CS8792 - Cryptography and Network Security

CS8792 - Cryptography and
Network Security
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Unit – I INTRODUCTION
• Security trends - Legal, Ethical and
Professional Aspects of Security, Need for
Security at Multiple levels, Security Policies -
Model of network security – Security attacks,
services and mechanisms – OSI security
architecture – Classical encryption techniques:
substitution techniques, transposition
techniques, steganography- Foundations of
modern cryptography: perfect security –
information theory – product cryptosystem –

Some Basic Terminology
• Plaintext - original message
• Ciphertext - coded message
• Cipher - algorithm for transforming plaintext to ciphertext
• Key - information used in cipher known only to
sender/receiver
• Encipher (encrypt) - converting plaintext to ciphertext
• Decipher (decrypt) - recovering ciphertext from plaintext
• Cryptography - study of encryption principles/methods
• Cryptanalysis (codebreaking) - study of principles/ methods
of deciphering ciphertext without knowing key

Data Transmission Steps
PT
PT
CT
CT
Encryption
Transmission
DecryptionX – Plain text
Y – Cipher text
K – Key
Y = Ek (X)
X = Dk (Y)

Cryptography
• Characterize cryptographic system by:
– Type of encryption operations used
• Substitution / Transposition / Product
– Number of keys used
• Single-key or Private / Two-key or Public
– Way in which plaintext is processed
• Block / Stream

Cryptanalysis
• Objective to recover key not just message
• General approaches:
– Cryptanalytic attack
• Knowledge of algorithm and some part of plaintext
– Brute-force attack
• Try every possible key on cipher text to get a meaningful
plain text

3-1 INTRODUCTION
Figure 3.1 shows the general idea behind a symmetric-key
cipher. The original message from Alice to Bob is called
plaintext; the message that is sent through the channel is
called the ciphertext. To create the ciphertext from the
plaintext, Alice uses an encryption algorithm and a shared
secret key. To create the plaintext from ciphertext, Bob
uses a decryption algorithm and the same secret key.
3.1.1 Kerckhoff’s Principle
3.1.2 Cryptanalysis
3.1.3 Categories of Traditional Ciphers
Topics discussed in this section:

Figure 3.1 General idea of symmetric-key cipher
3.1 Continued

3.1 Continued
If P is the plaintext, C is the ciphertext, and K is the key,
We assume that Bob creates P1; we prove that P1 = P:

Figure 3.2 Locking and unlocking with the same key
3.1 Continued

3.1.1 Kerckhoff’s Principle
Based on Kerckhoff’s principle, one should always
assume that the adversary, Eve, knows the
encryption/decryption algorithm. The resistance of the
cipher to attack must be based only on the secrecy of the
key.

3.1.2 Cryptanalysis
As cryptography is the science and art of creating secret
codes, cryptanalysis is the science and art of breaking
those codes.
Figure 3.3 Cryptanalysis attacks

3.1.2 Continued
Figure 3.4 Ciphertext-only attack
Ciphertext-Only Attack

3.1.2 Continued
Figure 3.5 Known-plaintext attack
Known-Plaintext Attack

3.1.2 Continued
Figure 3.6 Chosen-plaintext attack
Chosen-Plaintext Attack

3.1.2 Continued
Figure 3.7 Chosen-ciphertext attack
Chosen-Ciphertext Attack

Classical Encryption
Techniques
1. Substitution Techniques
2. Transposition Techniques

Substitution Techniques
• Caesar cipher
• Monoalphabetic cipher
• Play fair cipher
• Hill cipher
• Polyalphabetic cipher
• One time pad

Classical Substitution Ciphers
• Letters of plaintext are replaced by other
letters or by numbers or symbols
• If plaintext is viewed as a sequence of bits,
then substitution involves replacing plaintext
bit patterns with cipher text bit patterns

3-2 SUBSTITUTION CIPHERS
A substitution cipher replaces one symbol with another.
Substitution ciphers can be categorized as either
monoalphabetic ciphers or polyalphabetic ciphers.
3.2.1 Monoalphabetic Ciphres
3.2.2 Polyalphabetic Ciphers
A substitution cipher replaces one
symbol with another.
Note

3.2.1 Monoalphabetic Ciphers
In monoalphabetic substitution, the
relationship between a symbol in the
plaintext to a symbol in the ciphertext is
always one-to-one.
Note

3.2.1 Continued
The following shows a plaintext and its corresponding ciphertext.
The cipher is probably monoalphabetic because both l’s (els) are
encrypted as O’s.
Example 3.1

3.2.1 Continued
The simplest monoalphabetic cipher is the additive cipher. This
cipher is sometimes called a shift cipher and sometimes a Caesar
cipher, but the term additive cipher better reveals its
mathematical nature.
Additive Cipher
Figure 3.8 Plaintext and ciphertext in Z26

Figure 3.9 Additive cipher
3.2.1 Continued
When the cipher is additive, the
plaintext, ciphertext, and key are
integers in Z26.
Note

3.2.1 Continued
Use the additive cipher with key = 15 to encrypt the message
“hello”.
Example 3.3
We apply the encryption algorithm to the plaintext, character by
character:
Solution

3.2.1 Continued
Use the additive cipher with key = 15 to decrypt the message
“WTAAD”.
Example 3.4
We apply the decryption algorithm to the plaintext character by
character:
Solution

3.2.1 Continued
Historically, additive ciphers are called shift ciphers. Julius Caesar
used an additive cipher to communicate with his officers. For this
reason, additive ciphers are sometimes referred to as the Caesar
cipher. Caesar used a key of 3 for his communications.
Shift Cipher and Caesar Cipher
Additive ciphers are sometimes referred
to as shift ciphers or Caesar cipher.
Note

3.2.1 Continued
Eve has intercepted the ciphertext “UVACLYFZLJBYL”. Show
how she can use a brute-force attack to break the cipher.
Example 3.5
Eve tries keys from 1 to 7. With a key of 7, the plaintext is “not
very secure”, which makes sense.
Solution

3.2.1 Continued
Table 3.1 Frequency of characters in English
Table 3.2 Frequency of diagrams and trigrams

3.2.1 Continued
Multiplicative Ciphers
In a multiplicative cipher, the plaintext
and ciphertext are integers in Z26; the
key is an integer in Z26*.
Note
Figure 3.10 Multiplicative cipher

3.2.1 Continued
What is the key domain for any multiplicative cipher?
Example 3.7
The key needs to be in Z26*. This set has only 12 members: 1, 3, 5,
7, 9, 11, 15, 17, 19, 21, 23, 25.
Solution
We use a multiplicative cipher to encrypt the message “hello” with
a key of 7. The ciphertext is “XCZZU”.
Example 3.8

3.2.1 Continued
Affine Ciphers
Figure 3.11 Affine cipher

3.2.1 Continued
The affine cipher uses a pair of keys in which the first key is from
Z26* and the second is from Z26. The size of the key domain is
26 × 12 = 312.
Example 3.09
Use an affine cipher to encrypt the message “hello” with the key
pair (7, 2).
Example 3.10

3.2.1 Continued
Use the affine cipher to decrypt the message “ZEBBW” with the
key pair (7, 2) in modulus 26.
Example 3.11
Solution
The additive cipher is a special case of an affine cipher in which
k1 = 1. The multiplicative cipher is a special case of affine cipher in
which k2 = 0.
Example 3.12

3.2.1 Continued
Because additive, multiplicative, and affine ciphers have small key
domains, they are very vulnerable to brute-force attack.
Monoalphabetic Substitution Cipher
A better solution is to create a mapping between each plaintext
character and the corresponding ciphertext character. Alice and
Bob can agree on a table showing the mapping for each character.
Figure 3.12 An example key for monoalphabetic substitution cipher

3.2.1 Continued
We can use the key in Figure 3.12 to encrypt the message
Example 3.13
The ciphertext is

3.2.2 Polyalphabetic Ciphers
In polyalphabetic substitution, each occurrence of a
character may have a different substitute. The
relationship between a character in the plaintext to a
character in the ciphertext is one-to-many.
Autokey Cipher

3.2.2 Continued
Assume that Alice and Bob agreed to use an autokey cipher with
initial key value k1 = 12. Now Alice wants to send Bob the message
“Attack is today”. Enciphering is done character by character.
Example 3.14

Playfair Cipher
• Not even the large number of keys in a
monoalphabetic cipher provides security
• One approach to improving security was to
encrypt multiple letters
• Playfair Cipher is an example

Playfair Key Matrix
• 5X5 matrix of letters based on a keyword
• Fill in letters of keyword (sans duplicates)
• Fill rest of matrix with other letters
• Eg. using the keyword MONARCHY

Encrypting and Decrypting
Plaintext is encrypted two letters at a time
1. If a pair is a repeated letter, insert filler like 'X’
2. If both letters fall in the same row, replace each with
letter to right (wrapping back to start from end)
3. If both letters fall in the same column, replace each
with the letter below it (again wrapping to top from
bottom)
4. Otherwise each letter is replaced by the letter in the

Playfair Key Matrix
• Eg. Using the keyword MONARCHY
• Encrypt: Ballon -> Ba lx lo nx
• Cipher: IB SU PM AW
M O N A R
C H Y B D
E F G I/J K
L P Q S T
U V W X Z

3.2.2 Continued
Playfair Cipher
Figure 3.13 An example of a secret key in the Playfair cipher
Let us encrypt the plaintext “hello” using the key in Figure 3.13.
Example 3.15

Security of Playfair Cipher
• Much improved over monoalphabetic
• Since have 26 x 26 = 676 digrams
• Would need a 676 entry frequency table to analyse
(verses 26 for a monoalphabetic)
• Correspondingly more ciphertext
• Was widely used for many years
– eg. by US & British military in WW1
• It can be broken, given a few hundred letters

Vigenère Cipher
• Simplest polyalphabetic substitution cipher
• Effectively multiple caesar ciphers
• Key is multiple letters long K = k1 k2 ... kd
• ith letter specifies ith alphabet to use
• Use each alphabet in turn
• Repeat from start after d letters in message
• Decryption simply works in reverse

3.2.2 Continued
Vigenere Cipher
We can encrypt the message “She is listening” using the 6-
character keyword “PASCAL”.
Example 3.16

3.2.2 Continued
Using Example 3.18, we can say that the additive cipher is a
special case of Vigenere cipher in which m = 1.
Example 3.18
Table 3.3
A Vigenere Tableau

CS8792 - Cryptography and Network Security

3.2.2 Continued
Hill Cipher
Figure 3.15 Key in the Hill cipher
The key matrix in the Hill cipher needs to
have a multiplicative inverse.
Note

3.2.2 Continued
One of the goals of cryptography is perfect secrecy. A
study by Shannon has shown that perfect secrecy can be
achieved if each plaintext symbol is encrypted with a key
randomly chosen from a key domain. This idea is used in
a cipher called one-time pad, invented by Vernam.
One-Time Pad

3.2.2 Continued
Rotor Cipher
Figure 3.19 A rotor cipher

3.2.2 Continued
Enigma Machine
Figure 3.20 A schematic of the Enigma machine

3-3 TRANSPOSITION CIPHERS
A transposition cipher does not substitute one symbol for
another, instead it changes the location of the symbols.
3.3.1 Keyless Transposition Ciphers
3.3.2 Keyed Transposition Ciphers
3.3.3 Combining Two Approaches
A transposition cipher reorders symbols.
Note

3.3.1 Keyless Transposition Ciphers
Simple transposition ciphers, which were used in the
past, are keyless.
A good example of a keyless cipher using the first method is the
rail fence cipher. The ciphertext is created reading the pattern row
by row. For example, to send the message “Meet me at the park”
to Bob, Alice writes
Example 3.22
She then creates the ciphertext “MEMATEAKETETHPR”.

3.3.1 Continued
Alice and Bob can agree on the number of columns and use the
second method. Alice writes the same plaintext, row by row, in a
table of four columns.
Example 3.23
She then creates the ciphertext “MMTAEEHREAEKTTP”.

3.3.1 Continued
The cipher in Example 3.23 is actually a transposition cipher. The
following shows the permutation of each character in the plaintext
into the ciphertext based on the positions.
Example 3.24
The second character in the plaintext has moved to the fifth
position in the ciphertext; the third character has moved to the
ninth position; and so on. Although the characters are permuted,
there is a pattern in the permutation: (01, 05, 09, 13), (02, 06, 10,
13), (03, 07, 11, 15), and (08, 12). In each section, the difference
between the two adjacent numbers is 4.

3.3.2 Keyed Transposition Ciphers
The keyless ciphers permute the characters by using
writing plaintext in one way and reading it in another
way The permutation is done on the whole plaintext to
create the whole ciphertext. Another method is to divide
the plaintext into groups of predetermined size, called
blocks, and then use a key to permute the characters in
each block separately.

3.3.2 Continued
Alice needs to send the message “Enemy attacks tonight” to Bob..
Example 3.25
The key used for encryption and decryption is a permutation key,
which shows how the character are permuted.
The permutation yields

3.3.3 Combining Two Approaches
Example 3.26
Figure 3.21

Figure 3.22 Encryption/decryption keys in transpositional ciphers
3.3.3 Continued
Keys
In Example 3.27, a single key was used in two directions for the
column exchange: downward for encryption, upward for
decryption. It is customary to create two keys.

Figure 3.23 Key inversion in a transposition cipher
3.3.3 Continued

3.3.3 Continued
Using Matrices
We can use matrices to show the encryption/decryption process for
a transposition cipher.
Figure 3.24 Representation of the key as a matrix in the transposition cipher
Example 3.27

Figure 3.24 Representation of the key as a matrix in the transposition cipher
3.3.3 Continued
Figure 3.24 shows the encryption process. Multiplying the 4 × 5
plaintext matrix by the 5 × 5 encryption key gives the 4 × 5
ciphertext matrix.
Example 3.27

3.3.3 Continued
Double Transposition Ciphers
Figure 3.25 Double transposition cipher

CS8792 - Cryptography and Network Security

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