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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