Information Technology Reference
In-Depth Information
Case 1a includes the following elementary events:
1. The difference
∆
2
|i,i
+1
is formed at the output of the operation
G
with
2
=Pr
∆
2
|i,i
+1
δ
1
|i
.
2. The difference
(
i,i
+1)
p
probability
∆
P
2
|i,i
+1
P
with
is formed at the output of the CP box
=Pr
∆
P
2
+1
δ
P
0
.
(
i,i
+1)
3
probability
p
|i,i
∆
P
0
P
with prob-
3. The difference
is formed at the output of the CP box
p
1
=2
−m
=Pr
∆
P
0
δ
P
0
, where
m
ability
is the number of the elementary
P
2
/
1
controlled with active bit (
m
,
i
boxes
=2
3 depending on
).
∆
P
2
∆
P
0
∆
2
|i,i
+1
,
4. After XORing differences
+1
, and
we have zero dif-
|i,i
∆
P
∗
0
P
∗
ference
at the input of the
box. It passes this box with probability
p
4
=Pr
∆
P
0
δ
P
0
=2
−m
.
Case 1a corresponds to the following set of the events in the second round:
∆
2
|i,i
+1
δ
1
|i
,
∆
P
2
|i,i
+1
δ
P
0
,
∆
P
0
δ
P
0
,
∆
P
0
δ
P
0
.
Other cases can be described as follows (
∀i, k
:
k ∈{
1
,
2
, ...,
32
}
,
k
=
i
, and
k
i
=
+1):
Case 1b:
∆
2
|i,i
+1
δ
1
|i
,
∆
P
2
|i,i
+1
δ
P
0
,
∆
P
0
δ
P
0
,
∆
P
0
δ
P
0
.
∆
2
|i,i
+1
δ
1
|i
,
∆
P
0
δ
P
0
,
∆
P
0
δ
P
0
,
∆
P
0
δ
P
∗
2
|i,i
+1
.
Case 1c:
R
p
= 2
-5
L
0
Crypt
R
0
1|
i
p
(
i
,
i+
1)
3
U
V
1
3
P
=
P
32/80
E
>>>11
P
p
1
0
U
V
P
1
3
P
=
P
32/80
E
2|
i
,
i+
1
>>>17
p
(
i,i+
1)
2
P
R
L
G
G
0
2|
i
,
i+
1
1|
i
1|
i
2|
i
,
i+
1
G
p
4
= 2
-
m
0
U
V
-
1
1
3
E
>>>11
P
*
=
P
32/80
0
L
R
0
1|
i
Fig. 1.
Formation of the two-round characteristic (Case 1a)
∆
2
|i,i
+1
δ
1
|i
,
∆
P
2
|i
+1
,k
δ
P
0
,
∆
P
2
|i,k
δ
P
0
,
∆
P
0
δ
P
0
.
Case 2a:
∆
2
|i,i
+1
δ
1
|i
,
∆
P
2
|i,k
δ
P
0
,
∆
P
2
|i
+1
,k
δ
P
0
,
∆
P
0
δ
P
0
.
Case 2b:
∆
2
|i,i
+1
δ
1
|i
,
∆
P
0
δ
P
0
,
∆
P
2
δ
P
0
,
∆
P
0
δ
P
∗
.
Case 3a:
|i
+1
,k
2
|i,k
∆
2
|i,i
+1
δ
1
|i
,
∆
P
0
δ
P
0
,
∆
P
2
|i,k
δ
P
0
,
∆
P
0
δ
P
∗
.
Case 3b:
2
|i
+1
,k
∆
2
|i,i
+1
δ
1
|i
,
∆
P
0
δ
P
0
,
∆
P
2
|i
+1
,k
δ
P
0
,
∆
P
0
δ
P
∗
.
Case 4a:
2
|i,k
∆
2
|i,i
+1
δ
1
|i
,
∆
P
0
δ
P
0
,
∆
P
2
δ
P
0
,
∆
P
0
δ
P
∗
.
Case 4b:
|i,k
2
|i
+1
,k
