<s>
In	O
anonymity	B-Application
networks	I-Application
(	O
e.g.	O
,	O
Tor	B-Application
,	O
Crowds	B-Protocol
,	O
Mixmaster	B-Protocol
,	O
I2P	B-Protocol
,	O
etc	O
.	O
</s>
<s>
The	O
degree	B-Application
of	I-Application
anonymity	I-Application
is	O
a	O
device	O
that	O
was	O
proposed	O
at	O
the	O
2002	O
Privacy	O
Enhancing	O
Technology	O
(	O
PET	O
)	O
conference	O
.	O
</s>
<s>
Two	O
papers	O
put	O
forth	O
the	O
idea	O
of	O
using	O
entropy	B-Algorithm
as	O
the	O
basis	O
for	O
formally	O
measuring	O
anonymity	O
:	O
"	O
Towards	O
an	O
Information	O
Theoretic	O
Metric	O
for	O
Anonymity	O
"	O
,	O
and	O
"	O
Towards	O
Measuring	O
Anonymity	O
"	O
.	O
</s>
<s>
Anonymity	B-Application
networks	I-Application
have	O
been	O
developed	O
and	O
many	O
have	O
introduced	O
methods	O
of	O
proving	O
the	O
anonymity	O
guarantees	O
that	O
are	O
possible	O
,	O
originally	O
with	O
simple	O
Chaum	B-Protocol
Mixes	I-Protocol
and	O
Pool	O
Mixes	O
the	O
size	O
of	O
the	O
set	O
of	O
users	O
was	O
seen	O
as	O
the	O
security	O
that	O
the	O
system	O
could	O
provide	O
to	O
a	O
user	O
.	O
</s>
<s>
Information	O
like	O
this	O
and	O
via	O
methods	O
like	O
the	O
predecessor	B-Protocol
attack	I-Protocol
and	O
intersection	B-Protocol
attack	I-Protocol
helps	O
an	O
attacker	O
increase	O
the	O
probability	O
that	O
a	O
user	O
sent	O
the	O
message	O
.	O
</s>
<s>
The	O
degree	B-Application
of	I-Application
anonymity	I-Application
takes	O
into	O
account	O
the	O
probability	O
associated	O
with	O
each	O
user	O
,	O
it	O
begins	O
by	O
defining	O
the	O
entropy	B-Algorithm
of	O
the	O
system	O
(	O
here	O
is	O
where	O
the	O
papers	O
differ	O
slightly	O
but	O
only	O
with	O
notation	O
,	O
we	O
will	O
use	O
the	O
notation	O
from	O
.	O
</s>
<s>
where	O
is	O
the	O
entropy	B-Algorithm
of	O
the	O
network	O
,	O
is	O
the	O
number	O
of	O
nodes	O
in	O
the	O
network	O
,	O
and	O
is	O
the	O
probability	O
associated	O
with	O
node	O
.	O
</s>
<s>
Now	O
the	O
maximal	O
entropy	B-Algorithm
of	O
a	O
network	O
occurs	O
when	O
there	O
is	O
uniform	O
probability	O
associated	O
with	O
each	O
node	O
and	O
this	O
yields	O
.	O
</s>
<s>
In	O
Crowds	B-Protocol
there	O
is	O
a	O
global	O
probability	O
of	O
forwarding	O
(	O
)	O
,	O
which	O
is	O
the	O
probability	O
a	O
node	O
will	O
forward	O
the	O
message	O
internally	O
instead	O
of	O
routing	O
it	O
to	O
the	O
final	O
destination	O
.	O
</s>
<s>
In	O
Crowds	B-Protocol
the	O
attacker	O
is	O
internal	O
,	O
passive	O
,	O
and	O
local	O
.	O
</s>
<s>
Trivially	O
,	O
and	O
overall	O
the	O
entropy	B-Algorithm
is	O
,	O
is	O
this	O
value	O
divided	O
by	O
.	O
</s>
<s>
In	O
onion	B-Protocol
routing	I-Protocol
let	O
's	O
assume	O
the	O
attacker	O
can	O
exclude	O
a	O
subset	O
of	O
the	O
nodes	O
from	O
the	O
network	O
,	O
then	O
the	O
entropy	B-Algorithm
would	O
easily	O
be	O
,	O
where	O
is	O
the	O
size	O
of	O
the	O
subset	O
of	O
non-excluded	O
nodes	O
.	O
</s>
<s>
Under	O
an	O
attack	O
model	O
where	O
a	O
node	O
can	O
both	O
globally	O
listen	O
to	O
message	O
passing	O
and	O
is	O
a	O
node	O
on	O
the	O
path	O
this	O
decreases	O
to	O
,	O
where	O
is	O
the	O
length	O
of	O
the	O
onion	O
route	O
(	O
this	O
could	O
be	O
larger	O
or	O
smaller	O
than	O
)	O
,	O
as	O
there	O
is	O
no	O
attempt	O
in	O
onion	B-Protocol
routing	I-Protocol
to	O
remove	O
the	O
correlation	O
between	O
the	O
incoming	O
and	O
outgoing	O
messages	O
.	O
</s>
<s>
In	O
2004	O
,	O
Diaz	O
,	O
Sassaman	O
,	O
and	O
DeWitte	O
presented	O
an	O
analysis	O
of	O
two	O
anonymous	B-Application
remailers	I-Application
using	O
the	O
Serjantov	O
and	O
Danezis	O
metric	O
,	O
showing	O
one	O
of	O
them	O
to	O
provide	O
zero	O
anonymity	O
under	O
certain	O
realistic	O
conditions	O
.	O
</s>
