<s>
In	O
cryptography	O
,	O
FEAL	B-Algorithm
(	O
the	O
Fast	O
data	O
Encipherment	O
Algorithm	O
)	O
is	O
a	O
block	O
cipher	O
proposed	O
as	O
an	O
alternative	O
to	O
the	O
Data	B-Algorithm
Encryption	I-Algorithm
Standard	I-Algorithm
(	O
DES	B-Algorithm
)	O
,	O
and	O
designed	O
to	O
be	O
much	O
faster	O
in	O
software	O
.	O
</s>
<s>
The	O
Feistel	B-Algorithm
based	O
algorithm	O
was	O
first	O
published	O
in	O
1987	O
by	O
Akihiro	O
Shimizu	O
and	O
Shoji	O
Miyaguchi	O
from	O
NTT	O
.	O
</s>
<s>
There	O
have	O
been	O
several	O
different	O
revisions	O
of	O
FEAL	B-Algorithm
,	O
though	O
all	O
are	O
Feistel	B-Algorithm
ciphers	I-Algorithm
,	O
and	O
make	O
use	O
of	O
the	O
same	O
basic	O
round	O
function	O
and	O
operate	O
on	O
a	O
64-bit	O
block	O
.	O
</s>
<s>
One	O
of	O
the	O
earliest	O
designs	O
is	O
now	O
termed	O
FEAL-4	O
,	O
which	O
has	O
four	O
rounds	O
and	O
a	O
64-bit	O
key	O
.	O
</s>
<s>
Problems	O
were	O
found	O
with	O
FEAL-4	O
from	O
the	O
start	O
:	O
Bert	O
den	O
Boer	O
related	O
a	O
weakness	O
in	O
an	O
unpublished	O
rump	O
session	O
at	O
the	O
same	O
conference	O
where	O
the	O
cipher	O
was	O
first	O
presented	O
.	O
</s>
<s>
The	O
designers	O
countered	O
by	O
doubling	O
the	O
number	O
of	O
rounds	O
,	O
FEAL-8	O
(	O
Shimizu	O
and	O
Miyaguchi	O
,	O
1988	O
)	O
.	O
</s>
<s>
In	O
response	O
,	O
the	O
designers	O
introduced	O
a	O
variable-round	O
cipher	O
,	O
FEAL-N	O
(	O
Miyaguchi	O
,	O
1990	O
)	O
,	O
where	O
"	O
N	O
"	O
was	O
chosen	O
by	O
the	O
user	O
,	O
together	O
with	O
FEAL-NX	O
,	O
which	O
had	O
a	O
larger	O
128-bit	O
key	O
.	O
</s>
<s>
Biham	O
and	O
Shamir	O
's	O
differential	O
cryptanalysis	O
(	O
1991	O
)	O
showed	O
that	O
both	O
FEAL-N	O
and	O
FEAL-NX	O
could	O
be	O
broken	O
faster	O
than	O
exhaustive	O
search	O
for	O
N	O
≤	O
31	O
.	O
</s>
<s>
Later	O
attacks	O
,	O
precursors	O
to	O
linear	O
cryptanalysis	O
,	O
could	O
break	O
versions	O
under	O
the	O
known	O
plaintext	O
assumption	O
,	O
first	O
(	O
Tardy-Corfdir	O
and	O
Gilbert	O
,	O
1991	O
)	O
and	O
then	O
(	O
Matsui	O
and	O
Yamagishi	O
,	O
1992	O
)	O
,	O
the	O
latter	O
breaking	O
FEAL-4	O
with	O
5	O
known	O
plaintexts	O
,	O
FEAL-6	O
with	O
100	O
,	O
and	O
FEAL-8	O
with	O
215	O
.	O
</s>
<s>
In	O
1994	O
,	O
Ohta	O
and	O
Aoki	O
presented	O
a	O
linear	O
cryptanalytic	O
attack	O
against	O
FEAL-8	O
that	O
required	O
212	O
known	O
plaintexts	O
.	O
</s>
