<s>
SHA-2	B-Algorithm
(	O
Secure	O
Hash	B-Algorithm
Algorithm	O
2	O
)	O
is	O
a	O
set	O
of	O
cryptographic	B-Algorithm
hash	I-Algorithm
functions	I-Algorithm
designed	O
by	O
the	O
United	O
States	O
National	O
Security	O
Agency	O
(	O
NSA	O
)	O
and	O
first	O
published	O
in	O
2001	O
.	O
</s>
<s>
They	O
are	O
built	O
using	O
the	O
Merkle	B-Algorithm
–	I-Algorithm
Damgård	I-Algorithm
construction	I-Algorithm
,	O
from	O
a	O
one-way	B-Algorithm
compression	I-Algorithm
function	I-Algorithm
itself	O
built	O
using	O
the	O
Davies	O
–	O
Meyer	O
structure	O
from	O
a	O
specialized	O
block	O
cipher	O
.	O
</s>
<s>
SHA-2	B-Algorithm
includes	O
significant	O
changes	O
from	O
its	O
predecessor	O
,	O
SHA-1	B-Algorithm
.	O
</s>
<s>
The	O
SHA-2	B-Algorithm
family	O
consists	O
of	O
six	O
hash	B-Algorithm
functions	I-Algorithm
with	O
digests	O
(	O
hash	B-Algorithm
values	O
)	O
that	O
are	O
224	O
,	O
256	O
,	O
384	O
or	O
512	O
bits	O
:	O
SHA-224	B-Algorithm
,	O
SHA-256	B-Algorithm
,	O
SHA-384	B-Algorithm
,	O
SHA-512	B-Algorithm
,	O
SHA-512/224	B-Algorithm
,	O
SHA-512/256	B-Algorithm
.	O
</s>
<s>
SHA-256	B-Algorithm
and	O
SHA-512	B-Algorithm
are	O
novel	O
hash	B-Algorithm
functions	I-Algorithm
computed	O
with	O
eight	O
32-bit	O
and	O
64-bit	O
words	O
,	O
respectively	O
.	O
</s>
<s>
SHA-224	B-Algorithm
and	O
SHA-384	B-Algorithm
are	O
truncated	O
versions	O
of	O
SHA-256	B-Algorithm
and	O
SHA-512	B-Algorithm
respectively	O
,	O
computed	O
with	O
different	O
initial	O
values	O
.	O
</s>
<s>
SHA-512/224	B-Algorithm
and	O
SHA-512/256	B-Algorithm
are	O
also	O
truncated	O
versions	O
of	O
SHA-512	B-Algorithm
,	O
but	O
the	O
initial	O
values	O
are	O
generated	O
using	O
the	O
method	O
described	O
in	O
Federal	O
Information	O
Processing	O
Standards	O
(	O
FIPS	O
)	O
PUB	O
180-4	O
.	O
</s>
<s>
SHA-2	B-Algorithm
was	O
first	O
published	O
by	O
the	O
National	O
Institute	O
of	O
Standards	O
and	O
Technology	O
(	O
NIST	O
)	O
as	O
a	O
U.S.	O
federal	O
standard	O
.	O
</s>
<s>
The	O
SHA-2	B-Algorithm
family	O
of	O
algorithms	O
are	O
patented	O
in	O
the	O
S	O
..	O
</s>
<s>
As	O
of	O
2011	O
,	O
the	O
best	O
public	O
attacks	O
break	O
preimage	O
resistance	O
for	O
52	O
out	O
of	O
64	O
rounds	O
of	O
SHA-256	B-Algorithm
or	O
57	O
out	O
of	O
80	O
rounds	O
of	O
SHA-512	B-Algorithm
,	O
and	O
collision	B-Algorithm
resistance	I-Algorithm
for	O
46	O
out	O
of	O
64	O
rounds	O
of	O
SHA-256	B-Algorithm
.	O
</s>
<s>
With	O
the	O
publication	O
of	O
FIPS	O
PUB	O
180-2	O
,	O
NIST	O
added	O
three	O
additional	O
hash	B-Algorithm
functions	I-Algorithm
in	O
the	O
SHA	O
family	O
.	O
</s>
<s>
The	O
algorithms	O
are	O
collectively	O
known	O
as	O
SHA-2	B-Algorithm
,	O
named	O
after	O
their	O
digest	O
lengths	O
(	O
in	O
bits	O
)	O
:	O
SHA-256	B-Algorithm
,	O
SHA-384	B-Algorithm
,	O
and	O
SHA-512	B-Algorithm
.	O
</s>
<s>
In	O
August	O
2002	O
,	O
FIPS	O
PUB	O
180-2	O
became	O
the	O
new	O
Secure	O
Hash	B-Algorithm
Standard	O
,	O
replacing	O
FIPS	O
PUB	O
180-1	O
,	O
which	O
was	O
released	O
in	O
April	O
1995	O
.	O
</s>
<s>
The	O
updated	O
standard	O
included	O
the	O
original	O
SHA-1	B-Algorithm
algorithm	O
,	O
with	O
updated	O
technical	O
notation	O
consistent	O
with	O
that	O
describing	O
the	O
inner	O
workings	O
of	O
the	O
SHA-2	B-Algorithm
family	O
.	O
</s>
<s>
In	O
February	O
2004	O
,	O
a	O
change	O
notice	O
was	O
published	O
for	O
FIPS	O
PUB	O
180-2	O
,	O
specifying	O
an	O
additional	O
variant	O
,	O
SHA-224	B-Algorithm
,	O
defined	O
to	O
match	O
the	O
key	O
length	O
of	O
two-key	O
Triple	B-Algorithm
DES	I-Algorithm
.	O
</s>
<s>
In	O
October	O
2008	O
,	O
the	O
standard	O
was	O
updated	O
in	O
FIPS	O
PUB	O
180-3	O
,	O
including	O
SHA-224	B-Algorithm
from	O
the	O
change	O
notice	O
,	O
but	O
otherwise	O
making	O
no	O
fundamental	O
changes	O
to	O
the	O
standard	O
.	O
</s>
<s>
The	O
primary	O
motivation	O
for	O
updating	O
the	O
standard	O
was	O
relocating	O
security	O
information	O
about	O
the	O
hash	B-Algorithm
algorithms	O
and	O
recommendations	O
for	O
their	O
use	O
to	O
Special	O
Publications	O
800-107	O
and	O
800-57	O
.	O
</s>
<s>
Detailed	O
test	O
data	O
and	O
example	O
message	B-Algorithm
digests	I-Algorithm
were	O
also	O
removed	O
from	O
the	O
standard	O
,	O
and	O
provided	O
as	O
separate	O
documents	O
.	O
</s>
<s>
In	O
January	O
2011	O
,	O
NIST	O
published	O
SP800-131A	O
,	O
which	O
specified	O
a	O
move	O
from	O
the	O
then-current	O
minimum	O
of	O
80-bit	O
security	O
(	O
provided	O
by	O
SHA-1	B-Algorithm
)	O
allowable	O
for	O
federal	O
government	O
use	O
until	O
the	O
end	O
of	O
2013	O
,	O
to	O
112-bit	O
security	O
(	O
provided	O
by	O
SHA-2	B-Algorithm
)	O
being	O
both	O
the	O
minimum	O
requirement	O
(	O
starting	O
in	O
2014	O
)	O
and	O
the	O
recommended	O
security	O
level	O
(	O
starting	O
from	O
the	O
publication	O
date	O
in	O
2011	O
)	O
.	O
</s>
<s>
In	O
March	O
2012	O
,	O
the	O
standard	O
was	O
updated	O
in	O
FIPS	O
PUB	O
180-4	O
,	O
adding	O
the	O
hash	B-Algorithm
functions	I-Algorithm
SHA-512/224	B-Algorithm
and	O
SHA-512/256	B-Algorithm
,	O
and	O
describing	O
a	O
method	O
for	O
generating	O
initial	O
values	O
for	O
truncated	O
versions	O
of	O
SHA-512	B-Algorithm
.	O
</s>
<s>
Additionally	O
,	O
a	O
restriction	O
on	O
padding	B-Algorithm
the	O
input	O
data	O
prior	O
to	O
hash	B-Algorithm
calculation	O
was	O
removed	O
,	O
allowing	O
hash	B-Algorithm
data	O
to	O
be	O
calculated	O
simultaneously	O
with	O
content	O
generation	O
,	O
such	O
as	O
a	O
real-time	O
video	O
or	O
audio	O
feed	O
.	O
</s>
<s>
Padding	B-Algorithm
the	O
final	O
data	O
block	O
must	O
still	O
occur	O
prior	O
to	O
hash	B-Algorithm
output	O
.	O
</s>
<s>
The	O
publication	O
disallowed	O
creation	O
of	O
digital	O
signatures	O
with	O
a	O
hash	B-Algorithm
security	I-Algorithm
lower	O
than	O
112	O
bits	O
after	O
2013	O
.	O
</s>
<s>
The	O
NIST	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
competition	I-Algorithm
selected	O
a	O
new	O
hash	B-Algorithm
function	I-Algorithm
,	O
SHA-3	B-Algorithm
,	O
in	O
2012	O
.	O
</s>
<s>
The	O
SHA-3	B-Algorithm
algorithm	O
is	O
not	O
derived	O
from	O
SHA-2	B-Algorithm
.	O
</s>
<s>
The	O
SHA-2	B-Algorithm
hash	B-Algorithm
function	I-Algorithm
is	O
implemented	O
in	O
some	O
widely	O
used	O
security	O
applications	O
and	O
protocols	O
,	O
including	O
TLS	B-Protocol
and	O
SSL	B-Protocol
,	O
PGP	B-Application
,	O
SSH	B-Protocol
,	O
S/MIME	B-Protocol
,	O
and	O
IPsec	B-Protocol
.	O
</s>
<s>
SHA-256	B-Algorithm
is	O
used	O
for	O
authenticating	O
Debian	O
software	O
packages	O
and	O
in	O
the	O
DKIM	B-Protocol
message	O
signing	O
standard	O
;	O
SHA-512	B-Algorithm
is	O
part	O
of	O
a	O
system	O
to	O
authenticate	O
archival	O
video	O
from	O
the	O
International	O
Criminal	O
Tribunal	O
of	O
the	O
Rwandan	O
genocide	O
.	O
</s>
<s>
SHA-256	B-Algorithm
and	O
SHA-512	B-Algorithm
are	O
proposed	O
for	O
use	O
in	O
DNSSEC	B-Protocol
.	O
</s>
<s>
Unix	O
and	O
Linux	O
vendors	O
are	O
moving	O
to	O
using	O
256	O
-	O
and	O
512-bit	O
SHA-2	B-Algorithm
for	O
secure	O
password	O
hashing	O
.	O
</s>
<s>
Several	O
cryptocurrencies	O
,	O
including	O
Bitcoin	B-Protocol
,	O
use	O
SHA-256	B-Algorithm
for	O
verifying	O
transactions	O
and	O
calculating	O
proof	O
of	O
work	O
or	O
proof	B-Protocol
of	I-Protocol
stake	I-Protocol
.	O
</s>
<s>
The	O
rise	O
of	O
ASIC	O
SHA-2	B-Algorithm
accelerator	O
chips	O
has	O
led	O
to	O
the	O
use	O
of	O
scrypt-based	O
proof-of-work	O
schemes	O
.	O
</s>
<s>
SHA-1	B-Algorithm
and	O
SHA-2	B-Algorithm
are	O
the	O
Secure	O
Hash	B-Algorithm
Algorithms	O
required	O
by	O
law	O
for	O
use	O
in	O
certain	O
U.S.	O
Government	O
applications	O
,	O
including	O
use	O
within	O
other	O
cryptographic	O
algorithms	O
and	O
protocols	O
,	O
for	O
the	O
protection	O
of	O
sensitive	O
unclassified	O
information	O
.	O
</s>
<s>
FIPS	O
PUB	O
180-1	O
also	O
encouraged	O
adoption	O
and	O
use	O
of	O
SHA-1	B-Algorithm
by	O
private	O
and	O
commercial	O
organizations	O
.	O
</s>
<s>
SHA-1	B-Algorithm
is	O
being	O
retired	O
for	O
most	O
government	O
uses	O
;	O
the	O
U.S.	O
National	O
Institute	O
of	O
Standards	O
and	O
Technology	O
says	O
,	O
"	O
Federal	O
agencies	O
should	O
stop	O
using	O
SHA-1	B-Algorithm
for	O
...	O
applications	O
that	O
require	O
collision	B-Algorithm
resistance	I-Algorithm
as	O
soon	O
as	O
practical	O
,	O
and	O
must	O
use	O
the	O
SHA-2	B-Algorithm
family	O
of	O
hash	B-Algorithm
functions	I-Algorithm
for	O
these	O
applications	O
after	O
2010	O
"	O
(	O
emphasis	O
in	O
original	O
)	O
.	O
</s>
<s>
NIST	O
's	O
directive	O
that	O
U.S.	O
government	O
agencies	O
ought	O
to	O
,	O
but	O
not	O
explicitly	O
must	O
,	O
stop	O
uses	O
of	O
SHA-1	B-Algorithm
after	O
2010	O
was	O
hoped	O
to	O
accelerate	O
migration	O
away	O
from	O
SHA-1	B-Algorithm
.	O
</s>
<s>
The	O
SHA-2	B-Algorithm
functions	O
were	O
not	O
quickly	O
adopted	O
initially	O
,	O
despite	O
better	O
security	O
than	O
SHA-1	B-Algorithm
.	O
</s>
<s>
Reasons	O
might	O
include	O
lack	O
of	O
support	O
for	O
SHA-2	B-Algorithm
on	O
systems	O
running	O
Windows	O
XP	O
SP2	O
or	O
older	O
and	O
a	O
lack	O
of	O
perceived	O
urgency	O
since	O
SHA-1	B-Algorithm
collisions	O
had	O
not	O
yet	O
been	O
found	O
.	O
</s>
<s>
The	O
Google	B-Application
Chrome	I-Application
team	O
announced	O
a	O
plan	O
to	O
make	O
their	O
web	O
browser	O
gradually	O
stop	O
honoring	O
SHA-1-dependent	O
TLS	B-Protocol
certificates	O
over	O
a	O
period	O
from	O
late	O
2014	O
and	O
early	O
2015	O
.	O
</s>
<s>
Similarly	O
,	O
Microsoft	O
announced	O
that	O
Internet	B-Application
Explorer	I-Application
and	O
Edge	B-Application
would	O
stop	O
honoring	O
public	O
SHA-1-signed	O
TLS	B-Protocol
certificates	O
from	O
February	O
2017	O
.	O
</s>
<s>
Mozilla	B-Operating_System
disabled	O
SHA-1	B-Algorithm
in	O
early	O
January	O
2016	O
,	O
but	O
had	O
to	O
re-enable	O
it	O
temporarily	O
via	O
a	O
Firefox	B-Application
update	O
,	O
after	O
problems	O
with	O
web-based	O
user	O
interfaces	O
of	O
some	O
router	O
models	O
and	O
security	B-Application
appliances	I-Application
.	O
</s>
<s>
For	O
a	O
hash	B-Algorithm
function	I-Algorithm
for	O
which	O
L	O
is	O
the	O
number	O
of	O
bits	O
in	O
the	O
message	B-Algorithm
digest	I-Algorithm
,	O
finding	O
a	O
message	O
that	O
corresponds	O
to	O
a	O
given	O
message	B-Algorithm
digest	I-Algorithm
can	O
always	O
be	O
done	O
using	O
a	O
brute	O
force	O
search	O
in	O
2L	O
evaluations	O
.	O
</s>
<s>
The	O
second	O
criterion	O
,	O
finding	O
two	O
different	O
messages	O
that	O
produce	O
the	O
same	O
message	B-Algorithm
digest	I-Algorithm
,	O
known	O
as	O
a	O
collision	B-Algorithm
,	O
requires	O
on	O
average	O
only	O
2L/2	O
evaluations	O
using	O
a	O
birthday	O
attack	O
.	O
</s>
<s>
Some	O
of	O
the	O
applications	O
that	O
use	O
cryptographic	B-Algorithm
hashes	I-Algorithm
,	O
such	O
as	O
password	O
storage	O
,	O
are	O
only	O
minimally	O
affected	O
by	O
a	O
collision	B-Algorithm
attack	I-Algorithm
.	O
</s>
<s>
Constructing	O
a	O
password	O
that	O
works	O
for	O
a	O
given	O
account	O
requires	O
a	O
preimage	O
attack	O
,	O
as	O
well	O
as	O
access	O
to	O
the	O
hash	B-Algorithm
of	O
the	O
original	O
password	O
(	O
typically	O
in	O
the	O
shadow	O
file	O
)	O
which	O
may	O
or	O
may	O
not	O
be	O
trivial	O
.	O
</s>
<s>
(	O
However	O
,	O
even	O
a	O
secure	O
password	O
hash	B-Algorithm
cannot	O
prevent	O
brute-force	O
attacks	O
on	O
weak	O
passwords	O
.	O
)	O
</s>
<s>
There	O
are	O
practical	O
circumstances	O
in	O
which	O
this	O
is	O
possible	O
;	O
until	O
the	O
end	O
of	O
2008	O
,	O
it	O
was	O
possible	O
to	O
create	O
forged	O
SSL	B-Protocol
certificates	O
using	O
an	O
MD5	B-Algorithm
collision	B-Algorithm
which	O
would	O
be	O
accepted	O
by	O
widely	O
used	O
web	O
browsers	O
.	O
</s>
<s>
Increased	O
interest	O
in	O
cryptographic	B-Algorithm
hash	I-Algorithm
analysis	O
during	O
the	O
SHA-3	B-Algorithm
competition	I-Algorithm
produced	O
several	O
new	O
attacks	O
on	O
the	O
SHA-2	B-Algorithm
family	O
,	O
the	O
best	O
of	O
which	O
are	O
given	O
in	O
the	O
table	O
below	O
.	O
</s>
<s>
Only	O
the	O
collision	B-Algorithm
attacks	I-Algorithm
are	O
of	O
practical	O
complexity	O
;	O
none	O
of	O
the	O
attacks	O
extend	O
to	O
the	O
full	O
round	O
hash	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
At	O
FSE	O
2012	O
,	O
researchers	O
at	O
Sony	O
gave	O
a	O
presentation	O
suggesting	O
pseudo-collision	O
attacks	O
could	O
be	O
extended	O
to	O
52	O
rounds	O
on	O
SHA-256	B-Algorithm
and	O
57	O
rounds	O
on	O
SHA-512	B-Algorithm
by	O
building	O
upon	O
the	O
biclique	O
pseudo-preimage	O
attack	O
.	O
</s>
<s>
Implementations	O
of	O
all	O
FIPS-approved	O
security	O
functions	O
can	O
be	O
officially	O
validated	O
through	O
the	O
CMVP	B-General_Concept
program	I-General_Concept
,	O
jointly	O
run	O
by	O
the	O
National	O
Institute	O
of	O
Standards	O
and	O
Technology	O
(	O
NIST	O
)	O
and	O
the	O
Communications	O
Security	O
Establishment	O
(	O
CSE	O
)	O
.	O
</s>
<s>
For	O
informal	O
verification	O
,	O
a	O
package	O
to	O
generate	O
a	O
high	O
number	O
of	O
test	O
vectors	O
is	O
made	O
available	O
for	O
download	O
on	O
the	O
NIST	O
site	O
;	O
the	O
resulting	O
verification	O
,	O
however	O
,	O
does	O
not	O
replace	O
the	O
formal	O
CMVP	B-General_Concept
validation	O
,	O
which	O
is	O
required	O
by	O
law	O
for	O
certain	O
applications	O
.	O
</s>
<s>
,	O
there	O
are	O
over	O
1300	O
validated	O
implementations	O
of	O
SHA-256	B-Algorithm
and	O
over	O
900	O
of	O
SHA-512	B-Algorithm
,	O
with	O
only	O
5	O
of	O
them	O
being	O
capable	O
of	O
handling	O
messages	O
with	O
a	O
length	O
in	O
bits	O
not	O
a	O
multiple	O
of	O
eight	O
while	O
supporting	O
both	O
variants	O
.	O
</s>
<s>
Hash	B-Algorithm
values	O
of	O
an	O
empty	O
string	O
(	O
i.e.	O
,	O
a	O
zero-length	O
input	O
text	O
)	O
.	O
</s>
<s>
Even	O
a	O
small	O
change	O
in	O
the	O
message	O
will	O
(	O
with	O
overwhelming	O
probability	O
)	O
result	O
in	O
a	O
different	O
hash	B-Algorithm
,	O
due	O
to	O
the	O
avalanche	O
effect	O
.	O
</s>
<s>
For	O
example	O
,	O
adding	O
a	O
period	O
to	O
the	O
end	O
of	O
the	O
following	O
sentence	O
changes	O
almost	O
half	O
(	O
111	O
out	O
of	O
224	O
)	O
of	O
the	O
bits	O
in	O
the	O
hash	B-Algorithm
,	O
equivalent	O
to	O
picking	O
a	O
new	O
hash	B-Algorithm
at	O
random	O
:	O
</s>
<s>
Pseudocode	B-Language
for	O
the	O
SHA-256	B-Algorithm
algorithm	O
follows	O
.	O
</s>
<s>
Note	O
the	O
great	O
increase	O
in	O
mixing	O
between	O
bits	O
of	O
the	O
16	O
..	O
63	O
words	O
compared	O
to	O
SHA-1	B-Algorithm
.	O
</s>
<s>
The	O
computation	O
of	O
the	O
ch	O
and	O
maj	O
values	O
can	O
be	O
optimized	O
the	O
same	O
way	O
as	O
described	O
for	O
SHA-1	B-Algorithm
.	O
</s>
<s>
SHA-224	B-Algorithm
is	O
identical	O
to	O
SHA-256	B-Algorithm
,	O
except	O
that	O
:	O
</s>
<s>
SHA-512	B-Algorithm
is	O
identical	O
in	O
structure	O
to	O
SHA-256	B-Algorithm
,	O
but	O
:	O
</s>
<s>
the	O
initial	O
hash	B-Algorithm
values	O
and	O
round	O
constants	O
are	O
extended	O
to	O
64	O
bits	O
,	O
</s>
<s>
SHA-384	B-Algorithm
is	O
identical	O
to	O
SHA-512	B-Algorithm
,	O
except	O
that	O
:	O
</s>
<s>
SHA-512/t	B-Algorithm
is	O
identical	O
to	O
SHA-512	B-Algorithm
except	O
that	O
:	O
</s>
<s>
the	O
initial	O
hash	B-Algorithm
values	O
h0	O
through	O
h7	O
are	O
given	O
by	O
the	O
SHA-512/t	B-Algorithm
IV	O
generation	O
function	O
,	O
</s>
<s>
The	O
SHA-512/t	B-Algorithm
IV	O
generation	O
function	O
evaluates	O
a	O
modified	O
SHA-512	B-Algorithm
on	O
the	O
ASCII	O
string	O
"	O
SHA-512/t	B-Algorithm
"	O
,	O
substituted	O
with	O
the	O
decimal	O
representation	O
of	O
t	O
.	O
The	O
modified	O
SHA-512	B-Algorithm
is	O
the	O
same	O
as	O
SHA-512	B-Algorithm
except	O
its	O
initial	O
values	O
h0	O
through	O
h7	O
have	O
each	O
been	O
XORed	O
with	O
the	O
hexadecimal	O
constant	O
0xa5a5a5a5a5a5a5a5	O
.	O
</s>
<s>
Sample	O
C	O
implementation	O
for	O
SHA-2	B-Algorithm
family	O
of	O
hash	B-Algorithm
functions	I-Algorithm
can	O
be	O
found	O
in	O
RFC	O
6234	O
.	O
</s>
<s>
In	O
the	O
table	O
below	O
,	O
internal	O
state''	O
means	O
the	O
"	O
internal	O
hash	B-Algorithm
sum	O
"	O
after	O
each	O
compression	O
of	O
a	O
data	O
block	O
.	O
</s>
<s>
All	O
of	O
these	O
algorithms	O
employ	O
modular	O
addition	O
in	O
some	O
fashion	O
except	O
for	O
SHA-3	B-Algorithm
.	O
</s>
<s>
The	O
performance	O
numbers	O
labeled	O
'	O
x86	B-Operating_System
 '	O
were	O
running	O
using	O
32-bit	O
code	O
on	O
64-bit	O
processors	O
,	O
whereas	O
the	O
'	O
x86-64	B-Device
'	O
numbers	O
are	O
native	O
64-bit	O
code	O
.	O
</s>
<s>
While	O
SHA-256	B-Algorithm
is	O
designed	O
for	O
32-bit	O
calculations	O
,	O
it	O
does	O
benefit	O
from	O
code	O
optimized	O
for	O
64-bit	O
processors	O
on	O
the	O
x86	B-Operating_System
architecture	I-Operating_System
.	O
</s>
<s>
32-bit	O
implementations	O
of	O
SHA-512	B-Algorithm
are	O
significantly	O
slower	O
than	O
their	O
64-bit	O
counterparts	O
.	O
</s>
<s>
Variants	O
of	O
both	O
algorithms	O
with	O
different	O
output	O
sizes	O
will	O
perform	O
similarly	O
,	O
since	O
the	O
message	O
expansion	O
and	O
compression	O
functions	O
are	O
identical	O
,	O
and	O
only	O
the	O
initial	O
hash	B-Algorithm
values	O
and	O
output	O
sizes	O
are	O
different	O
.	O
</s>
<s>
The	O
best	O
implementations	O
of	O
MD5	B-Algorithm
and	O
SHA-1	B-Algorithm
perform	O
between	O
4.5	O
and	O
6	O
cycles	O
per	O
byte	O
on	O
modern	O
processors	O
.	O
</s>
<s>
Below	O
is	O
a	O
list	O
of	O
cryptography	O
libraries	O
that	O
support	O
SHA-2	B-Algorithm
:	O
</s>
<s>
Intel	B-Device
SHA	I-Device
extensions	I-Device
:	O
Available	O
on	O
some	O
Intel	O
and	O
AMD	O
x86	B-Operating_System
processors	O
.	O
</s>
