<s>
In	O
cryptography	O
,	O
MD5CRK	B-Operating_System
was	O
a	O
volunteer	B-Operating_System
computing	I-Operating_System
effort	O
(	O
similar	O
to	O
distributed.net	O
)	O
launched	O
by	O
Jean-Luc	O
Cooke	O
and	O
his	O
company	O
,	O
CertainKey	O
Cryptosystems	O
,	O
to	O
demonstrate	O
that	O
the	O
MD5	B-Algorithm
message	B-Algorithm
digest	I-Algorithm
algorithm	O
is	O
insecure	O
by	O
finding	O
a	O
collision	B-Algorithm
two	O
messages	O
that	O
produce	O
the	O
same	O
MD5	B-Algorithm
hash	I-Algorithm
.	O
</s>
<s>
The	O
project	O
ended	O
on	O
August	O
24	O
,	O
2004	O
after	O
researchers	O
independently	O
demonstrated	O
a	O
technique	O
for	O
generating	O
collisions	O
in	O
MD5	B-Algorithm
using	O
analytical	O
methods	O
by	O
Xiaoyun	O
Wang	O
,	O
Feng	O
,	O
Xuejia	O
Lai	O
,	O
and	O
Yu	O
.	O
</s>
<s>
A	O
technique	O
called	O
Floyd	O
's	O
cycle-finding	O
algorithm	O
was	O
used	O
to	O
try	O
to	O
find	O
a	O
collision	B-Algorithm
for	O
MD5	B-Algorithm
.	O
</s>
<s>
These	O
markers	O
are	O
called	O
distinguished	O
points	O
,	O
the	O
point	O
where	O
two	O
inputs	O
produce	O
the	O
same	O
output	O
is	O
called	O
a	O
collision	B-Algorithm
point	O
.	O
</s>
<s>
MD5CRK	B-Operating_System
considered	O
any	O
point	O
whose	O
first	O
32	O
bits	O
were	O
zeroes	O
to	O
be	O
a	O
distinguished	O
point	O
.	O
</s>
<s>
The	O
expected	O
time	O
to	O
find	O
a	O
collision	B-Algorithm
is	O
not	O
equal	O
to	O
where	O
is	O
the	O
number	O
of	O
bits	O
in	O
the	O
digest	O
output	O
.	O
</s>
<s>
For	O
this	O
project	O
,	O
the	O
probability	O
of	O
success	O
after	O
MD5	B-Algorithm
computations	O
can	O
be	O
approximated	O
by	O
:	O
.	O
</s>
<s>
The	O
expected	O
number	O
of	O
computations	O
required	O
to	O
produce	O
a	O
collision	B-Algorithm
in	O
the	O
128-bit	O
MD5	B-Algorithm
message	B-Algorithm
digest	I-Algorithm
function	O
is	O
thus	O
:	O
</s>
<s>
To	O
give	O
some	O
perspective	O
to	O
this	O
,	O
using	O
Virginia	O
Tech	O
's	O
System	B-Device
X	I-Device
with	O
a	O
maximum	O
performance	O
of	O
12.25	O
Teraflops	O
,	O
it	O
would	O
take	O
approximately	O
seconds	O
or	O
about	O
3	O
weeks	O
.	O
</s>
