Frequency Analysis – in Cryptography

What You’ll Learn 📚

• Understand the concept of frequency analysis and its role in cryptography
• Learn key terminology and definitions
• Explore simple to complex examples with step-by-step explanations
• Common questions and troubleshooting tips
• Hands-on practice exercises

Introduction to Frequency Analysis

Frequency analysis is a fascinating technique used in cryptography to break ciphers by studying the frequency of letters or groups of letters in a ciphertext. It’s like being a detective, looking for clues hidden in the text! 🕵️‍♂️

Core Concepts

At its core, frequency analysis relies on the fact that in any given piece of text, certain letters and combinations of letters appear with predictable frequencies. For example, in English, the letter ‘E’ is the most common. By analyzing these frequencies, we can make educated guesses about the original message.

Key Terminology

• Plaintext: The original message before encryption.
• Ciphertext: The encrypted message.
• Frequency: How often a particular letter or group of letters appears.

Simple Example: Letter Frequency in English

# Simple frequency analysis example in Python
text = "hello world"
frequency = {}

# Count the frequency of each letter
for letter in text:
    if letter in frequency:
        frequency[letter] += 1
    else:
        frequency[letter] = 1

print(frequency)

Progressively Complex Examples

Example 1: Frequency Analysis on a Simple Cipher

# Frequency analysis on a simple substitution cipher
ciphertext = "khoor zruog"
frequency = {}

for letter in ciphertext:
    if letter in frequency:
        frequency[letter] += 1
    else:
        frequency[letter] = 1

print(frequency)

Example 2: Decrypting with Frequency Analysis

# Decrypting a simple substitution cipher using frequency analysis
ciphertext = "khoor zruog"
frequency = {}

for letter in ciphertext:
    if letter in frequency:
        frequency[letter] += 1
    else:
        frequency[letter] = 1

# Assume 'k' -> 'h', 'h' -> 'e', 'o' -> 'l', 'r' -> 'o', 'z' -> 'w', 'u' -> 'r', 'g' -> 'd'
key = {'k': 'h', 'h': 'e', 'o': 'l', 'r': 'o', 'z': 'w', 'u': 'r', 'g': 'd'}
plaintext = "".join(key.get(c, c) for c in ciphertext)

print(plaintext)

Example 3: Frequency Analysis on Larger Text

# Frequency analysis on a larger piece of text
text = "the quick brown fox jumps over the lazy dog"
frequency = {}

for letter in text:
    if letter in frequency:
        frequency[letter] += 1
    else:
        frequency[letter] = 1

print(frequency)

Common Questions and Answers

1. What is frequency analysis used for?

   It’s used to break ciphers by analyzing the frequency of letters in a ciphertext.

2. Why is ‘E’ the most common letter in English?

   Due to its frequent use in common words and grammatical structures.

3. Can frequency analysis break all ciphers?

   No, it’s most effective against simple substitution ciphers.

4. How can I practice frequency analysis?

   Try encrypting simple messages and analyzing their frequencies!

5. What are common pitfalls?

   Assuming frequencies are the same across different languages or texts.

Troubleshooting Common Issues

If your frequency analysis isn’t working, check if the text is too short or if you’re using the wrong language frequency assumptions.

Remember, practice makes perfect! Try analyzing different texts to get a feel for frequency patterns.

Practice Exercises

• Encrypt a message using a simple substitution cipher and perform frequency analysis on it.
• Try frequency analysis on a paragraph from a book and compare it to known letter frequencies.
• Create a program that automatically suggests possible plaintexts based on frequency analysis.

Keep experimenting and have fun with it! 🎉