Polyalphabetic Substitution Ciphers Quiz

Polyalphabetic Substitution Ciphers

• A polyalphabetic cipher uses multiple substitution alphabets.
• A sequence of monoalphabetic ciphers (like M1, M2, M3...) encrypts letters in turn.
• A key determines the cipher sequence.
• Each plaintext letter has multiple corresponding ciphertext letters.
• Cryptanalysis is more difficult because letter frequency distribution is flatter.

Vigenère Cipher

• Simplest polyalphabetic substitution cipher.
• Uses a set of Caesar ciphers (Ca, Cb, Cc...).
• Key example: security
• Encrypts each letter using corresponding Caesar cipher, then repeats from start after the key.
• Decryption reverses the process.

Example of Vigenère Cipher

• Keyword: deceptive
• Key: deceptivedeceptivedeceptive
• Plaintext: wearediscoveredsaveyourself
• Ciphertext: ZICVTWQNGRZGVTWAVZHCQYGLMGJ

Vigenère Cipher Key Length

• Key length is 9.
• Consists of 9 Caesar ciphers.
• Plaintext letters at positions 0, 9, 18, 27... are encoded with the same cipher.

Security of Vigenère Ciphers

• Multiple ciphertext letters correspond to each plaintext letter.
• Letter frequencies are obscured but not lost.
• To break Vigenère:
  • Guess the key length.
  • The cipher consists of N Caesar ciphers if the key length is N.
  • Plaintext letters at positions k, k+N, k+2N... are encoded with the same cipher.
  • Attack each individual cipher.

Guessing the Key Length

• Plaintext words separated by multiples of the key length are encoded the same way.
• Look for repeated patterns in the ciphertext to find potential key lengths.
• For example, repeated "VTW" in a ciphertext may suggest a key length of 3 or 9.

Rotor Cipher Machines

• Developed before modern ciphers, rotor machines were common complex ciphers.
• Frequently used in WWII.
• Multiple rotating cylinders (rotors) implement substitution.
• Each rotor change state as it rotates which means it changes the substitution cipher.
• A m-cylinder machine has 26^m different substitutions.
• The Enigma machine is a renowned example.

Rotor Cipher Machine Details

• Each rotor has 26 states (like the alphabet).
• At each state, it has a substitution cipher (wiring).
• Each cylinder rotates to change states according to a different schedule.
• A m-cylinder rotor machine has 26^m different substitutions.

Transposition Ciphers

• Also called permutation ciphers.
• Shuffle plaintext without altering the letters.
• Example: Row Transposition Ciphers

Row Transposition Ciphers

• Plaintext is written row-by-row in a rectangle.
• Ciphertext: Order columns based on a key.
• Key example: 3 4 2 1 5 6 7
• Ciphertext is obtained by writing out the columns in an order determined by the key.

Product Ciphers

• Uses a sequence of substitutions and transpositions.
• Harder to break than substitutions or transpositions alone.
• A bridge between classical and modern ciphers.

Product Cipher Alternative Description

• Substitutions or transpositions alone are insecure due to language characteristics.
• Using multiple ciphers in succession makes them more secure.
• Two substitutions do not create a more complex substitution.
• Two transpositions may create a more complex transposition.
• A substitution followed by a transposition encrypts harder than just substitution or transposition alone.

Unconditional & Computational Security

• A cipher is unconditionally secure if it is secure no matter how much resources (time, space) the attacker has.
• A cipher is computationally secure if breaking it would require so much time that the system is essentially secure despite its possible flaws or weaknesses.

Unconditionally Secure Cipher - Vernam's One-Time Pad

• Key: k₁k₂k₃... is random and used only once.
• Plaintext: m₁m₂m₃...
• Ciphertext: c₁c₂c₃... (c_i = m_i ⊕ k_i)
• Proven to be unconditionally secure.

Steganography

• Hiding a message within another message (like a graphic image).
• Example: Changing least significant bits (LSBs) in an image to hide a message.
• Advantage: Hiding the message's existence.
• Drawback: High overhead.

Test your knowledge on polyalphabetic substitution ciphers, focusing on the Vigenère cipher. This quiz covers the structure, encryption, and decryption processes of the cipher, including examples and key length considerations. Delve into the complexities and cryptanalysis of these ciphers as you enhance your understanding of this cryptographic technique.