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In-Depth Information
Ta b l e 4 .
Hardware evaluation of SCO-1 against some well-known ciphers
Cipher,
Gate count
Critical path,
t
⊕
(implementation)
key schedule encryption key setup, encryption
SCO-1, (C)
500
36
,
200
-
218
SCO-1, (E)
500
77
,
800
-
122
DES, ([7])
12
,
000
42
,
000
-
80
Triple-DES, ([7])
23
,
000
120
,
000
-
220
Rijndael, ([7])
94
,
000
520
,
000
83
95
RC6, ([7])
900
,
000
740
,
000
3000
880
Twofish, ([7])
230
,
000
200
,
000
23
470
∆
output difference when passing through
r
rounds. For the considered ciphers
the most efficient is the two-round iterative DC with the difference
into the
0
1
(
∆
,
∆
)
,where
indices indicates the number of active bits and
∆
1
denotes arbitrary difference with one
1
denotes a batch of the one-bit differences in the right data subblock. We
have obtained the following evaluations:
p
active bit, i.e.
∆
2
−
28
,
p
2
−
112
for SCO-1;
p
(
2
)
<
(
8
)
<
(
2
)
<
2
−
16
,
p
2
−
78
for SCO-3. These results
show that the described ciphers are indistinguishable from a random cipher with DA
using the considered iterative DC.
2
−
96
for SCO-2; and
p
2
−
13
,
p
(
12
)
<
(
2
)
<
(
12
)
<
5Con lu ion
This research has shown that using controlled permutation and substitution-permutation
networks with symmetric topology one can efficiently implement different switchable
DDOs. Using class of elementary controlled involutions
S
2;1
[2] different variants of
SCOs can be designed the given fixed topology. For fixed type of the
S
2;1
box different
SCOs can be constructed using different topologies. One can extend the class of SCOs
using different pairs of the mutually inverse elementary boxes
S
2;1
and
S
−
1
2;1
that are not
involutions. In this case one should place them in a symmetric manner in a symmetric
topology. The COS boxes used as DDOs are highly non-linear primitives [2] and it is
evident that SCOs have the same non-linear properties (for fixed topology and fixed
type of the boxes
S
2;1
).
The paper proposes several SCO-based block ciphers, however they are presumably
only implementation examples. Using methodology [3] of the block cipher design based
on the use of the DDOs the reader can easy construct many other cryptosystems using
very simple key scheduling and having high security against known attacks. While us-
ing SKS in the block cipher design one can apply the SCO boxes that should provide
(1) avoiding the weak keys and (2) security against slide attacks based on chosen key.
An interesting peculiarity of SCO-1 is that it uses no reversing the key scheduling to
change encryption mode. This is due to symmetry of the used keys scheduling. This
peculiarity makes the implementation to be cheaper.
Our preliminary security estimations of the proposed ciphers show that they are in-
distinguishable from a random cipher with differential, linear and other attacks. Differ-
ential cryptanalysis appears to be more efficient against proposed SCO-based ciphers
