Cryptography Reference
In-Depth Information
Thus,
P
10
(
k
)=(
e
3
e
5
e
2
e
7
e
4
e
10
e
1
e
9
e
8
e
6
).
Secondly, there is a circular left shift of 1 place, denoted by
LS1
, on each
of the left five bits and the right five bits, as follows.
LS1
(
e
3
e
5
e
2
e
7
e
4
)=
(
e
5
e
2
e
7
e
4
e
3
), and
LS1
(
e
10
e
1
e
9
e
8
e
6
)=(
e
1
e
9
e
8
e
6
e
10
). Hence, under this shifting
process, (
e
3
e
5
e
2
e
7
e
4
e
10
e
1
e
9
e
8
e
6
) becomes
(
e
5
e
2
e
7
e
4
e
3
e
1
e
9
e
8
e
6
e
10
)
.
(3.2)
Then we apply yet another permutation called
P
8
, which selects 8 of the 10
bits and permutes them as follows.
P
8
j
123456 7 8
P
8
(
j
) 637485 09
Applying
P
8
to (3.2) yields
P
8
(
e
5
e
2
e
7
e
4
e
3
e
1
e
9
e
8
e
6
e
10
)=(
e
1
e
7
e
9
e
4
e
8
e
3
e
10
e
6
)=
k
1
,
where
k
1
is now our first subkey for use later.
Now, we return to (3.2) and perform a left shift of two places, denoted by
LS2
, on both the left and right 5-bit pieces to get
LS2
(
e
5
e
2
e
7
e
4
e
3
)=(
e
7
e
4
e
3
e
5
e
2
), and
LS2
(
e
1
e
9
e
8
e
6
e
10
)=(
e
8
e
6
e
10
e
1
e
9
)
,
yielding (
e
7
e
4
e
3
e
5
e
2
e
8
e
6
e
10
e
1
e
9
) to which we apply
P
8
to get
P
8
(
e
7
e
4
e
3
e
5
e
2
e
8
e
6
e
10
e
1
e
9
)=(
e
8
e
3
e
6
e
5
e
10
e
2
e
9
e
1
)=
k
2
,
where
k
2
is our second subkey for use in the S-DES cipher.
The next essential component of the S-DES cryptosystem is an important
method of substitution, and an innovation of Feistel in his development of the
original DES. (However, it is believed, in some quarters, that Feistel got the
idea from the NSA; see [151, page 42]).
S-Boxes
An S-Box or
substitution box
for S-DES is a 4
×
4 matrix with entries from
Z
(put into binary) with rows and columns labelled from 0 to 3 (put into
binary), that takes a 4-bit input and outputs a 2-bit string as follows.
If (
x
1
x
2
x
3
x
4
) is the input, then the output is given by one of the two S-Boxes
used in S-DES, defined as follows.
/
4
Z
S
0
x
2
0011
S
1
x
2
0011
x
3
0101
x
3
0101
x
1
x
4
00
x
1
x
4
00
and
01 00 11 10
00 01 10 11
01
11 10 01 00
01
10 00 01 11
10
00 10 01 11
10
11 00 01 00
11
11 01 11 10
11
10 01 00 11
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