Caesar Cipher

The Foundation of Substitution Cryptography

Julius Caesar's Secret Communication Method

Historical Origins

Julius Caesar (100-44 BCE) used this cipher to communicate with his generals during military campaigns, shifting each letter by 3 positions in the alphabet.

Historical Context:

Roman Empire: Need for secure military communication
Literacy Rates: Most people couldn't read, adding security
Simple Implementation: Could be done by hand without tools
Effective for its Time: Adequate against contemporary threats

Caesar Cipher Definition

Caesar Cipher is a type of substitution cipher where each letter in the plaintext is shifted a certain number of places down or up the alphabet.

Key Characteristics:

Shift Cipher: Also known as shift cipher
Monoalphabetic: One alphabet used for entire message
Symmetric: Same key for encryption and decryption
Additive Cipher: Each letter replaced by letter k positions ahead

Caesar Cipher Algorithm

Encryption Formula:

C = (P + K) mod 26

C = Ciphertext letter position
P = Plaintext letter position (A=0, B=1, ..., Z=25)
K = Key (shift value)

Decryption Formula:

P = (C - K) mod 26

Alphabet Shift Example (K=3)

Original Alphabet:
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

Shifted Alphabet (Shift +3):
D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 0 1 2

Mapping:
A→D, B→E, C→F, D→G, E→H, F→I, G→J, H→K, I→L, J→M
K→N, L→O, M→P, N→Q, O→R, P→S, Q→T, R→U, S→V, T→W
U→X, V→Y, W→Z, X→A, Y→B, Z→C

Encryption Example

Plaintext: "HELLO WORLD"
Key (Shift): 3

Step-by-step Encryption:
H (7) + 3 = 10 = K
E (4) + 3 = 7 = H
L (11) + 3 = 14 = O
L (11) + 3 = 14 = O
O (14) + 3 = 17 = R

W (22) + 3 = 25 = Z
O (14) + 3 = 17 = R
R (17) + 3 = 20 = U
L (11) + 3 = 14 = O
D (3) + 3 = 6 = G

Ciphertext: "KHOOR ZRUOG"

Decryption Example

Ciphertext: "KHOOR ZRUOG"
Key (Shift): 3

Step-by-step Decryption:
K (10) - 3 = 7 = H
H (7) - 3 = 4 = E
O (14) - 3 = 11 = L
O (14) - 3 = 11 = L
R (17) - 3 = 14 = O

Z (25) - 3 = 22 = W
R (17) - 3 = 14 = O
U (20) - 3 = 17 = R
O (14) - 3 = 11 = L
G (6) - 3 = 3 = D

Plaintext: "HELLO WORLD"

Handling Wrap-Around

Problem: What happens when we go past Z?

Example with Shift 3:

X (23) + 3 = 26 mod 26 = 0 = A
Y (24) + 3 = 27 mod 26 = 1 = B
Z (25) + 3 = 28 mod 26 = 2 = C

Decryption Wrap-Around:
A (0) - 3 = -3 mod 26 = 23 = X
B (1) - 3 = -2 mod 26 = 24 = Y
C (2) - 3 = -1 mod 26 = 25 = Z

Rule: If result is negative, add 26

Different Shift Values

Message: "ATTACK"

Shift 1: BUUBDL
Shift 5: FYYFHP
Shift 10: KDDKMU
Shift 13: NGGNPX (ROT13)
Shift 20: UFFUGE
Shift 25: ZSSZBJZ

Note: Shift 0 = original text
Note: Shift 26 = same as shift 0

ROT13 - Special Case

ROT13: Caesar cipher with shift of 13, has special property that encryption and decryption use the same operation.

Why ROT13 is Special:
26 ÷ 2 = 13

Applying ROT13 twice returns original text:
HELLO → URYYB → HELLO

Modern Uses:
• Hide spoilers in online forums
• Obscure potentially offensive content
• Simple text obfuscation
• Not for real security!

Programming Implementation

Python Implementation:

def caesar_encrypt(text, shift):
    result = ""
    for char in text:
        if char.isalpha():
            ascii_offset = 65 if char.isupper() else 97
            shifted = (ord(char) - ascii_offset + shift) % 26
            result += chr(shifted + ascii_offset)
        else:
            result += char
    return result

Usage:
caesar_encrypt("HELLO", 3) → "KHOOR"

Breaking Caesar Cipher

Frequency Analysis Attack:

Caesar cipher preserves letter frequencies
Most common letter in English is 'E'
Find most frequent letter in ciphertext
Calculate shift from 'E' to that letter

Example:
If 'H' is most frequent in ciphertext:
E → H means shift of 3
Try decryption with shift -3

Brute Force Attack

Small Key Space: Only 25 possible keys (excluding 0)

Ciphertext: "KHOOR"

Shift 1: JGNNQ
Shift 2: IFMMP
Shift 3: HELLO ← Readable!
Shift 4: GDKKN
Shift 5: FCJJM
...

Result: Can try all possibilities in seconds

Security Weaknesses

Small Key Space: Only 25 possible keys
Frequency Preservation: Statistical patterns maintained
Pattern Recognition: Word patterns remain visible
Known Plaintext: One word can reveal entire key
No Key Distribution: Key must be shared beforehand

Conclusion: Caesar cipher provides no real security against modern cryptanalysis

Caesar Cipher Variations

Historical Improvements:

Keyword Caesar: Shift based on keyword letters
Progressive Caesar: Increase shift for each letter
Random Caesar: Different shift for each letter
Affine Cipher: Combine shift with multiplication

Modern Context: These variations led to development of polyalphabetic ciphers like Vigenère

Educational Importance

Why Study Caesar Cipher?

Foundation Concepts: Introduces substitution cryptography
Modular Arithmetic: Teaches basic mathematical operations
Cryptanalysis: Simple to attack and understand weaknesses
Historical Context: Shows evolution of cryptography
Programming Practice: Easy to implement and experiment

Modern Uses

Legitimate Uses Today:

Education: Teaching cryptography basics
Puzzles: Word games and brain teasers
Obfuscation: Simple text hiding (not security)
CTF Competitions: Capture-the-flag challenges

Warning: Never use Caesar cipher for actual security purposes!

Try It Yourself

Exercise 1: Decrypt this message (Caesar cipher)
"WKH TXLFN EURZQ IRA"

Exercise 2: Encrypt your name with shift 5

Exercise 3: Find the key for this ciphertext:
"EBIIL ILDPH"
(Hint: Common greeting)

Tools:
• Online Caesar cipher tools
• Write your own program
• Do it by hand with alphabet wheel

Key Takeaways

Caesar cipher is simplest form of substitution cipher
Uses fixed shift value for entire alphabet
Easy to implement but very insecure
Vulnerable to frequency analysis and brute force
Important for understanding cryptographic principles
Led to development of more complex ciphers

Remember: Historical significance ≠ Modern security

Thank You

Questions & Discussion

Next: Columnar Transposition Cipher