Caesar Cipher and Frequency Analysis

Introduction

• Lecture covers cracking Caesar Cipher using frequency analysis.
• Utilizes source code from a previous lecture.

Frequency Analysis

• Objective: Analyze ciphertext to detect letter frequency.
• Method:
  • Iterate through the ciphertext.
  • Count frequency of each letter.
  • Use a dictionary where:
    • Key = character.
    • Value = number of occurrences.

Plotting Frequency Distribution

• Use pylab to plot the distribution.
• Focus on the second most frequent letter because:
  • Most frequent is often whitespace.

Calculating the Cipher Key

• Steps:
  1. Calculate relative frequency distribution of ciphertext letters.
  2. Identify the second most frequent letter.
  3. Determine the key using:
     • Key = Value of second most frequent letter - Value of 'E'.
• Example:
  • Suppose the most frequent letter is 'I'.
  • English texts often have 'E' as the most frequent letter.
  • Transformation results: 'E' -> 'I', 'F' -> 'J', etc.
  • Key is 4 (shift right by 4).

Testing the Decryption

• Decryption with the identified key should yield the original plaintext.
  • Example text: "My name is Marshal Sir, I'm from Budapest, Hungary."
• Special characters are transformed but don't affect the text integrity.

Conclusion on Frequency Analysis

• Allows identifying the Caesar cipher key via relative frequency.
• Shows the distance between letters to determine the shift required.

Security of Caesar Cipher

• Multiple Caesar encryptions (e.g., key 2 then key 3) do not increase security.
  • Equivalent to a single Caesar encryption with key 5.
• Alternative algorithms:
  • Data Encryption Standard (DES).
  • Advanced Encryption Standard (AES).

Conclusion

• Frequency analysis exploits information leakage in letter distribution.
• Caesar cipher's vulnerability lies in predictable letter frequency patterns.
• Further encryptions don't enhance security for Caesar cipher.

End of Lecture