Cryptography Reference
In-Depth Information
Table 10.1
The Growth Rate of
f
(
n
)=(2
n
)! for
n
=1
,...,
10
(2
n
)!
n
2
1
!=2!=2
1
2
2
!=4!=24
2
2
3
!=8!=40
320
3
2
4
! = 16! = 20
922
789
888
000
4
2
5
! = 32!
≈
2
.
63
·
10
35
5
2
6
! = 64!
≈
1
.
27
·
10
89
6
2
7
! = 128!
≈
3
.
86
·
10
215
7
2
8
! = 256!
≈
8
.
58
·
10
506
8
2
9
! = 512!
≈
3
.
48
·
10
1166
9
2
10
! = 1024!
≈
5
.
42
·
10
2639
10
In the design of symmetric encryption systems, permutations and substitutions
are usually used and combined to provide confusion and diffusion.
•
The purpose of
confusion
is to make the relation between the key and the
ciphertext as complex as possible.
•
The purpose of
diffusion
is to spread the influence of a single plaintext bit over
many ciphertext bits. In a block cipher, diffusion propagates bit changes from
one part of a block to other parts of the block.
Symmetric encryption systems that combine permutations and substitutions
in multiple rounds (to provide a maximum level of confusion and diffusion) are
sometimes also referred to as
substitution-permutation ciphers
. Many practically
relevant symmetric encryption systems, including, for example, the DES overviewed
and discussed next, are substitution-permutation ciphers. When we describe DES
and a few other symmetric encryption systems in this chapter, we are not as formal
and formally correct as one could possibly be. Instead, we adopt some terminology
and notation used in the original descriptions and specifications of the encryption
systems (mainly to make it simpler for the reader to get into these documents).
10.2.1
DES
The DES was developed by IBM in the 1970s
7
and was adopted by the National
Bureau of Standards (NBS) as FIPS PUB 46 in 1977. Nowadays, the FIPS PUBS are
developed and maintained by the NIST. The standard was reaffirmed in 1983, 1988,
7
The symmetric encryption system was called
Lucifer
internally at IBM.
