<s>
SHA-3	B-Algorithm
(	O
Secure	O
Hash	O
Algorithm	O
3	O
)	O
is	O
the	O
latest	O
member	O
of	O
the	O
Secure	O
Hash	O
Algorithm	O
family	O
of	O
standards	O
,	O
released	O
by	O
NIST	O
on	O
August	O
5	O
,	O
2015	O
.	O
</s>
<s>
Although	O
part	O
of	O
the	O
same	O
series	O
of	O
standards	O
,	O
SHA-3	B-Algorithm
is	O
internally	O
different	O
from	O
the	O
MD5-like	O
structure	O
of	O
SHA-1	B-Algorithm
and	O
SHA-2	B-Algorithm
.	O
</s>
<s>
SHA-3	B-Algorithm
is	O
a	O
subset	O
of	O
the	O
broader	O
cryptographic	O
primitive	O
family	O
Keccak	B-Algorithm
(	O
or	O
)	O
,	O
designed	O
by	O
Guido	O
Bertoni	O
,	O
Joan	O
Daemen	O
,	O
Michaël	O
Peeters	O
,	O
and	O
Gilles	O
Van	O
Assche	O
,	O
building	O
upon	O
RadioGatún	B-Algorithm
.	O
</s>
<s>
Keccak	B-Algorithm
's	O
authors	O
have	O
proposed	O
additional	O
uses	O
for	O
the	O
function	O
,	O
not	O
(	O
yet	O
)	O
standardized	O
by	O
NIST	O
,	O
including	O
a	O
stream	B-Algorithm
cipher	I-Algorithm
,	O
an	O
authenticated	B-Algorithm
encryption	I-Algorithm
system	O
,	O
a	O
"	O
tree	O
"	O
hashing	O
scheme	O
for	O
faster	O
hashing	O
on	O
certain	O
architectures	O
,	O
and	O
AEAD	O
ciphers	O
Keyak	O
and	O
Ketje	O
.	O
</s>
<s>
Keccak	B-Algorithm
is	O
based	O
on	O
a	O
novel	O
approach	O
called	O
sponge	B-Algorithm
construction	I-Algorithm
.	O
</s>
<s>
Sponge	B-Algorithm
construction	I-Algorithm
is	O
based	O
on	O
a	O
wide	O
random	O
function	O
or	O
random	O
permutation	O
,	O
and	O
allows	O
inputting	O
(	O
"	O
absorbing	O
"	O
in	O
sponge	O
terminology	O
)	O
any	O
amount	O
of	O
data	O
,	O
and	O
outputting	O
(	O
"	O
squeezing	O
"	O
)	O
any	O
amount	O
of	O
data	O
,	O
while	O
acting	O
as	O
a	O
pseudorandom	O
function	O
with	O
regard	O
to	O
all	O
previous	O
inputs	O
.	O
</s>
<s>
NIST	O
does	O
not	O
currently	O
plan	O
to	O
withdraw	O
SHA-2	B-Algorithm
or	O
remove	O
it	O
from	O
the	O
revised	O
Secure	O
Hash	O
Standard	O
.	O
</s>
<s>
The	O
purpose	O
of	O
SHA-3	B-Algorithm
is	O
that	O
it	O
can	O
be	O
directly	O
substituted	O
for	O
SHA-2	B-Algorithm
in	O
current	O
applications	O
if	O
necessary	O
,	O
and	O
to	O
significantly	O
improve	O
the	O
robustness	O
of	O
NIST	O
's	O
overall	O
hash	O
algorithm	O
toolkit	O
.	O
</s>
<s>
For	O
small	O
message	O
sizes	O
,	O
the	O
creators	O
of	O
the	O
Keccak	B-Algorithm
algorithms	O
and	O
the	O
SHA-3	B-Algorithm
functions	O
suggest	O
using	O
the	O
faster	O
function	O
KangarooTwelve	O
with	O
adjusted	O
parameters	O
and	O
a	O
new	O
tree	B-Algorithm
hashing	I-Algorithm
mode	O
without	O
extra	O
overhead	O
.	O
</s>
<s>
The	O
Keccak	B-Algorithm
algorithm	O
is	O
the	O
work	O
of	O
Guido	O
Bertoni	O
,	O
Joan	O
Daemen	O
(	O
who	O
also	O
co-designed	O
the	O
Rijndael	B-Algorithm
cipher	I-Algorithm
with	O
Vincent	O
Rijmen	O
)	O
,	O
Michaël	O
Peeters	O
,	O
and	O
Gilles	O
Van	O
Assche	O
.	O
</s>
<s>
It	O
is	O
based	O
on	O
earlier	O
hash	O
function	O
designs	O
PANAMA	B-Algorithm
and	O
RadioGatún	B-Algorithm
.	O
</s>
<s>
PANAMA	B-Algorithm
was	O
designed	O
by	O
Daemen	O
and	O
Craig	O
Clapp	O
in	O
1998	O
.	O
</s>
<s>
RadioGatún	B-Algorithm
,	O
a	O
successor	O
of	O
PANAMA	B-Algorithm
,	O
was	O
designed	O
by	O
Daemen	O
,	O
Peeters	O
,	O
and	O
Van	O
Assche	O
,	O
and	O
was	O
presented	O
at	O
the	O
NIST	O
Hash	O
Workshop	O
in	O
2006	O
.	O
</s>
<s>
In	O
2006	O
,	O
NIST	O
started	O
to	O
organize	O
the	O
NIST	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
competition	I-Algorithm
to	O
create	O
a	O
new	O
hash	O
standard	O
,	O
SHA-3	B-Algorithm
.	O
</s>
<s>
SHA-3	B-Algorithm
is	O
not	O
meant	O
to	O
replace	O
SHA-2	B-Algorithm
,	O
as	O
no	O
significant	O
attack	O
on	O
SHA-2	B-Algorithm
has	O
been	O
demonstrated	O
.	O
</s>
<s>
Because	O
of	O
the	O
successful	O
attacks	O
on	O
MD5	B-Algorithm
,	O
SHA-0	B-Algorithm
and	O
SHA-1	B-Algorithm
,	O
</s>
<s>
NIST	O
perceived	O
a	O
need	O
for	O
an	O
alternative	O
,	O
dissimilar	O
cryptographic	O
hash	O
,	O
which	O
became	O
SHA-3	B-Algorithm
.	O
</s>
<s>
Keccak	B-Algorithm
was	O
accepted	O
as	O
one	O
of	O
the	O
51	O
candidates	O
.	O
</s>
<s>
Keccak	B-Algorithm
advanced	O
to	O
the	O
last	O
round	O
in	O
December	O
2010	O
.	O
</s>
<s>
Changes	O
that	O
have	O
been	O
made	O
to	O
Keccak	B-Algorithm
are	O
:	O
</s>
<s>
On	O
October	O
2	O
,	O
2012	O
,	O
Keccak	B-Algorithm
was	O
selected	O
as	O
the	O
winner	O
of	O
the	O
competition	O
.	O
</s>
<s>
In	O
2014	O
,	O
the	O
NIST	O
published	O
a	O
draft	O
FIPS	B-Algorithm
202	I-Algorithm
"	O
SHA-3	B-Algorithm
Standard	O
:	O
Permutation-Based	O
Hash	O
and	O
Extendable-Output	O
Functions	O
"	O
.	O
</s>
<s>
FIPS	B-Algorithm
202	I-Algorithm
was	O
approved	O
on	O
August	O
5	O
,	O
2015	O
.	O
</s>
<s>
On	O
August	O
5	O
,	O
2015	O
,	O
NIST	O
announced	O
that	O
SHA-3	B-Algorithm
had	O
become	O
a	O
hashing	O
standard	O
.	O
</s>
<s>
In	O
early	O
2013	O
NIST	O
announced	O
they	O
would	O
select	O
different	O
values	O
for	O
the	O
"	O
capacity	O
"	O
,	O
the	O
overall	O
strength	O
vs.	O
speed	O
parameter	O
,	O
for	O
the	O
SHA-3	B-Algorithm
standard	O
,	O
compared	O
to	O
the	O
submission	O
.	O
</s>
<s>
The	O
hash	O
function	O
competition	O
called	O
for	O
hash	O
functions	O
at	O
least	O
as	O
secure	O
as	O
the	O
SHA-2	B-Algorithm
instances	O
.	O
</s>
<s>
It	O
means	O
that	O
a	O
d-bit	O
output	O
should	O
have	O
d/2	O
-bit	O
resistance	O
to	O
collision	B-Algorithm
attacks	I-Algorithm
and	O
d-bit	O
resistance	O
to	O
preimage	O
attacks	O
,	O
the	O
maximum	O
achievable	O
for	O
d	O
bits	O
of	O
output	O
.	O
</s>
<s>
Keccak	B-Algorithm
's	O
security	O
proof	O
allows	O
an	O
adjustable	O
level	O
of	O
security	O
based	O
on	O
a	O
"	O
capacity	O
"	O
c	O
,	O
providing	O
c/2	O
-bit	O
resistance	O
to	O
both	O
collision	B-Algorithm
and	O
preimage	O
attacks	O
.	O
</s>
<s>
To	O
meet	O
the	O
original	O
competition	O
rules	O
,	O
Keccak	B-Algorithm
's	O
authors	O
proposed	O
.	O
</s>
<s>
This	O
would	O
have	O
sped	O
up	O
Keccak	B-Algorithm
by	O
allowing	O
an	O
additional	O
d	O
bits	O
of	O
input	O
to	O
be	O
hashed	O
each	O
iteration	O
.	O
</s>
<s>
However	O
,	O
the	O
hash	O
functions	O
would	O
not	O
have	O
been	O
drop-in	O
replacements	O
with	O
the	O
same	O
preimage	O
resistance	O
as	O
SHA-2	B-Algorithm
any	O
more	O
;	O
it	O
would	O
have	O
been	O
cut	O
in	O
half	O
,	O
making	O
it	O
vulnerable	O
to	O
advances	O
in	O
quantum	O
computing	O
,	O
which	O
effectively	O
would	O
cut	O
it	O
in	O
half	O
once	O
more	O
.	O
</s>
<s>
In	O
September	O
2013	O
,	O
Daniel	O
J	O
.	O
Bernstein	O
suggested	O
on	O
the	O
NIST	O
hash-forum	O
mailing	O
list	O
to	O
strengthen	O
the	O
security	O
to	O
the	O
576-bit	O
capacity	O
that	O
was	O
originally	O
proposed	O
as	O
the	O
default	O
Keccak	B-Algorithm
,	O
in	O
addition	O
to	O
and	O
not	O
included	O
in	O
the	O
SHA-3	B-Algorithm
specifications	O
.	O
</s>
<s>
This	O
would	O
have	O
provided	O
at	O
least	O
a	O
SHA3-224	B-Algorithm
and	O
SHA3-256	B-Algorithm
with	O
the	O
same	O
preimage	O
resistance	O
as	O
their	O
SHA-2	B-Algorithm
predecessors	O
,	O
but	O
SHA3-384	B-Algorithm
and	O
SHA3-512	B-Algorithm
would	O
have	O
had	O
significantly	O
less	O
preimage	O
resistance	O
than	O
their	O
SHA-2	B-Algorithm
predecessors	O
.	O
</s>
<s>
In	O
late	O
September	O
,	O
the	O
Keccak	B-Algorithm
team	O
responded	O
by	O
stating	O
that	O
they	O
had	O
proposed	O
128-bit	O
security	O
by	O
setting	O
as	O
an	O
option	O
already	O
in	O
their	O
SHA-3	B-Algorithm
proposal	O
.	O
</s>
<s>
This	O
would	O
be	O
as	O
much	O
as	O
any	O
previous	O
standard	O
up	O
to	O
the	O
256-bit	O
security	O
level	O
,	O
while	O
providing	O
reasonable	O
efficiency	O
,	O
but	O
not	O
the	O
384-/512	O
-bit	O
preimage	O
resistance	O
offered	O
by	O
SHA2-384	O
and	O
SHA2-512	O
.	O
</s>
<s>
Paul	O
Crowley	O
,	O
a	O
cryptographer	O
and	O
senior	O
developer	O
at	O
an	O
independent	O
software	O
development	O
company	O
,	O
expressed	O
his	O
support	O
of	O
the	O
decision	O
,	O
saying	O
that	O
Keccak	B-Algorithm
is	O
supposed	O
to	O
be	O
tunable	O
and	O
there	O
is	O
no	O
reason	O
for	O
different	O
security	O
levels	O
within	O
one	O
primitive	O
.	O
</s>
<s>
There	O
was	O
some	O
confusion	O
that	O
internal	O
changes	O
may	O
have	O
been	O
made	O
to	O
Keccak	B-Algorithm
,	O
which	O
were	O
cleared	O
up	O
by	O
the	O
original	O
team	O
,	O
stating	O
that	O
NIST	O
's	O
proposal	O
for	O
SHA-3	B-Algorithm
is	O
a	O
subset	O
of	O
the	O
Keccak	B-Algorithm
family	O
,	O
for	O
which	O
one	O
can	O
generate	O
test	O
vectors	O
using	O
their	O
reference	O
code	O
submitted	O
to	O
the	O
contest	O
,	O
and	O
that	O
this	O
proposal	O
was	O
the	O
result	O
of	O
a	O
series	O
of	O
discussions	O
between	O
them	O
and	O
the	O
NIST	O
hash	O
team	O
.	O
</s>
<s>
In	O
response	O
to	O
the	O
controversy	O
,	O
in	O
November	O
2013	O
John	O
Kelsey	O
of	O
NIST	O
proposed	O
to	O
go	O
back	O
to	O
the	O
original	O
proposal	O
for	O
all	O
SHA-2	B-Algorithm
drop-in	O
replacement	O
instances	O
.	O
</s>
<s>
SHA-3	B-Algorithm
uses	O
the	O
sponge	B-Algorithm
construction	I-Algorithm
,	O
in	O
which	O
data	O
is	O
"	O
absorbed	O
"	O
into	O
the	O
sponge	O
,	O
then	O
the	O
result	O
is	O
"	O
squeezed	O
"	O
out	O
.	O
</s>
<s>
Given	O
an	O
input	O
bit	O
string	O
,	O
a	O
padding	O
function	O
,	O
a	O
permutation	O
function	O
that	O
operates	O
on	O
bit	O
blocks	O
of	O
width	O
,	O
a	O
rate	O
and	O
an	O
output	O
length	O
,	O
we	O
have	O
capacity	O
and	O
the	O
sponge	B-Algorithm
construction	I-Algorithm
,	O
yielding	O
a	O
bit	O
string	O
of	O
length	O
,	O
works	O
as	O
follows	O
:	O
</s>
<s>
The	O
fact	O
that	O
the	O
internal	O
state	O
S	O
contains	O
c	O
additional	O
bits	O
of	O
information	O
in	O
addition	O
to	O
what	O
is	O
output	O
to	O
Z	O
prevents	O
the	O
length	O
extension	O
attacks	O
that	O
SHA-2	B-Algorithm
,	O
SHA-1	B-Algorithm
,	O
MD5	B-Algorithm
and	O
other	O
hashes	O
based	O
on	O
the	O
Merkle	B-Algorithm
–	I-Algorithm
Damgård	I-Algorithm
construction	I-Algorithm
are	O
susceptible	O
to	O
.	O
</s>
<s>
In	O
SHA-3	B-Algorithm
,	O
the	O
state	O
S	O
consists	O
of	O
a	O
array	O
of	O
w-bit	O
words	O
(	O
with	O
w	O
=	O
64	O
)	O
,	O
b	O
=	O
5	O
×	O
5	O
×	O
w	O
=	O
5	O
×	O
5	O
×	O
64	O
=	O
1600	O
bits	O
total	O
.	O
</s>
<s>
Keccak	B-Algorithm
is	O
also	O
defined	O
for	O
smaller	O
power-of-2	O
word	O
sizes	O
w	O
down	O
to	O
1	O
bit	O
(	O
total	O
state	O
of	O
25	O
bits	O
)	O
.	O
</s>
<s>
For	O
SHA3-224	B-Algorithm
,	O
SHA3-256	B-Algorithm
,	O
SHA3-384	B-Algorithm
,	O
and	O
SHA3-512	B-Algorithm
instances	O
,	O
r	O
is	O
greater	O
than	O
d	O
,	O
so	O
there	O
is	O
no	O
need	O
for	O
additional	O
block	O
permutations	O
in	O
the	O
squeezing	O
phase	O
;	O
the	O
leading	O
d	O
bits	O
of	O
the	O
state	O
are	O
the	O
desired	O
hash	O
.	O
</s>
<s>
However	O
,	O
SHAKE128	B-Algorithm
and	O
SHAKE256	B-Algorithm
allow	O
an	O
arbitrary	O
output	O
length	O
,	O
which	O
is	O
useful	O
in	O
applications	O
such	O
as	O
optimal	B-Algorithm
asymmetric	I-Algorithm
encryption	I-Algorithm
padding	I-Algorithm
.	O
</s>
<s>
SHA-3	B-Algorithm
uses	O
the	O
pattern	O
10*1	O
in	O
its	O
padding	O
function	O
:	O
a	O
1	O
bit	O
,	O
followed	O
by	O
zero	O
or	O
more	O
0	O
bits	O
(	O
maximum	O
)	O
and	O
a	O
final	O
1	O
bit	O
.	O
</s>
<s>
The	O
block	O
transformation	O
f	O
,	O
which	O
is	O
Keccak-f[1600]	O
for	O
SHA-3	B-Algorithm
,	O
is	O
a	O
permutation	O
that	O
uses	O
XOR	O
,	O
AND	O
and	O
NOT	O
operations	O
,	O
and	O
is	O
designed	O
for	O
easy	O
implementation	O
in	O
both	O
software	O
and	O
hardware	O
.	O
</s>
<s>
The	O
main	O
SHA-3	B-Algorithm
submission	O
uses	O
64-bit	O
words	O
,	O
.	O
</s>
<s>
Let	O
be	O
bit	O
of	O
the	O
input	O
,	O
using	O
a	O
little-endian	O
bit	O
numbering	O
convention	O
and	O
row-major	B-Data_Structure
indexing	O
.	O
</s>
<s>
Bitwise	B-Algorithm
rotate	I-Algorithm
each	O
of	O
the	O
25	O
words	O
by	O
a	O
different	O
triangular	O
number	O
0	O
,	O
1	O
,	O
3	O
,	O
6	O
,	O
10	O
,	O
15	O
,	O
....	O
To	O
be	O
precise	O
,	O
a[0][0]	O
is	O
not	O
rotated	O
,	O
and	O
for	O
all	O
,	O
,	O
where	O
.	O
</s>
<s>
This	O
is	O
the	O
only	O
non-linear	O
operation	O
in	O
SHA-3	B-Algorithm
.	O
</s>
<s>
To	O
be	O
precise	O
,	O
in	O
round	O
,	O
for	O
,	O
is	O
XORed	O
with	O
bit	O
of	O
a	O
degree-8	O
LFSR	B-Architecture
sequence	O
.	O
</s>
<s>
The	O
speed	O
of	O
SHA-3	B-Algorithm
hashing	O
of	O
long	O
messages	O
is	O
dominated	O
by	O
the	O
computation	O
of	O
f	O
=	O
Keccak-f[1600]	O
and	O
XORing	O
S	O
with	O
the	O
extended	O
Pi	O
,	O
an	O
operation	O
on	O
b	O
=	O
1600	O
bits	O
.	O
</s>
<s>
However	O
,	O
since	O
the	O
last	O
c	O
bits	O
of	O
the	O
extended	O
Pi	O
are	O
0	O
anyway	O
,	O
and	O
XOR	O
with	O
0	O
is	O
a	O
NOP	O
,	O
it	O
is	O
sufficient	O
to	O
perform	O
XOR	O
operations	O
only	O
for	O
r	O
bits	O
(	O
r	O
=	O
1600	O
−	O
2	O
×	O
224	O
=	O
1152	O
bits	O
for	O
SHA3-224	B-Algorithm
,	O
1088	O
bits	O
for	O
SHA3-256	B-Algorithm
,	O
832	O
bits	O
for	O
SHA3-384	B-Algorithm
and	O
576	O
bits	O
for	O
SHA3-512	B-Algorithm
)	O
.	O
</s>
<s>
The	O
authors	O
report	O
the	O
following	O
speeds	O
for	O
software	O
implementations	O
of	O
Keccak-f[1600]	O
plus	O
XORing	O
1024	O
bits	O
,	O
which	O
roughly	O
corresponds	O
to	O
SHA3-256	B-Algorithm
:	O
</s>
<s>
For	O
the	O
exact	O
SHA3-256	B-Algorithm
on	O
x86-64	O
,	O
Bernstein	O
measures	O
11.7	O
–	O
12.25	O
cpb	O
depending	O
on	O
the	O
CPU	O
.	O
</s>
<s>
SHA-3	B-Algorithm
has	O
been	O
criticized	O
for	O
being	O
slow	O
on	O
instruction	O
set	O
architectures	O
(	O
CPUs	O
)	O
which	O
do	O
not	O
have	O
instructions	O
meant	O
specially	O
for	O
computing	O
Keccak	B-Algorithm
functions	O
faster	O
–	O
SHA2-512	O
is	O
more	O
than	O
twice	O
as	O
fast	O
as	O
SHA3-512	B-Algorithm
,	O
and	O
SHA-1	B-Algorithm
is	O
more	O
than	O
three	O
times	O
as	O
fast	O
on	O
an	O
Intel	B-Architecture
Skylake	I-Architecture
processor	O
clocked	O
at	O
3.2GHz	O
.	O
</s>
<s>
The	O
authors	O
have	O
reacted	O
to	O
this	O
criticism	O
by	O
suggesting	O
to	O
use	O
SHAKE128	B-Algorithm
and	O
SHAKE256	B-Algorithm
instead	O
of	O
SHA3-256	B-Algorithm
and	O
SHA3-512	B-Algorithm
,	O
at	O
the	O
expense	O
of	O
cutting	O
the	O
preimage	O
resistance	O
in	O
half	O
(	O
but	O
while	O
keeping	O
the	O
collision	B-Algorithm
resistance	O
)	O
.	O
</s>
<s>
With	O
this	O
,	O
performance	O
is	O
on	O
par	O
with	O
SHA2-256	O
and	O
SHA2-512	O
.	O
</s>
<s>
However	O
,	O
in	O
hardware	O
implementations	O
,	O
SHA-3	B-Algorithm
is	O
notably	O
faster	O
than	O
all	O
other	O
finalists	O
,	O
and	O
also	O
faster	O
than	O
SHA-2	B-Algorithm
and	O
SHA-1	B-Algorithm
.	O
</s>
<s>
As	O
of	O
2018	O
,	O
ARM	O
's	O
ARMv8	O
and	O
IBM	O
's	O
s390x	O
architectures	O
include	O
special	O
instructions	O
which	O
enable	O
Keccak	B-Algorithm
algorithms	O
to	O
execute	O
faster	O
.	O
</s>
<s>
SHA-3	B-Algorithm
instances	O
are	O
drop-in	O
replacements	O
for	O
SHA-2	B-Algorithm
,	O
intended	O
to	O
have	O
identical	O
security	O
properties	O
.	O
</s>
<s>
For	O
example	O
,	O
SHAKE128(M, 256 )	O
can	O
be	O
used	O
as	O
a	O
hash	O
function	O
with	O
a	O
256	O
character	O
bitstream	O
with	O
128-bit	O
security	O
strength	O
.	O
</s>
<s>
Alternately	O
,	O
SHAKE256(M, 128 )	O
can	O
be	O
used	O
as	O
a	O
hash	O
function	O
with	O
a	O
128-bit	O
length	O
and	O
128-bit	O
resistance	O
.	O
</s>
<s>
The	O
purpose	O
of	O
this	O
is	O
to	O
ensure	O
that	O
it	O
is	O
not	O
possible	O
to	O
construct	O
messages	O
that	O
produce	O
the	O
same	O
hash	O
output	O
for	O
different	O
applications	O
of	O
the	O
Keccak	B-Algorithm
hash	O
function	O
.	O
</s>
<s>
In	O
December	O
2016	O
NIST	O
published	O
a	O
new	O
document	O
,	O
NIST	O
SP.800-185	O
,	O
describing	O
additional	O
SHA-3	B-Algorithm
derived	O
functions	O
:	O
</s>
<s>
cSHAKE256(X, L, N, S )	O
KMAC128(K, X, L, S )	O
A	O
keyed	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
based	O
on	O
Keccak	B-Algorithm
.	O
</s>
<s>
KMAC256(K, X, L, S )	O
KMACXOF128(K, X, L, S )	O
KMACXOF256(K, X, L, S )	O
TupleHash128(X, L, S )	O
A	O
function	O
for	O
hashing	O
tuples	B-Application
of	O
strings	O
.	O
</s>
<s>
Unlike	O
KangarooTwelve	O
,	O
does	O
not	O
use	O
reduced-round	O
Keccak	B-Algorithm
.	O
</s>
<s>
In	O
2016	O
the	O
same	O
team	O
that	O
made	O
the	O
SHA-3	B-Algorithm
functions	O
and	O
the	O
Keccak	B-Algorithm
algorithm	O
introduced	O
faster	O
reduced-rounds	O
(	O
reduced	O
to	O
12	O
and	O
14	O
rounds	O
,	O
from	O
the	O
24	O
in	O
SHA-3	B-Algorithm
)	O
alternatives	O
which	O
can	O
exploit	O
the	O
availability	O
of	O
parallel	O
execution	O
because	O
of	O
using	O
tree	B-Algorithm
hashing	I-Algorithm
:	O
KangarooTwelve	O
and	O
MarsupilamiFourteen	O
.	O
</s>
<s>
These	O
functions	O
differ	O
from	O
ParallelHash	O
,	O
the	O
FIPS	O
standardized	O
Keccak-based	O
parallelizable	O
hash	O
function	O
,	O
with	O
regard	O
to	O
the	O
parallelism	O
,	O
in	O
that	O
they	O
are	O
faster	O
than	O
ParallelHash	O
for	O
small	O
message	O
sizes	O
.	O
</s>
<s>
The	O
reduced	O
number	O
of	O
rounds	O
is	O
justified	O
by	O
the	O
huge	O
cryptanalytic	O
effort	O
focused	O
on	O
Keccak	B-Algorithm
which	O
did	O
not	O
produce	O
practical	O
attacks	O
on	O
anything	O
close	O
to	O
twelve-round	O
Keccak	B-Algorithm
.	O
</s>
<s>
These	O
higher-speed	O
algorithms	O
are	O
not	O
part	O
of	O
SHA-3	B-Algorithm
(	O
as	O
they	O
are	O
a	O
later	O
development	O
)	O
,	O
and	O
thus	O
are	O
not	O
FIPS	O
compliant	O
;	O
but	O
because	O
they	O
use	O
the	O
same	O
Keccak	B-Algorithm
permutation	O
they	O
are	O
secure	O
for	O
as	O
long	O
as	O
there	O
are	O
no	O
attacks	O
on	O
SHA-3	B-Algorithm
reduced	O
to	O
12	O
rounds	O
.	O
</s>
<s>
KangarooTwelve	O
is	O
a	O
higher-performance	O
reduced-round	O
(	O
from	O
24	O
to	O
12	O
rounds	O
)	O
version	O
of	O
Keccak	B-Algorithm
which	O
claims	O
to	O
have	O
128	O
bits	O
of	O
security	O
while	O
having	O
performance	O
as	O
high	O
as	O
0.55	O
cycles	O
per	O
byte	O
on	O
a	O
Skylake	B-Architecture
CPU	O
.	O
</s>
<s>
MarsupilamiFourteen	O
,	O
a	O
slight	O
variation	O
on	O
KangarooTwelve	O
,	O
uses	O
14	O
rounds	O
of	O
the	O
Keccak	B-Algorithm
permutation	O
and	O
claims	O
256	O
bits	O
of	O
security	O
.	O
</s>
<s>
Such	O
property	O
is	O
not	O
exhibited	O
by	O
hash	O
functions	O
such	O
as	O
SHA-3	B-Algorithm
or	O
ParallelHash	O
(	O
except	O
of	O
XOF	O
variants	O
)	O
.	O
</s>
<s>
RawSHAKE	O
is	O
the	O
basis	O
for	O
the	O
Sakura	O
coding	O
for	O
tree	B-Algorithm
hashing	I-Algorithm
,	O
which	O
has	O
not	O
been	O
standardized	O
yet	O
.	O
</s>
<s>
There	O
is	O
a	O
general	O
result	O
(	O
Grover	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
)	O
that	O
quantum	O
computers	O
can	O
perform	O
a	O
structured	O
preimage	O
attack	O
in	O
,	O
while	O
a	O
classical	O
brute-force	O
attack	O
needs	O
2d	O
.	O
</s>
<s>
A	O
structured	O
preimage	O
attack	O
implies	O
a	O
second	O
preimage	O
attack	O
and	O
thus	O
a	O
collision	B-Algorithm
attack	I-Algorithm
.	O
</s>
<s>
A	O
quantum	O
computer	O
can	O
also	O
perform	O
a	O
birthday	O
attack	O
,	O
thus	O
break	O
collision	B-Algorithm
resistance	O
,	O
in	O
(	O
although	O
that	O
is	O
disputed	O
)	O
.	O
</s>
<s>
Noting	O
that	O
the	O
maximum	O
strength	O
can	O
be	O
,	O
this	O
gives	O
the	O
following	O
upper	O
bounds	O
on	O
the	O
quantum	O
security	O
of	O
SHA-3	B-Algorithm
:	O
</s>
<s>
Instance	O
Security	O
strengths	O
in	O
bits	O
Collision( Brassard	O
et	O
al	O
.	O
)	O
</s>
<s>
It	O
has	O
been	O
shown	O
that	O
the	O
Merkle	B-Algorithm
–	I-Algorithm
Damgård	I-Algorithm
construction	I-Algorithm
,	O
as	O
used	O
by	O
SHA-2	B-Algorithm
,	O
is	O
collapsing	O
and	O
,	O
by	O
consequence	O
,	O
quantum	O
collision-resistant	O
,	O
but	O
for	O
the	O
sponge	B-Algorithm
construction	I-Algorithm
used	O
by	O
SHA-3	B-Algorithm
,	O
the	O
authors	O
provide	O
proofs	O
only	O
for	O
the	O
case	O
when	O
the	O
block	O
function	O
f	O
is	O
not	O
efficiently	O
invertible	O
;	O
Keccak-f[1600],	O
however	O
,	O
is	O
efficiently	O
invertible	O
,	O
and	O
so	O
their	O
proof	O
does	O
not	O
apply	O
.	O
</s>
<s>
Optimized	O
implementation	O
using	O
AVX-512VL	B-General_Concept
(	O
i.e.	O
</s>
<s>
from	O
OpenSSL	B-Language
,	O
running	O
on	O
Skylake-X	B-Architecture
CPUs	O
)	O
of	O
SHA3-256	B-Algorithm
do	O
achieve	O
about	O
6.4	O
cycles	O
per	O
byte	O
for	O
large	O
messages	O
,	O
and	O
about	O
7.8	O
cycles	O
per	O
byte	O
when	O
using	O
AVX2	O
on	O
Skylake	B-Architecture
CPUs	O
.	O
</s>
<s>
Below	O
is	O
a	O
list	O
of	O
cryptography	O
libraries	O
that	O
support	O
SHA-3	B-Algorithm
:	O
</s>
<s>
Apple	B-Device
A13	I-Device
ARMv8	O
six-core	O
SoC	B-Architecture
CPU	O
cores	O
have	O
support	O
for	O
accelerating	O
SHA-3	B-Algorithm
(	O
and	O
SHA-512	B-Algorithm
)	O
using	O
specialized	O
instructions	O
(	O
EOR3	O
,	O
RAX1	O
,	O
XAR	O
,	O
BCAX	O
)	O
from	O
ARMv8.2-SHA	O
crypto	O
extension	O
set	O
.	O
</s>
<s>
Some	O
software	O
libraries	O
use	O
vectorization	B-Device
facilities	O
of	O
CPUs	O
to	O
accelerate	O
usage	O
of	O
SHA-3	B-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
Crypto++	B-Language
can	O
use	O
SSE2	B-General_Concept
on	O
x86	O
for	O
accelerating	O
SHA3	B-Algorithm
,	O
and	O
OpenSSL	B-Language
can	O
use	O
MMX	B-Architecture
,	O
AVX-512	B-General_Concept
or	O
AVX-512VL	B-General_Concept
on	O
many	O
x86	O
systems	O
too	O
.	O
</s>
<s>
Also	O
POWER8	B-Device
CPUs	O
implement	O
2x64-bit	O
vector	O
rotate	O
,	O
defined	O
in	O
PowerISA	O
2.07	O
,	O
which	O
can	O
accelerate	O
SHA-3	B-Algorithm
implementations	O
somehow	O
.	O
</s>
<s>
Most	O
implementations	O
for	O
ARM	O
do	O
not	O
use	O
Neon	O
vector	O
instructions	O
as	O
scalar	B-Operating_System
code	I-Operating_System
is	O
faster	O
.	O
</s>
<s>
ARM	O
implementations	O
can	O
however	O
be	O
accelerated	O
using	O
SVE	O
and	O
SVE2	O
vector	O
instructions	O
;	O
these	O
are	O
available	O
in	O
the	O
Fujitsu	B-Device
A64FX	I-Device
CPU	O
for	O
instance	O
.	O
</s>
<s>
The	O
IBM	B-Device
z/Architecture	I-Device
supports	O
SHA-3	B-Algorithm
since	O
2017	O
as	O
part	O
of	O
the	O
Message-Security-Assist	O
Extension	O
6	O
.	O
</s>
<s>
The	O
processors	O
support	O
a	O
complete	O
implementation	O
of	O
the	O
entire	O
SHA-3	B-Algorithm
and	O
SHAKE	O
algorithms	O
via	O
the	O
KIMD	O
and	O
KLMD	O
instructions	O
using	O
a	O
hardware	O
assist	O
engine	O
built	O
into	O
each	O
core	O
.	O
</s>
