crypto-1	B-Algorithm
exploiting	O
a	O
poorly	O
initialized	O
random	O
number	O
generator	O
.	O
</s>
<s>
In	O
May	O
2008	O
,	O
security	O
researcher	O
Luciano	O
Bello	O
revealed	O
his	O
discovery	O
that	O
changes	O
made	O
in	O
2006	O
to	O
the	O
random	O
number	O
generator	O
in	O
the	O
version	O
of	O
the	O
OpenSSL	B-Language
package	O
distributed	O
with	O
Debian	O
Linux	B-Application
and	O
other	O
Debian-based	O
distributions	O
,	O
such	O
as	O
Ubuntu	B-Operating_System
,	O
dramatically	O
reduced	O
the	O
entropy	B-Algorithm
of	O
generated	O
values	O
and	O
made	O
a	O
variety	O
of	O
security	O
keys	O
vulnerable	O
to	O
attack	O
.	O
</s>
<s>
The	O
security	O
weakness	O
was	O
caused	O
by	O
changes	O
made	O
to	O
the	O
openssl	B-Language
code	O
by	O
a	O
Debian	O
developer	O
in	O
response	O
to	O
compiler	O
warnings	O
of	O
apparently	O
redundant	O
code	O
.	O
</s>
<s>
Key	O
types	O
affected	O
include	O
SSH	B-Protocol
keys	I-Protocol
,	O
OpenVPN	B-Language
keys	O
,	O
DNSSEC	B-Protocol
keys	O
,	O
key	O
material	O
for	O
use	O
in	O
X.509	O
certificates	O
and	O
session	O
keys	O
used	O
in	O
SSL/TLS	B-Protocol
connections	O
.	O
</s>
<s>
Keys	O
generated	O
by	O
non-Debian-based	O
Linux	B-Application
distributions	O
are	O
also	O
unaffected	O
.	O
</s>
<s>
In	O
December	O
2010	O
,	O
a	O
group	O
calling	O
itself	O
fail0verflow	O
announced	O
recovery	O
of	O
the	O
elliptic	O
curve	O
digital	O
signature	O
algorithm	O
(	O
ECDSA	O
)	O
private	O
key	O
used	O
by	O
Sony	O
to	O
sign	O
software	O
for	O
the	O
PlayStation	B-Operating_System
3	I-Operating_System
game	O
console	O
.	O
</s>
<s>
An	O
analysis	O
comparing	O
millions	O
of	O
RSA	B-Architecture
public	O
keys	O
gathered	O
from	O
the	O
Internet	O
was	O
announced	O
in	O
2012	O
by	O
Lenstra	O
,	O
Hughes	O
,	O
Augier	O
,	O
Bos	O
,	O
Kleinjung	O
,	O
and	O
Wachter	O
.	O
</s>
<s>
Nadia	O
Heninger	O
,	O
part	O
of	O
a	O
group	O
that	O
did	O
a	O
similar	O
experiment	O
,	O
said	O
that	O
the	O
bad	O
keys	O
occurred	O
almost	O
entirely	O
in	O
embedded	O
applications	O
,	O
and	O
explains	O
that	O
the	O
one-shared-prime	O
problem	O
uncovered	O
by	O
the	O
two	O
groups	O
results	O
from	O
situations	O
where	O
the	O
pseudorandom	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
is	O
poorly	O
seeded	O
initially	O
and	O
then	O
reseeded	O
between	O
the	O
generation	O
of	O
the	O
first	O
and	O
second	O
primes	O
.	O
</s>
<s>
In	O
August	O
2013	O
,	O
it	O
was	O
revealed	O
that	O
bugs	O
in	O
the	O
Java	B-Language
class	O
could	O
generate	O
collisions	O
in	O
the	O
k	O
nonce	O
values	O
used	O
for	O
ECDSA	O
in	O
implementations	O
of	O
Bitcoin	B-Protocol
on	O
Android	B-Application
.	O
</s>
<s>
When	O
this	O
occurred	O
the	O
private	O
key	O
could	O
be	O
recovered	O
,	O
in	O
turn	O
allowing	O
stealing	O
Bitcoins	B-Protocol
from	O
the	O
containing	O
wallet	B-Protocol
.	O
</s>
