Cryptography Reference
In-Depth Information
The output difference of
40080000
XORs onto the difference of
405c0000
of the
left half of the DES input. We obtain a difference of
00540000
. Therefore, after the
first round, we have a difference of
04000000 00540000
with probability
1
4
.
If this holds, the input difference of
00540000
of the second-round function leads
to an input difference (in octal) of
00 00 12 30 00 00 00 00
to the
S
-boxes. From the
definition of
S
3
and
S
4
we obtain that
10
64
,
16
64
.
DP
S
3
(
12
DP
S
4
(
30
,
1
)
=
,
0
)
=
We thus obtain an output difference of
00100000
from the
S
-boxes with probability
10
16
5
64
×
64
=
128
. After the permutation, this difference becomes
04000000
. This means
that
5
128
.
DP
F
(
00540000
,
=
04000000
)
The output difference of
04000000
finally XORs onto the difference of
04000000
,
which therefore vanishes. Hence, after the second round, we have a difference of
00540000 00000000
with probability
1
5
5
4
×
128
=
512
.
The input difference of zero in the third-round function leads to an output difference
of zero with probability 1. Therefore, after the third-round, we have a difference of
00000000 00540000
with probability
5
512
.
In the fourth round, we can use the same property as that in the second round,
namely
5
128
.
DP
F
(
00540000
,
04000000
)
=
Thus after the fourth round, we have a difference of
00540000 04000000
with proba-
bility
5
5
25
512
×
128
=
2
16
.
In the fifth round, we can use the same property as that in the first round, namely
1
4
.
DP
F
(
04000000
,
40080000
)
=
The
40080000
XORs onto
00540000
and leads to
405c0000
. Hence, after the
fifth round, we have a difference of
04000000 405c0000
with probability
25
2
16
1
×
4
=
2
−
13
.
4
. This explains where the announced five-round differential characteristic
comes from.
25
2
18
≈
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