CNS_06 DES ALGORITHM AND ITS IMPLEMENTAT

6.1
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 6
Data Encryption Standard
(DES)

6.3
6-1 INTRODUCTION
The Data Encryption Standard (DES) is a symmetric-
key block cipher published by the National Institute of
Standards and Technology (NIST).
6.1.1 History
6.1.2 Overview
Topics discussed in this section:

6.4
In 1973, NIST published a request for proposals for a
national symmetric-key cryptosystem. A proposal from
IBM, a modification of a project called Lucifer, was
accepted as DES. DES was published in the Federal
Register in March 1975 as a draft of the Federal
Information Processing Standard (FIPS).
6.1.1 History

6.5
DES is a block cipher, as shown in Figure 6.1.
6.1.2 Overview
Figure 6.1 Encryption and decryption with DES

6.6
6-2 DES STRUCTURE
The encryption process is made of two permutations
(P-boxes), which we call initial and final
permutations, and sixteen Feistel rounds.
6.2.1 Initial and Final Permutations
6.2.2 Rounds
6.2.3 Cipher and Reverse Cipher
6.2.4 Examples

6.7
6-2 Continue
Figure 6.2 General structure of DES

6.8
6.2.1 Initial and Final Permutations
Figure 6.3 Initial and final permutation steps in DES

6.9
6.2.1 Continue
Table 6.1 Initial and final permutation tables

6.12
6.2.1 Continued
The initial and final permutations are
straight P-boxes that are inverses
of each other.
They have no cryptography significance in
DES.
Note

6.13
DES uses 16 rounds. Each round of DES is a Feistel
cipher.
6.2.2 Rounds
Figure 6.4
A round in DES
(encryption site)

6.14
The heart of DES is the DES function. The DES function
applies a 48-bit key to the rightmost 32 bits to produce a
32-bit output.
6.2.2 Continued
DES Function
Figure 6.5
DES function

6.15
Expansion P-box
Since RI−1 is a 32-bit input and KI is a 48-bit key, we first
need to expand RI−1 to 48 bits.
6.2.2 Continue
Figure 6.6 Expansion permutation

6.16
Although the relationship between the input and output
can be defined mathematically, DES uses Table 6.2 to
define this P-box.
6.2.2 Continue
Table 6.6 Expansion P-box table

6.17
Whitener (XOR)
After the expansion permutation, DES uses the XOR
operation on the expanded right section and the round
key. Note that both the right section and the key are 48-
bits in length. Also note that the round key is used only in
this operation.
6.2.2 Continue

6.18
S-Boxes
The S-boxes do the real mixing (confusion). DES uses 8
S-boxes, each with a 6-bit input and a 4-bit output. See
Figure 6.7.
6.2.2 Continue
Figure 6.7 S-boxes

6.19
6.2.2 Continue
Figure 6.8 S-box rule

6.20
Table 6.3 shows the permutation for S-box 1. For the rest
of the boxes see the textbook.
6.2.2 Continue
Table 6.3 S-box 1

6.23
Straight Permutation
6.2.2 Continue
Table 6.11 Straight permutation table

6.24
Using mixers and swappers, we can create the cipher and
reverse cipher, each having 16 rounds.
6.2.3 Cipher and Reverse Cipher
First Approach
To achieve this goal, one approach is to make the last
round (round 16) different from the others; it has only a
mixer and no swapper.
In the first approach, there is no swapper in
the last round.
Note

6.25
6.2.3 Continued
Figure 6.9 DES cipher and reverse cipher for the first approach

6.26
6.2.3 Continued
Algorithm 6.1 Pseudocode for DES cipher

6.27
6.2.3 Continued
Algorithm 6.1 Pseudocode for DES cipher (Continued)

6.28
6.2.3 Continued

6.29
6.2.3 Continued

6.30
Alternative Approach
6.2.3 Continued
We can make all 16 rounds the same by including one
swapper to the 16th round and add an extra swapper after
that (two swappers cancel the effect of each other).
Key Generation
The round-key generator creates sixteen 48-bit keys out
of a 56-bit cipher key.

6.31
6.2.3 Continued
Figure 6.10
Key generation

6.32
6.2.3 Continued
Table 6.12 Parity-bit drop table
Table 6.13 Number of bits shifts

6.33
6.2.3 Continued
Table 6.14 Key-compression table

6.34
6.2.3 Continued
Algorithm 6.2 Algorithm for round-key generation

6.35
6.2.3 Continued
Algorithm 6.2 Algorithm for round-key generation (Continue)

6.36
Example 6.5
6.2.4 Examples
We choose a random plaintext block and a random key, and
determine what the ciphertext block would be (all in
hexadecimal):
Table 6.15 Trace of data for Example 6.5

6.37
Example 6.5
Table 6.15 Trace of data for Example 6.5 (Conintued
6.2.4 Continued
Continued

6.38
Example 6.6
6.2.4 Continued
Let us see how Bob, at the destination, can decipher the
ciphertext received from Alice using the same key. Table 6.16
shows some interesting points.

6.39
6-3 DES ANALYSIS
Critics have used a strong magnifier to analyze DES.
Tests have been done to measure the strength of some
desired properties in a block cipher.
6.3.1 Properties
6.3.2 Design Criteria
6.3.3 DES Weaknesses

6.40
Two desired properties of a block cipher are the
avalanche effect and the completeness.
6.3.1 Properties
Example 6.7
To check the avalanche effect in DES, let us encrypt two
plaintext blocks (with the same key) that differ only in one bit
and observe the differences in the number of bits in each
round.

6.41
Example 6.7
6.3.1 Continued
Although the two plaintext blocks differ only in the rightmost
bit, the ciphertext blocks differ in 29 bits. This means that
changing approximately 1.5 percent of the plaintext creates a
change of approximately 45 percent in the ciphertext.
Table 6.17 Number of bit differences for Example 6.7
Continued

6.42
6.3.1 Continued
Completeness effect
Completeness effect means that each bit of the ciphertext
needs to depend on many bits on the plaintext.

6.43
6.3.2 Design Criteria
S-Boxe
The design provides confusion and diffusion of bits from
each round to the next.
P-Boxes
They provide diffusion of bits.
Number of Rounds
DES uses sixteen rounds of Feistel ciphers. the ciphertext
is thoroughly a random function of plaintext and
ciphertext.

6.44
During the last few years critics have found some
weaknesses in DES.
6.3.3 DES Weaknesses
Weaknesses in Cipher Design
1. Weaknesses in S-boxes
2. Weaknesses in P-boxes
3. Weaknesses in Key

6.46
6.3.3 Continued
Figure 6.11 Double encryption and decryption with a weak key

6.49
6.3.3 Continued
Figure 6.12 A pair of semi-weak keys in encryption and decryption

6.53
6-4 Multiple DES
The major criticism of DES regards its key length.
Fortunately DES is not a group. This means that we
can use double or triple DES to increase the key size.
6.4.1 Double DES
6.4.4 Triple DES

6.55
The first approach is to use double DES (2DES).
6.4.1 Double DES
Meet-in-the-Middle Attack
However, using a known-plaintext attack called meet-in-
the-middle attack proves that double DES improves this
vulnerability slightly (to 257 tests), but not tremendously
(to 2112).

6.56
6.4.1 Continued
Figure 6.14 Meet-in-the-middle attack for double DES

6.57
6.4.1 Continued
Figure 6.15 Tables for meet-in-the-middle attack

6.58
6.4.2 Triple DES
Figure 6.16 Triple DES with two keys

6.59
6.4.2 Continuous
Triple DES with Three Keys
The possibility of known-plaintext attacks on triple DES
with two keys has enticed some applications to use triple
DES with three keys. Triple DES with three keys is used
by many applications such as PGP (See Chapter 16).

CNS_06 DES ALGORITHM AND ITS IMPLEMENTAT

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