Cryptography Reference
In-Depth Information
Appendix D: Technical and Advanced Details
In this appendix, we sequester certain technical details about some of the
ciphers or other algorithms. Otherwise, the explanation, left in the main text,
could present a more onerous task, leaving the novice reader stranded in some
cases. Hence, we provide the particulars of these algorithmic fine points for
those interested in pursuing the depths of a given cipher or methodology more
exhaustively. Moreover, for the reader interested in pursuing material beyond
that given in the main text, we provide some advanced algorithms that go well
beyond the boundaries of the standard presentations.
D.1 AES
We begin with some specifics concerning the AES cipher introduced in Sec-
tion 3.5.
The Rijndael S-Box
The means by which Rijndael's invertible S-box, explicitly given below, was
constructed consists of composing two functions. First, consider the 3
×
8 matrix
with entries,
a
i,j
=8
i
+
j
−
9 for 1
≤
i
≤
32 and 1
≤
j
≤
8
.
Let the map
g
defined by taking 0 to 0 and for
a
i,j
=0,
7
a
−
1
b
k
2
j
,
g
:
a
i,j
→
i,j
=
k
=0
the binary representation of the multiplicative inverse of
a
i,j
in
F
2
8
. If we view
the image of
g
as a column vector,
b
7
b
6
b
5
b
4
b
3
b
2
b
1
b
0
g
(
a
i,j
)=
,
then we let
f
be the AGne function that is applied to the output of
g
via
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