Foundations of Security Week6 Lecture

Lecture Outline#

1. Introduction to classical cryptography
2. Caesar Cipher, Monoalphabetic Substitution Cipher
3. Polyalphabetic Cipher - Vigenère Cipher
4. Introduction to symmetric key encryption
5. Overview of cryptanalysis and cryptographic attacks

Learning Outcomes#

By the end of this lecture, students should be able to:

1. Know the various classical cryptographies
2. Explain Caesar Cipher, Monoalphabetic Substitution Cipher, Polyalphabetic Cipher
3. Perform Brute force Attacks on Caesar Cipher
4. Understand the Polyalphabetic Cipher - Vigenère Cipher
5. Understand Symmetric key encryption
6. Understand cryptanalysis and cryptographic attacks

Classical Cryptographies#

Caesar Cipher#

The Caesar Cipher is one of the simplest and oldest methods of encryption. It is a type of substitution cipher, where each letter in the plaintext is shifted a certain number of positions down or up the alphabet.

It works by shifting the letters of the alphabet by a fixed number, called the shift key. For example, a shift of 3 would replace ‘A’ with ‘D’, ‘B’ with ‘E’, and so on.

For example, a shift of 3 would replace ‘A’ with ‘D’, ‘B’ with ‘E’, and so on.

Then the algorithm can be expressed as follows. For each plaintext letter $\textcolor{blue}p$, substitute the ciphertext letter $\textcolor{blue}C$:

$\mathbf{C = E(p, 3) = (p + 3) ~ mod ~ 26}$

A shift may be of any amount, so that the general Caesar algorithm is

$\mathbf{C = E(p, k) = (p + k) ~ mod ~ 26}$

where $\textcolor{blue}k$ takes on a value in the range 1 to 25. The decryption algorithm is simply

$\mathbf{p = D(c, k) = (c − k) ~ mod ~ 26}$

Monoalphabetic Substitution Cipher#

Is a type of substitution cipher in which each letter of the plaintext is replaced by a unique letter of the alphabet. This means that a single letter of the plaintext is always substituted by the same letter of ciphertext, and the same substitution is used throughout the message.

Key Characteristics

1. One-to-One Mapping: Each letter in the plaintext corresponds to exactly one letter in the ciphertext, and vice versa. For example, ‘A’ might be replaced with ‘D’, ‘B’ with ‘Q’, and so on.
2. Fixed Substitution: The substitution pattern remains the same throughout the entire message. If a letter ‘A’ is replaced with ‘D’ in one part of the message, it will be replaced with ‘D’ wherever ‘A’ appears in the plaintext.
3. Key: The cipher is defined by a key, which is a permutation of the alphabet. The key determines the substitution of each letter. For example, the key might look like this:

Encryption Process:

• Step 1: Take the plaintext message.
• Step 2: For each letter in the plaintext, substitute it with the corresponding letter from the ciphertext alphabet according to the key.
• Step 3: The result is the ciphertext, which can be transmitted securely.

Example:

• Plaintext: “HELLO”
• Key (example substitution): A -> Q, B -> W, C -> E, D -> R, E -> T, F -> Y, etc.
• Ciphertext (using the example key): “ITSSG”
• Decryption Process: To decrypt the message, the recipient needs the same key to reverse the substitution, mapping the ciphertext back to the original plaintext.

Polyalphabetic Cipher - Vigenère Cipher#

Symmetric Key Encryption#

Symmetric Key Encryption is a cryptographic method where the same key is used for both encryption and decryption.

In this system, both the sender and the receiver share a secret key, and they use it to transform plaintext (original message) into ciphertext (encrypted message) and vice versa.

Key Characteristics

Single Shared Key:

The key used for encryption and decryption is the same, which is why it is called “symmetric.” Both the sender and receiver must securely share and protect the key.

Encryption and Decryption Process:

• Encryption: The plaintext is transformed into ciphertext using an encryption algorithm and the shared secret key.
• Decryption: The ciphertext is transformed back into plaintext using the same algorithm and key.

Confidentiality:

The security of the system relies on keeping the key secret. If an attacker gains access to the key, they can easily decrypt the message.

Efficiency:

They are generally faster and more efficient than asymmetric key encryption algorithms, making them suitable for encrypting large amounts of data.

They use less computational power and resources compared to asymmetric encryption

Cryptanalysis Attacks#

Cryptanalysis is the study of methods for breaking or undermining the security of cryptographic systems. It involves trying to decipher ciphertext without access to the secret key, in order to retrieve the plaintext or gain other useful information.

Reading Assignment#

Read on the below 4 cryptanalysis attacks