<s>
The	O
MD2	B-Algorithm
Message-Digest	B-Algorithm
Algorithm	I-Algorithm
is	O
a	O
cryptographic	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
developed	O
by	O
Ronald	O
Rivest	O
in	O
1989	O
.	O
</s>
<s>
MD2	B-Algorithm
is	O
specified	O
in	O
IETF	O
RFC	O
1319	O
.	O
</s>
<s>
The	O
"	O
MD	O
"	O
in	O
MD2	B-Algorithm
stands	O
for	O
"	O
Message	B-Algorithm
Digest	I-Algorithm
"	O
.	O
</s>
<s>
Even	O
though	O
MD2	B-Algorithm
is	O
not	O
yet	O
fully	O
compromised	O
,	O
the	O
IETF	O
retired	O
MD2	B-Algorithm
to	O
"	O
historic	O
"	O
status	O
in	O
2011	O
,	O
citing	O
"	O
signs	O
of	O
weakness	O
"	O
.	O
</s>
<s>
It	O
is	O
deprecated	O
in	O
favor	O
of	O
SHA-256	B-Algorithm
and	O
other	O
strong	O
hashing	O
algorithms	O
.	O
</s>
<s>
Nevertheless	O
,	O
,	O
it	O
remained	O
in	O
use	O
in	O
public	B-Architecture
key	I-Architecture
infrastructures	I-Architecture
as	O
part	O
of	O
certificates	O
generated	O
with	O
MD2	B-Algorithm
and	O
RSA	B-Architecture
.	O
</s>
<s>
The	O
128-bit	O
hash	B-Algorithm
value	O
of	O
any	O
message	O
is	O
formed	O
by	O
padding	O
it	O
to	O
a	O
multiple	O
of	O
the	O
block	O
length	O
(	O
128	O
bits	O
or	O
16	O
bytes	B-Application
)	O
and	O
adding	O
a	O
16-byte	O
checksum	B-Algorithm
to	O
it	O
.	O
</s>
<s>
For	O
the	O
actual	O
calculation	O
,	O
a	O
48-byte	O
auxiliary	O
block	O
and	O
a	O
256-byte	O
S-table	B-Algorithm
.	O
</s>
<s>
The	O
constants	O
were	O
generated	O
by	O
shuffling	O
the	O
integers	O
0	O
through	O
255	O
using	O
a	O
variant	O
of	O
Durstenfeld	O
's	O
algorithm	O
with	O
a	O
pseudorandom	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
based	O
on	O
decimal	O
digits	O
of	O
(	O
pi	O
)	O
(	O
see	O
nothing	O
up	O
my	O
sleeve	O
number	O
)	O
.	O
</s>
<s>
The	O
algorithm	O
runs	O
through	O
a	O
loop	O
where	O
it	O
permutes	O
each	O
byte	B-Application
in	O
the	O
auxiliary	O
block	O
18	O
times	O
for	O
every	O
16	O
input	O
bytes	B-Application
processed	O
.	O
</s>
<s>
Once	O
all	O
of	O
the	O
blocks	O
of	O
the	O
(	O
lengthened	O
)	O
message	O
have	O
been	O
processed	O
,	O
the	O
first	O
partial	O
block	O
of	O
the	O
auxiliary	O
block	O
becomes	O
the	O
hash	B-Algorithm
value	O
of	O
the	O
message	O
.	O
</s>
<s>
The	O
S-table	B-Algorithm
values	O
in	O
hex	O
are	O
:	O
</s>
<s>
The	O
128-bit	O
(	O
16-byte	O
)	O
MD2	B-Algorithm
hashes	B-Algorithm
(	O
also	O
termed	O
message	B-Algorithm
digests	I-Algorithm
)	O
are	O
typically	O
represented	O
as	O
32-digit	O
hexadecimal	O
numbers	O
.	O
</s>
<s>
The	O
following	O
demonstrates	O
a	O
43-byte	O
ASCII	B-Protocol
input	O
and	O
the	O
corresponding	O
MD2	B-Algorithm
hash	B-Algorithm
:	O
</s>
<s>
As	O
the	O
result	O
of	O
the	O
avalanche	O
effect	O
in	O
MD2	B-Algorithm
,	O
even	O
a	O
small	O
change	O
in	O
the	O
input	O
message	O
will	O
(	O
with	O
overwhelming	O
probability	O
)	O
result	O
in	O
a	O
completely	O
different	O
hash	B-Algorithm
.	O
</s>
<s>
The	O
hash	B-Algorithm
of	O
the	O
zero-length	O
string	O
is	O
:	O
</s>
<s>
Rogier	O
and	O
Chauvaud	O
(	O
1997	O
)	O
described	O
collisions	O
of	O
MD2	B-Algorithm
's	O
compression	B-Algorithm
function	I-Algorithm
,	O
although	O
they	O
were	O
unable	O
to	O
extend	O
the	O
attack	O
to	O
the	O
full	O
MD2	B-Algorithm
.	O
</s>
<s>
In	O
2004	O
,	O
MD2	B-Algorithm
was	O
shown	O
to	O
be	O
vulnerable	O
to	O
a	O
preimage	O
attack	O
with	O
time	O
complexity	O
equivalent	O
to	O
2104	O
applications	O
of	O
the	O
compression	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
The	O
author	O
concludes	O
,	O
"	O
MD2	B-Algorithm
can	O
no	O
longer	O
be	O
considered	O
a	O
secure	O
one-way	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
"	O
.	O
</s>
<s>
In	O
2008	O
,	O
MD2	B-Algorithm
has	O
further	O
improvements	O
on	O
a	O
preimage	O
attack	O
with	O
time	O
complexity	O
of	O
273	O
compression	B-Algorithm
function	I-Algorithm
evaluations	O
and	O
memory	O
requirements	O
of	O
273	O
message	O
blocks	O
.	O
</s>
<s>
In	O
2009	O
,	O
MD2	B-Algorithm
was	O
shown	O
to	O
be	O
vulnerable	O
to	O
a	O
collision	B-Algorithm
attack	I-Algorithm
with	O
time	O
complexity	O
of	O
263.3	O
compression	B-Algorithm
function	I-Algorithm
evaluations	O
and	O
memory	O
requirements	O
of	O
252	O
hash	B-Algorithm
values	O
.	O
</s>
<s>
This	O
is	O
slightly	O
better	O
than	O
the	O
birthday	O
attack	O
which	O
is	O
expected	O
to	O
take	O
265.5	O
compression	B-Algorithm
function	I-Algorithm
evaluations	O
.	O
</s>
<s>
In	O
2009	O
,	O
security	O
updates	O
were	O
issued	O
disabling	O
MD2	B-Algorithm
in	O
OpenSSL	B-Language
,	O
GnuTLS	B-Application
,	O
and	O
Network	B-Protocol
Security	I-Protocol
Services	I-Protocol
.	O
</s>
