<s>
In	O
cryptography	O
,	O
LOKI89	B-Algorithm
and	O
LOKI91	B-Algorithm
are	O
symmetric-key	B-Algorithm
block	O
ciphers	O
designed	O
as	O
possible	O
replacements	O
for	O
the	O
Data	B-Algorithm
Encryption	I-Algorithm
Standard	I-Algorithm
(	O
DES	B-Algorithm
)	O
.	O
</s>
<s>
The	O
ciphers	O
were	O
developed	O
based	O
on	O
a	O
body	O
of	O
work	O
analysing	O
DES	B-Algorithm
,	O
and	O
are	O
very	O
similar	O
to	O
DES	B-Algorithm
in	O
structure	O
.	O
</s>
<s>
The	O
LOKI	B-Device
algorithms	O
were	O
named	O
for	O
Loki	B-Device
,	O
the	O
god	O
of	O
mischief	O
in	O
Norse	O
mythology	O
.	O
</s>
<s>
LOKI89	B-Algorithm
was	O
first	O
published	O
in	O
1990	O
,	O
then	O
named	O
just	O
"	O
LOKI	B-Device
"	O
,	O
by	O
Australian	O
cryptographers	O
Lawrie	O
Brown	O
,	O
Josef	O
Pieprzyk	O
,	O
and	O
Jennifer	O
Seberry	O
.	O
</s>
<s>
LOKI89	B-Algorithm
was	O
submitted	O
to	O
the	O
European	O
RIPE	O
project	O
for	O
evaluation	O
,	O
but	O
was	O
not	O
selected	O
.	O
</s>
<s>
Like	O
DES	B-Algorithm
,	O
it	O
is	O
a	O
16-round	O
Feistel	B-Algorithm
cipher	I-Algorithm
and	O
has	O
a	O
similar	O
general	O
structure	O
,	O
but	O
differs	O
in	O
the	O
choice	O
of	O
the	O
particular	O
S-boxes	B-Algorithm
,	O
the	O
"	O
P-permutation	O
"	O
,	O
and	O
the	O
"	O
Expansion	O
permutation	O
"	O
.	O
</s>
<s>
against	O
the	O
known	O
design	O
criteria	O
for	O
the	O
DES	B-Algorithm
S-boxes	B-Algorithm
.	O
</s>
<s>
properties	O
,	O
essential	O
for	O
a	O
good	O
Feistel	B-Algorithm
cipher	I-Algorithm
.	O
</s>
<s>
This	O
resulted	O
in	O
the	O
design	O
being	O
changed	O
to	O
become	O
LOKI91	B-Algorithm
.	O
</s>
<s>
LOKI	B-Device
91	O
was	O
designed	O
in	O
response	O
to	O
the	O
attacks	O
on	O
LOKI89	B-Algorithm
(	O
Brown	O
et	O
al.	O
,	O
1991	O
)	O
.	O
</s>
<s>
The	O
changes	O
included	O
removing	O
the	O
initial	O
and	O
final	O
key	B-Algorithm
whitening	I-Algorithm
,	O
a	O
new	O
S-box	B-Algorithm
,	O
and	O
small	O
alterations	O
to	O
the	O
key	B-Algorithm
schedule	I-Algorithm
.	O
</s>
<s>
More	O
specifically	O
,	O
the	O
S-boxes	B-Algorithm
were	O
changed	O
to	O
minimise	O
the	O
probability	O
of	O
seeing	O
different	O
inputs	O
resulting	O
in	O
the	O
same	O
output	O
(	O
a	O
hook	O
which	O
Differential	O
cryptanalysis	O
uses	O
)	O
,	O
thus	O
improving	O
LOKI91	B-Algorithm
's	O
immunity	O
to	O
this	O
attack	O
,	O
as	O
detailed	O
by	O
the	O
attacks	O
authors	O
(	O
Biham	O
and	O
Shamir	O
1991	O
)	O
.	O
</s>
<s>
The	O
changes	O
to	O
the	O
key	B-Algorithm
schedule	I-Algorithm
were	O
designed	O
to	O
reduce	O
the	O
number	O
of	O
"	O
equivalent	O
"	O
or	O
"	O
related	O
"	O
keys	O
,	O
which	O
resulted	O
in	O
the	O
exhaustive	O
search	O
space	O
for	O
the	O
cipher	O
being	O
reduced	O
.	O
</s>
<s>
Whilst	O
the	O
resulting	O
cipher	O
is	O
clearly	O
stronger	O
and	O
more	O
secure	O
than	O
LOKI89	B-Algorithm
,	O
there	O
are	O
a	O
number	O
of	O
potential	O
attacks	O
,	O
as	O
detailed	O
in	O
the	O
papers	O
by	O
Knudsen	O
and	O
Biham	O
.	O
</s>
