Lecture 2 - Classical Encryption Techniques

Question 1

What are Classical Encryption Techniques?

Answer 1

• Recall: secret key ciphers use a secret key for encryption
• Almost all secret key ciphers (no matter how complicated) are essentially a combination of two simple techniques:
• Substitution: replace characters of plaintext by other characters
  
  • Example: Rot-n (also called Caesar cipher), which replaces each letter with a letter n positions down the alphabet
• Transposition: permuting order of the plaintext characters

Question 2

Give an example of a Monoalphabetic cipher?

Answer 2

• Recall Rot-n: shift letters n positions
  
  • Rot-n is easy to break
  • The search space is small (only 25 possible key values)
• Each letter shifted by the same fixed amount
• 26 Possible different substitutions

Question 3

What is a weekness of Monoalphabetic ciphers?

Answer 3

• Weakness of monoalphabetic ciphers: letter frequency remains
  
  • In normal English, different letters have different frequencies
  • If you are the attacker and check that “q” ~ 13% in the ciphertext, what would you guess?
  • Given enough ciphertext, these statistics can aid cryptanalysis
• Ways to lessen the survival of plaintext structures
  
  • Encrypts a letter into a number of ciphertext symbols
  • Encrypts multiple letters of plaintext as a unit
  • Use multiple cipher alphabets

Question 4

What is a Polyalphabetic Cipher and give an example of one?

Answer 4

• Polyalphabetic cipher
  
  • A set of monoalphabetic ciphers is used
  • Some rule determines which to be applied to a particular position
• Vigenère cipher: generalize the rotate cipher by shifting different plaintext letters by different amounts
  
  • Shift amount determined by the letter in the key (a: shift 0, b: shift 1, …, z: shift 25)
  • Repeat the key if necessary

Question 5

Weakness of Vigenère - How to decrypt & how to break Vigenère?

Answer 5

• How to decrypt?
  
  • Reverse process of encryption
• How to break Vigenère?
  
  • Observation: Repeated plaintext patterns separated by integer multiples of key length results in repeated ciphertext patterns

Question 6

Weakness of Vigenère - What are the 3 steps in breaking Vigenère?

Answer 6

1) Attacker looks for repeated ciphertext patterns and guess key length
2) If (say) key length = 9, the 1st, 10th, 19th, … letter is encrypted using same key letter
3) The problem reduces to solving a number of monoalphabetic ciphers

• Break each such monoalphabetic cipher as before
• Combine results

Question 7

What is an Autokey Version of Vigenère?

Answer 7

• The idea of appending plaintext as a key
• However still there are statistical relationships remaining

Question 8

What is One Time Pad?

Answer 8

• Use a truly random key that is as long as the message
• An unconditionally secure type of cipher
  
  • A brute force attack will fail: you will decrypt into many possible plaintexts
  • There is no way to distinguish which is the correct plaintext

Question 9

Why is a One Time Pad Unconditionally Secure?

Answer 9

• There are no statistical relationship between plaintext and ciphertext
  
  • The ciphertext contains no information about the plaintext
  • In fact, there is always a key to decrypt into whatever plaintext you want
• However, usually not feasible in practice
  
  • Need huge amount of random numbers
  • How to securely distribute the secret key, which is as long as the message?

Question 10

What is Transposition Ciphers?

Answer 10

• Change ordering of letters
• Example: writing letters in columns (“rail fence”)
• Better to have permuting columns
  
  • Using key e.g. 2413
• How to decrypt?
  
  • Easy to cryptanalyze (frequencies unchanged)
  • Can combine with substitution ciphers