Section 2.5 Polyaphabetic Substitutions
• The monalphabetic ciphers (e.g. shift, affine,
substitution) are vulnerable to frequency
• To increase security, we can change the cipher
alphabet as we are enciphering the message.
• Example 1: Encipher the even letters
according to one scheme and the odd letters
to another…
Polyalphabetic Substitutions
• Definition: A polyalphabetic cipher is a cipher
where different substitution alphabets are
used for various parts of the plaintext.
• Four more famous versions of this are
– The Alberti Cipher Disk
– Thomas Jefferson Cipher Wheel
– German Enigma Cipher Machine
– Vigenere Cipher (we talk about this next)…
Vigenere Cipher
• The Vigenere cipher is a polyalphabetic cipher invented by
the Frenchman Blaise de Vigenere in 1585.
– It was not widely used until the 1800’s when frequency analysis
was used to break the simpler monoalphabetic ciphers.
• Here is how it works:
– Pick a keyword
– Repeatedly write the keyword below the plaintext, one letter of
the keyword associated with one letter of the plaintext.
– Use the Vigenere Cipher Square to cipher the text. (See Mr.
Fisher’s Program, also.)
• The ciphertext letter is found by intersecting the row headed by the
plaintext letter, and the column headed by the keyword letter.
– Example 2: Vigenere cipher…
Decipher Vigenere Cipher
• To decipher a Vigenere cipher:
– On the second row write the ciphertext.
– On the first row write the keyword repeatedly, one
letter above each letter of the ciphertext.
– Read off the ciphertext letter by: (Using Vigenere
• Using the keyword letter to find the row.
• Find the ciphertext letter in that row.
• Go to the top of the column which contains the ciphertext
letter and read off the plaintext letter.
• Example 3: Decipher a message…
Finding the Keyword
• If you know the plaintext and the ciphertext
you can get the keyword:
– Find the plaintext letter across the top of the
Vigenere Square.
– Find the ciphertext letter in that column belonging
to that letter.
– The heading letter to the row containing the
ciphertext letter is the keyword letter.
• Example 4: Find six-letter keyword…!

Polyalphabetic Substitutions