<s>
Threefish	B-Algorithm
is	O
a	O
symmetric-key	B-Algorithm
tweakable	O
block	O
cipher	O
designed	O
as	O
part	O
of	O
the	O
Skein	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
,	O
an	O
entry	O
in	O
the	O
NIST	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
competition	I-Algorithm
.	O
</s>
<s>
Threefish	B-Algorithm
uses	O
no	O
S-boxes	B-Algorithm
or	O
other	O
table	O
lookups	O
in	O
order	O
to	O
avoid	O
cache	O
timing	O
attacks	O
;	O
its	O
nonlinearity	O
comes	O
from	O
alternating	O
additions	O
with	O
exclusive	O
ORs	O
.	O
</s>
<s>
In	O
that	O
respect	O
,	O
it	O
is	O
similar	O
to	O
Salsa20	B-Algorithm
,	O
TEA	B-Algorithm
,	O
and	O
the	O
SHA-3	O
candidates	O
CubeHash	B-Algorithm
and	O
BLAKE	B-Algorithm
.	O
</s>
<s>
Threefish	B-Algorithm
and	O
the	O
Skein	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
were	O
designed	O
by	O
Bruce	O
Schneier	O
,	O
Niels	O
Ferguson	O
,	O
Stefan	O
Lucks	O
,	O
Doug	O
Whiting	O
,	O
Mihir	O
Bellare	O
,	O
Tadayoshi	O
Kohno	O
,	O
Jon	O
Callas	O
,	O
and	O
Jesse	O
Walker	O
.	O
</s>
<s>
Threefish	B-Algorithm
works	O
on	O
words	O
of	O
64	O
bits	O
(	O
unsigned	O
Little	O
endian	O
integers	O
)	O
.	O
</s>
<s>
Threefish	B-Algorithm
encrypts	O
in	O
rounds	O
and	O
uses	O
different	O
round	B-Algorithm
keys	I-Algorithm
.	O
</s>
<s>
After	O
every	O
four	O
rounds	O
,	O
and	O
before	O
the	O
first	O
,	O
round	B-Algorithm
key	I-Algorithm
words	O
are	O
added	O
to	O
the	O
data	O
words	O
.	O
</s>
<s>
To	O
calculate	O
the	O
round	B-Algorithm
keys	I-Algorithm
an	O
additional	O
key	O
word	O
is	O
appended	O
to	O
the	O
original	O
key	O
words	O
.	O
</s>
<s>
The	O
round	B-Algorithm
key	I-Algorithm
words	O
are	O
now	O
defined	O
like	O
this	O
:	O
</s>
<s>
Here	O
,	O
where	O
is	O
the	O
number	O
of	O
the	O
round	O
in	O
which	O
the	O
round	B-Algorithm
key	I-Algorithm
word	O
is	O
used	O
.	O
</s>
<s>
The	O
mix	O
function	O
takes	O
a	O
tuple	B-Application
of	O
words	O
and	O
returns	O
another	O
tuple	B-Application
of	O
words	O
.	O
</s>
<s>
After	O
all	O
rounds	O
are	O
applied	O
,	O
the	O
last	O
round	B-Algorithm
key	I-Algorithm
words	O
are	O
added	O
to	O
the	O
words	O
and	O
the	O
words	O
are	O
converted	O
back	O
to	O
a	O
string	O
of	O
bytes	O
.	O
</s>
<s>
In	O
October	O
2010	O
,	O
an	O
attack	O
that	O
combines	O
rotational	B-General_Concept
cryptanalysis	I-General_Concept
with	O
the	O
rebound	O
attack	O
was	O
published	O
.	O
</s>
<s>
The	O
attack	O
mounts	O
a	O
known-key	B-General_Concept
distinguisher	I-General_Concept
against	O
53	O
of	O
72	O
rounds	O
in	O
Threefish-256	O
,	O
and	O
57	O
of	O
72	O
rounds	O
in	O
Threefish-512	O
.	O
</s>
<s>
It	O
also	O
affects	O
the	O
Skein	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
In	O
response	O
to	O
this	O
attack	O
,	O
the	O
Skein	B-Algorithm
team	O
tweaked	O
the	O
rotation	O
constants	O
used	O
in	O
Threefish	B-Algorithm
and	O
thereby	O
the	O
key	B-Algorithm
schedule	I-Algorithm
constants	O
for	O
round	O
3	O
of	O
the	O
NIST	B-Algorithm
hash	I-Algorithm
function	I-Algorithm
competition	I-Algorithm
.	O
</s>
<s>
In	O
2009	O
,	O
a	O
related	O
key	O
boomerang	O
attack	O
against	O
a	O
reduced	O
round	O
Threefish	B-Algorithm
version	O
was	O
published	O
.	O
</s>
<s>
The	O
attacks	O
also	O
work	O
against	O
the	O
tweaked	O
version	O
of	O
Threefish	B-Algorithm
:	O
for	O
the	O
32-round	O
version	O
,	O
the	O
time	O
complexity	O
is	O
and	O
the	O
memory	O
complexity	O
is	O
;	O
for	O
the	O
33-round	O
version	O
,	O
the	O
time	O
complexity	O
is	O
with	O
a	O
negligible	O
memory	O
usage	O
.	O
</s>
