This document provides an overview of the Caesar cipher, one of the earliest known substitution ciphers. It explains that the Caesar cipher involves shifting each letter of a plaintext message by a set number of positions (the key) in the alphabet to encrypt it. For example, with a shift of 3, A would become D, B would become E, etc. The document includes an example of encrypting the plaintext "ATTACK AT DAWN" with a shift of 3. It also describes how the cipher can be represented mathematically using modular arithmetic.

1. Caesar Cipher
 Presented By:
1. Ali (2020-SE-33)
2. Hashar Ahmed (2020-SE-12)

2. Terms:
 Plaintext
 Is a message to be communicated.
 Ciphertext
 A disguised version of a plaintext.
 Encryption
 The process of turning Plaintext into Ciphertext.
 Decryption
 The process of turning Ciphertext into Plaintext.

3. Caesar Cipher
 One of the earliest known examples of substitution cipher.
 Said to have been used by Julius Caesar to communicate with his army (secretly).
 Each character of a plaintext message is replaced by a character n position down in the alphabet.
 Belongs to Substitution Cipher.

4. Caesar Cipher
Example:
 The first row denotes the plaintext
 Second row denotes the ciphertext
 The ciphertext is obtained by "shifting" the original letter by the N position to the right.
 In this example, it is shifted by 3 to the right.
 A becomes D
 B becomes E
 X becomes A, and so on...
A B C D E … … X Y Z
D E F G H … … A B C

5. Caesar Cipher
 Suppose the following plaintext is to be encrypted:
ATTACK AT DAWN
 By shifting each letter by 3, to the right. Then the resulting ciphertext would be:
DWWDFN DW GDZQ
A B C D E … … X Y Z
D E F G H … … A B C

6. Caesar Cipher
 One could shift other than 3 letters apart.
 The offset (Number of shifts) is called the "Key"
Decryption Process:
 Given that the key is known, just shift back N letter to the left.
Example:
 Ciphertext: WJYZWS YT GFXJ
 Key used: 5
 Plaintext: RETURN TO BASE

7. Caesar Cipher
Math Behind Encryption:
 This can be represented using modular arithmetic.
 Assume that : A = 0, B = 1, C = 2, ..., Y = 24, Z = 25.
 Encryption process can be represented as:
 Such that: e(x) = (x + k) (mod 26)
 X → the plaintext.
 K → the number of shifts (offset).
 26 → There are 26 letters in the alphabet (English alphabet).

8. Caesar Cipher
Math Behind Decryption:
 Can be represented using modular arithmetic.
 Assume that : A = 0, B = 1, C = 2, ..., Y = 24, Z = 25.
 The decryption process can be represented as:
 Such that: e(x) = (x - k) (mod 26).
 X → the plaintext.
 k → the key (number of shifts or offset).
 26 → There are 26 letters in the alphabet (English alphabet).

9. Example
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
 Then have Caesar cipher as:
 c = E(p) = (p + k) mod (26)  12%26  12 = M
 p = D(c) = (c – k) mod (26)  7%26  7 = H
 Example: HOWDY (7,14,22,3,24) encrypted using key k (i.e a shift of 5) is MTBID
Can Define Transformation as:
Mathematically Give Each Letter a number :

10. Thank You