<s>
In	O
cryptography	O
,	O
a	O
Feistel	B-Algorithm
cipher	I-Algorithm
(	O
also	O
known	O
as	O
Luby	B-Algorithm
–	I-Algorithm
Rackoff	I-Algorithm
block	I-Algorithm
cipher	I-Algorithm
)	O
is	O
a	O
symmetric	O
structure	O
used	O
in	O
the	O
construction	O
of	O
block	O
ciphers	O
,	O
named	O
after	O
the	O
German-born	O
physicist	O
and	O
cryptographer	O
Horst	O
Feistel	O
,	O
who	O
did	O
pioneering	O
research	O
while	O
working	O
for	O
IBM	O
;	O
it	O
is	O
also	O
commonly	O
known	O
as	O
a	O
Feistel	B-Algorithm
network	I-Algorithm
.	O
</s>
<s>
A	O
large	O
proportion	O
of	O
block	O
ciphers	O
use	O
the	O
scheme	O
,	O
including	O
the	O
US	O
Data	B-Algorithm
Encryption	I-Algorithm
Standard	I-Algorithm
,	O
the	O
Soviet/Russian	O
GOST	B-Algorithm
and	O
the	O
more	O
recent	O
Blowfish	B-Algorithm
and	O
Twofish	B-Algorithm
ciphers	O
.	O
</s>
<s>
In	O
a	O
Feistel	B-Algorithm
cipher	I-Algorithm
,	O
encryption	O
and	O
decryption	O
are	O
very	O
similar	O
operations	O
,	O
and	O
both	O
consist	O
of	O
iteratively	O
running	O
a	O
function	O
called	O
a	O
"	O
round	O
function	O
"	O
a	O
fixed	O
number	O
of	O
times	O
.	O
</s>
<s>
Many	O
modern	O
symmetric	O
block	O
ciphers	O
are	O
based	O
on	O
Feistel	B-Algorithm
networks	I-Algorithm
.	O
</s>
<s>
Feistel	B-Algorithm
networks	I-Algorithm
were	O
first	O
seen	O
commercially	O
in	O
IBM	O
's	O
Lucifer	B-Algorithm
cipher	I-Algorithm
,	O
designed	O
by	O
Horst	O
Feistel	O
and	O
Don	O
Coppersmith	O
in	O
1973	O
.	O
</s>
<s>
Feistel	B-Algorithm
networks	I-Algorithm
gained	O
respectability	O
when	O
the	O
U.S.	O
Federal	O
Government	O
adopted	O
the	O
DES	B-Algorithm
(	O
a	O
cipher	O
based	O
on	O
Lucifer	B-Algorithm
,	O
with	O
changes	O
made	O
by	O
the	O
NSA	O
)	O
in	O
1976	O
.	O
</s>
<s>
Like	O
other	O
components	O
of	O
the	O
DES	B-Algorithm
,	O
the	O
iterative	O
nature	O
of	O
the	O
Feistel	O
construction	O
makes	O
implementing	O
the	O
cryptosystem	O
in	O
hardware	O
easier	O
(	O
particularly	O
on	O
the	O
hardware	O
available	O
at	O
the	O
time	O
of	O
DES	B-Algorithm
's	O
design	O
)	O
.	O
</s>
<s>
A	O
Feistel	B-Algorithm
network	I-Algorithm
uses	O
a	O
round	O
function	O
,	O
a	O
function	O
which	O
takes	O
two	O
inputs	O
a	O
data	O
block	O
and	O
a	O
subkey	O
and	O
returns	O
one	O
output	O
of	O
the	O
same	O
size	O
as	O
the	O
data	O
block	O
.	O
</s>
<s>
An	O
important	O
advantage	O
of	O
Feistel	B-Algorithm
networks	I-Algorithm
compared	O
to	O
other	O
cipher	O
designs	O
such	O
as	O
substitution	B-Algorithm
–	I-Algorithm
permutation	I-Algorithm
networks	I-Algorithm
is	O
that	O
the	O
entire	O
operation	O
is	O
guaranteed	O
to	O
be	O
invertible	O
(	O
that	O
is	O
,	O
encrypted	O
data	O
can	O
be	O
decrypted	O
)	O
,	O
even	O
if	O
the	O
round	O
function	O
is	O
not	O
itself	O
invertible	O
.	O
</s>
<s>
Furthermore	O
,	O
the	O
encryption	O
and	O
decryption	O
operations	O
are	O
very	O
similar	O
,	O
even	O
identical	O
in	O
some	O
cases	O
,	O
requiring	O
only	O
a	O
reversal	O
of	O
the	O
key	B-Algorithm
schedule	I-Algorithm
.	O
</s>
<s>
The	O
structure	O
and	O
properties	O
of	O
Feistel	B-Algorithm
ciphers	I-Algorithm
have	O
been	O
extensively	O
analyzed	O
by	O
cryptographers	O
.	O
</s>
<s>
Michael	O
Luby	O
and	O
Charles	O
Rackoff	O
analyzed	O
the	O
Feistel	B-Algorithm
cipher	I-Algorithm
construction	O
and	O
proved	O
that	O
if	O
the	O
round	O
function	O
is	O
a	O
cryptographically	O
secure	O
pseudorandom	O
function	O
,	O
with	O
Ki	O
used	O
as	O
the	O
seed	O
,	O
then	O
3	O
rounds	O
are	O
sufficient	O
to	O
make	O
the	O
block	O
cipher	O
a	O
pseudorandom	O
permutation	B-Algorithm
,	O
while	O
4	O
rounds	O
are	O
sufficient	O
to	O
make	O
it	O
a	O
"	O
strong	O
"	O
pseudorandom	O
permutation	B-Algorithm
(	O
which	O
means	O
that	O
it	O
remains	O
pseudorandom	O
even	O
to	O
an	O
adversary	O
who	O
gets	O
oracle	O
access	O
to	O
its	O
inverse	O
permutation	B-Algorithm
)	O
.	O
</s>
<s>
Because	O
of	O
this	O
very	O
important	O
result	O
of	O
Luby	O
and	O
Rackoff	O
,	O
Feistel	B-Algorithm
ciphers	I-Algorithm
are	O
sometimes	O
called	O
Luby	B-Algorithm
–	I-Algorithm
Rackoff	I-Algorithm
block	I-Algorithm
ciphers	I-Algorithm
.	O
</s>
<s>
where	O
means	O
XOR	B-Application
.	O
</s>
<s>
Unbalanced	B-Algorithm
Feistel	I-Algorithm
ciphers	I-Algorithm
use	O
a	O
modified	O
structure	O
where	O
and	O
are	O
not	O
of	O
equal	O
lengths	O
.	O
</s>
<s>
The	O
Skipjack	B-Algorithm
cipher	O
is	O
an	O
example	O
of	O
such	O
a	O
cipher	O
.	O
</s>
<s>
The	O
Texas	O
Instruments	O
digital	B-Device
signature	I-Device
transponder	I-Device
uses	O
a	O
proprietary	O
unbalanced	B-Algorithm
Feistel	I-Algorithm
cipher	I-Algorithm
to	O
perform	O
challenge	O
–	O
response	O
authentication	O
.	O
</s>
<s>
The	O
Thorp	O
shuffle	O
is	O
an	O
extreme	O
case	O
of	O
an	O
unbalanced	B-Algorithm
Feistel	I-Algorithm
cipher	I-Algorithm
in	O
which	O
one	O
side	O
is	O
a	O
single	O
bit	O
.	O
</s>
<s>
This	O
has	O
better	O
provable	O
security	O
than	O
a	O
balanced	B-Algorithm
Feistel	I-Algorithm
cipher	I-Algorithm
but	O
requires	O
more	O
rounds	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
optimal	B-Algorithm
asymmetric	I-Algorithm
encryption	I-Algorithm
padding	I-Algorithm
(	O
OAEP	B-Algorithm
)	O
scheme	O
uses	O
a	O
simple	O
Feistel	B-Algorithm
network	I-Algorithm
to	O
randomize	O
ciphertexts	O
in	O
certain	O
asymmetric-key	B-Application
encryption	I-Application
schemes	O
.	O
</s>
<s>
A	O
generalized	O
Feistel	O
algorithm	O
can	O
be	O
used	O
to	O
create	O
strong	O
permutations	B-Algorithm
on	O
small	O
domains	O
of	O
size	O
not	O
a	O
power	O
of	O
two	O
(	O
see	O
format-preserving	B-Algorithm
encryption	I-Algorithm
)	O
.	O
</s>
<s>
Whether	O
the	O
entire	O
cipher	O
is	O
a	O
Feistel	B-Algorithm
cipher	I-Algorithm
or	O
not	O
,	O
Feistel-like	O
networks	O
can	O
be	O
used	O
as	O
a	O
component	O
of	O
a	O
cipher	O
's	O
design	O
.	O
</s>
<s>
For	O
example	O
,	O
MISTY1	B-Algorithm
is	O
a	O
Feistel	B-Algorithm
cipher	I-Algorithm
using	O
a	O
three-round	O
Feistel	B-Algorithm
network	I-Algorithm
in	O
its	O
round	O
function	O
,	O
Skipjack	B-Algorithm
is	O
a	O
modified	O
Feistel	B-Algorithm
cipher	I-Algorithm
using	O
a	O
Feistel	B-Algorithm
network	I-Algorithm
in	O
its	O
G	O
permutation	B-Algorithm
,	O
and	O
Threefish	B-Algorithm
(	O
part	O
of	O
Skein	B-Algorithm
)	O
is	O
a	O
non-Feistel	O
block	O
cipher	O
that	O
uses	O
a	O
Feistel-like	O
MIX	O
function	O
.	O
</s>
