Information Technology Reference
In-Depth Information
Recently a generalization of the CP boxes has been proposed [2] leading to the class
of COSes that include the CPs as a particular case. The COS boxes can be constructed in
the same way as the CP boxes, except the use of the elementary controlled substitution
boxes
S
2;1
(Fig. 2) instead of
P
2;1
. The box
S
2;1
is described by two Boolean functions
in three variables:
y
1
=
,where
x
1
and
x
2
are input bits,
y
1
and
y
2
are output bits, and
v
is the controlling bit. Some
S
2;1
-boxes are involutions,
i. e. for
v
f
1
(
x
1
,
x
2
,
v
)
and
y
2
=
f
2
(
x
1
,
x
2
,
v
)
=
0and
v
=
1wehave
x
2
)
.
Table 1 presents some results of [2] giving examples of the pairs of the functions
f
1
and
f
2
defining involutions
S
2;1
. Replacing the
P
2;1
-boxes in the given CP-box topol-
ogy by different controlled elements
S
2;1
one can define different variants of the COS
boxes. Such COS boxes represent some controlled substitution-permutation networks.
Thus, the general structure of the COS boxes can be described by Fig. 1, where all
boxes
P
2;1
are replaced by the elementary controlled substitutions
S
2;1
.Ifweusean
elementary controlled involution
S
2;1
then such replacement in two mutually inverse
CP boxes
P
n
;
m
and
P
−
1
2;1
S
(
e
)
S
(
e
)
(
x
1
,
x
2
)=
(
x
1
,
2;1
n
;
m
produces two mutually inverse COS boxes
S
n
;
m
and
S
−
1
n
;
m
.In
spite of linearity of the substitutions performed by the elements
S
2;1
at fixed value of
the controlling bit the use of the COS boxes as DDOs defines the transformation with
high non-linearity [2]. Use of the CP and COS boxes as the key-dependent operation
is significantly less efficient, therefore we assume that switchable controlled operations
(SCOs) constructed on the bases of the considered networks should be used mainly as
switchable DDOs.
a)
x
1
x
1
x
2
b)
x
2
c)
x
1
x
2
P
2;1
v
v
v
S
2;1
f
1
f
2
y
1
y
2
y
1
=x
1
(
v
+
1)
+
x
2
v
y
1
y
2
y
2
=x
1
v
+
x
2
(
v
+
1)
y
1
y
2
Fig. 2.
Controlled element: a
−
notation, b
−
implementation, c
−
switching element
Below we describe the switchable COS boxes
S
(
V
,
e
)
32;96
and
S
(
V
,
e
)
64;192
representing practi-
cal interest in the design of the 64- and 128-bit ciphers, correspondingly. These switch-
able operational boxes are constructed on the bases of the COS boxes
S
32;96
and
S
64;192
with symmetric structure. The boxes
S
8;12
(Fig. 3a) and
S
−
1
8;12
(Fig. 3b) containing three
active layers are used as main building blocks while constructing the six-layer boxes
S
32;96
(Fig. 3c) and
S
64;192
(Fig. 3e).
The permutation
3
corresponding to connections between four (eight) parallel
boxes
S
8;12
and four (eight) parallel boxes
S
−
1
π
8;12
in the box
S
32;96
(
S
64;192
) is described
as the following fixed permutational involution
I
1
(
I
2
):