<s>
KASUMI	B-Algorithm
is	O
a	O
block	O
cipher	O
used	O
in	O
UMTS	B-Protocol
,	O
GSM	O
,	O
and	O
GPRS	B-General_Concept
mobile	O
communications	O
systems	O
.	O
</s>
<s>
In	O
UMTS	B-Protocol
,	O
KASUMI	B-Algorithm
is	O
used	O
in	O
the	O
confidentiality	O
(	O
f8	O
)	O
and	O
integrity	O
algorithms	O
(	O
f9	O
)	O
with	O
names	O
UEA1	O
and	O
UIA1	O
,	O
respectively	O
.	O
</s>
<s>
In	O
GSM	O
,	O
KASUMI	B-Algorithm
is	O
used	O
in	O
the	O
A5/3	B-Algorithm
key	O
stream	O
generator	O
and	O
in	O
GPRS	B-General_Concept
in	O
the	O
GEA3	O
key	O
stream	O
generator	O
.	O
</s>
<s>
KASUMI	B-Algorithm
is	O
named	O
after	O
the	O
original	O
algorithm	O
MISTY1	B-Algorithm
霞み	O
(	O
hiragana	O
かすみ	O
,	O
romaji	O
kasumi	B-Algorithm
)	O
is	O
the	O
Japanese	O
word	O
for	O
"	O
mist	O
"	O
.	O
</s>
<s>
In	O
January	O
2010	O
,	O
Orr	O
Dunkelman	O
,	O
Nathan	O
Keller	O
and	O
Adi	O
Shamir	O
released	O
a	O
paper	O
showing	O
that	O
they	O
could	O
break	O
Kasumi	B-Algorithm
with	O
a	O
related-key	O
attack	O
and	O
very	O
modest	O
computational	O
resources	O
;	O
this	O
attack	O
is	O
ineffective	O
against	O
MISTY1	B-Algorithm
.	O
</s>
<s>
KASUMI	B-Algorithm
algorithm	O
is	O
specified	O
in	O
a	O
3GPP	O
technical	O
specification	O
.	O
</s>
<s>
KASUMI	B-Algorithm
is	O
a	O
block	O
cipher	O
with	O
128-bit	O
key	O
and	O
64-bit	O
input	O
and	O
output	O
.	O
</s>
<s>
The	O
core	O
of	O
KASUMI	B-Algorithm
is	O
an	O
eight-round	O
Feistel	B-Algorithm
network	I-Algorithm
.	O
</s>
<s>
The	O
32-bit	O
input	O
x	O
of	O
is	O
divided	O
into	O
two	O
16-bit	O
halves	O
,	O
and	O
passed	O
through	O
three	O
rounds	O
of	O
a	O
Feistel	B-Algorithm
network	I-Algorithm
.	O
</s>
<s>
The	O
substitution	B-Algorithm
boxes	I-Algorithm
(	O
S-boxes	B-Algorithm
)	O
S7	O
and	O
S9	O
are	O
defined	O
by	O
both	O
bit-wise	O
AND-XOR	O
expressions	O
and	O
look-up	O
tables	O
in	O
the	O
specification	O
.	O
</s>
<s>
In	O
2001	O
,	O
an	O
impossible	O
differential	O
attack	O
on	O
six	O
rounds	O
of	O
KASUMI	B-Algorithm
was	O
presented	O
by	O
Kühn	O
(	O
2001	O
)	O
.	O
</s>
<s>
In	O
2003	O
Elad	O
Barkan	O
,	O
Eli	O
Biham	O
and	O
Nathan	O
Keller	O
demonstrated	O
man-in-the-middle	O
attacks	O
against	O
the	O
GSM	O
protocol	O
which	O
avoided	O
the	O
A5/3	B-Algorithm
cipher	O
and	O
thus	O
breaking	O
the	O
protocol	O
.	O
</s>
<s>
This	O
approach	O
does	O
not	O
attack	O
the	O
A5/3	B-Algorithm
cipher	O
,	O
however	O
.	O
</s>
<s>
In	O
2005	O
,	O
Israeli	O
researchers	O
Eli	O
Biham	O
,	O
Orr	O
Dunkelman	O
and	O
Nathan	O
Keller	O
published	O
a	O
related-key	O
rectangle	O
(	O
boomerang	O
)	O
attack	O
on	O
KASUMI	B-Algorithm
that	O
can	O
break	O
all	O
8	O
rounds	O
faster	O
than	O
exhaustive	O
search	O
.	O
</s>
<s>
The	O
attack	O
requires	O
254.6	O
chosen	O
plaintexts	O
,	O
each	O
of	O
which	O
has	O
been	O
encrypted	O
under	O
one	O
of	O
four	O
related	O
keys	O
,	O
and	O
has	O
a	O
time	O
complexity	O
equivalent	O
to	O
276.1	O
KASUMI	B-Algorithm
encryptions	O
.	O
</s>
<s>
While	O
this	O
is	O
obviously	O
not	O
a	O
practical	O
attack	O
,	O
it	O
invalidates	O
some	O
proofs	O
about	O
the	O
security	O
of	O
the	O
3GPP	O
protocols	O
that	O
had	O
relied	O
on	O
the	O
presumed	O
strength	O
of	O
KASUMI	B-Algorithm
.	O
</s>
<s>
In	O
2010	O
,	O
Dunkelman	O
,	O
Keller	O
and	O
Shamir	O
published	O
a	O
new	O
attack	O
that	O
allows	O
an	O
adversary	O
to	O
recover	O
a	O
full	O
A5/3	B-Algorithm
key	O
by	O
related-key	O
attack	O
.	O
</s>
<s>
The	O
time	O
and	O
space	O
complexities	O
of	O
the	O
attack	O
are	O
low	O
enough	O
that	O
the	O
authors	O
carried	O
out	O
the	O
attack	O
in	O
two	O
hours	O
on	O
an	O
Intel	O
Core	O
2	O
Duo	O
desktop	O
computer	O
even	O
using	O
the	O
unoptimized	O
reference	O
KASUMI	B-Algorithm
implementation	O
.	O
</s>
<s>
The	O
authors	O
note	O
that	O
this	O
attack	O
may	O
not	O
be	O
applicable	O
to	O
the	O
way	O
A5/3	B-Algorithm
is	O
used	O
in	O
3G	O
systems	O
;	O
their	O
main	O
purpose	O
was	O
to	O
discredit	O
3GPP	O
's	O
assurances	O
that	O
their	O
changes	O
to	O
MISTY	B-Algorithm
would	O
n't	O
significantly	O
impact	O
the	O
security	O
of	O
the	O
algorithm	O
.	O
</s>
