<s>
E0	B-Algorithm
is	O
a	O
stream	B-Algorithm
cipher	I-Algorithm
used	O
in	O
the	O
Bluetooth	B-Protocol
protocol	O
.	O
</s>
<s>
It	O
generates	O
a	O
sequence	O
of	O
pseudorandom	B-Error_Name
numbers	I-Error_Name
and	O
combines	O
it	O
with	O
the	O
data	O
using	O
the	O
XOR	B-Application
operator	O
.	O
</s>
<s>
At	O
each	O
iteration	O
,	O
E0	B-Algorithm
generates	O
a	O
bit	O
using	O
four	O
shift	B-General_Concept
registers	I-General_Concept
of	O
differing	O
lengths	O
(	O
25	O
,	O
31	O
,	O
33	O
,	O
39	O
bits	O
)	O
and	O
two	O
internal	O
states	O
,	O
each	O
2	O
bits	O
long	O
.	O
</s>
<s>
At	O
each	O
clock	O
tick	O
,	O
the	O
registers	O
are	O
shifted	O
and	O
the	O
two	O
states	O
are	O
updated	O
with	O
the	O
current	O
state	O
,	O
the	O
previous	O
state	O
and	O
the	O
values	O
in	O
the	O
shift	B-General_Concept
registers	I-General_Concept
.	O
</s>
<s>
Four	O
bits	O
are	O
then	O
extracted	O
from	O
the	O
shift	B-General_Concept
registers	I-General_Concept
and	O
added	O
together	O
.	O
</s>
<s>
The	O
algorithm	O
XORs	B-Application
that	O
sum	O
with	O
the	O
value	O
in	O
the	O
2-bit	O
register	O
.	O
</s>
<s>
E0	B-Algorithm
is	O
divided	O
in	O
three	O
parts	O
:	O
</s>
<s>
The	O
setup	O
of	O
the	O
initial	O
state	O
in	O
Bluetooth	B-Protocol
uses	O
the	O
same	O
structure	O
as	O
the	O
random	O
bit	O
stream	O
generator	O
.	O
</s>
<s>
We	O
are	O
thus	O
dealing	O
with	O
two	O
combined	O
E0	B-Algorithm
algorithms	O
.	O
</s>
<s>
An	O
initial	O
132-bit	O
state	O
is	O
produced	O
at	O
the	O
first	O
stage	O
using	O
four	O
inputs	O
(	O
the	O
128-bit	O
key	O
,	O
the	O
Bluetooth	B-Protocol
address	O
on	O
48	O
bits	O
and	O
the	O
26-bit	O
master	O
counter	O
)	O
.	O
</s>
<s>
These	O
are	O
stored	O
into	O
the	O
second	O
stage	O
's	O
shift	B-General_Concept
registers	I-General_Concept
.	O
</s>
<s>
200	O
pseudorandom	B-Error_Name
bits	O
are	O
then	O
produced	O
by	O
200	O
clock	O
ticks	O
,	O
and	O
the	O
last	O
128	O
bits	O
are	O
inserted	O
into	O
the	O
shift	B-General_Concept
registers	I-General_Concept
.	O
</s>
<s>
Several	O
attacks	O
and	O
attempts	O
at	O
cryptanalysis	O
of	O
E0	B-Algorithm
and	O
the	O
Bluetooth	B-Protocol
protocol	O
have	O
been	O
made	O
,	O
and	O
a	O
number	O
of	O
vulnerabilities	O
have	O
been	O
found	O
.	O
</s>
<s>
In	O
1999	O
,	O
Miia	O
Hermelin	O
and	O
Kaisa	O
Nyberg	O
showed	O
that	O
E0	B-Algorithm
could	O
be	O
broken	O
in	O
264	O
operations	O
(	O
instead	O
of	O
2128	O
)	O
,	O
if	O
264	O
bits	O
of	O
output	O
are	O
known	O
.	O
</s>
<s>
He	O
deduced	O
that	O
the	O
maximal	O
security	O
of	O
E0	B-Algorithm
is	O
equivalent	O
to	O
that	O
provided	O
by	O
65-bit	O
keys	O
,	O
and	O
that	O
longer	O
keys	O
do	O
not	O
improve	O
security	O
.	O
</s>
<s>
Fluhrer	O
's	O
attack	O
is	O
an	O
improvement	O
upon	O
earlier	O
work	O
by	O
Golic	O
,	O
Bagini	O
and	O
Morgari	O
,	O
who	O
devised	O
a	O
270	O
operations	O
attack	O
on	O
E0	B-Algorithm
.	O
</s>
<s>
In	O
2000	O
,	O
the	O
Finn	O
Juha	O
Vainio	O
showed	O
problems	O
related	O
to	O
misuse	O
of	O
E0	B-Algorithm
and	O
more	O
generally	O
,	O
possible	O
vulnerabilities	O
in	O
Bluetooth	B-Protocol
.	O
</s>
<s>
In	O
2004	O
,	O
Yi	O
Lu	O
and	O
Serge	O
Vaudenay	O
published	O
a	O
statistical	O
attack	O
requiring	O
the	O
24	O
first	O
bits	O
of	O
235	O
Bluetooth	B-Protocol
frames	O
(	O
a	O
frame	O
is	O
2745	O
bits	O
long	O
)	O
.	O
</s>
<s>
In	O
2005	O
,	O
Lu	O
,	O
Meier	O
and	O
Vaudenay	O
published	O
a	O
cryptanalysis	O
of	O
E0	B-Algorithm
based	O
on	O
a	O
conditional	O
correlation	O
attack	O
.	O
</s>
<s>
The	O
authors	O
assert	O
that	O
"	O
this	O
is	O
clearly	O
the	O
fastest	O
and	O
only	O
practical	O
known-plaintext	O
attack	O
on	O
Bluetooth	B-Protocol
encryption	O
compare	O
with	O
all	O
existing	O
attacks	O
"	O
.	O
</s>
