Polyalphabetic Substitution Ciphers

Introduction

The monoalphabetic (simple) substitution cipher uses only one replacement scheme for all letters of the plain text. Polyalphabetic ciphers use more than one replacement scheme.

The Vigenere Cipher 

Given a letter of the plain text and one letter of the key word, the following table is used for encryption:
 
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
B B C D E F G H I J K L M N O P Q R S T U V W X Y Z A
C C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
D D E F G H I J K L M N O P Q R S T U V W X Y Z A B C
E E F G H I J K L M N O P Q R S T U V W X Y Z A B C D
F F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
G G H I J K L M N O P Q R S T U V W X Y Z A B C D E F
H H I J K L M N O P Q R S T U V W X Y Z A B C D E F G
I I J K L M N O P Q R S T U V W X Y Z A B C D E F G H
J J K L M N O P Q R S T U V W X Y Z A B C D E F G H I
K K L M N O P Q R S T U V W X Y Z A B C D E F G H I J
L L M N O P Q R S T U V W X Y Z A B C D E F G H I J K
M M N O P Q R S T U V W X Y Z A B C D E F G H I J K L
N N O P Q R S T U V W X Y Z A B C D E F G H I J K L M
O O P Q R S T U V W X Y Z A B C D E F G H I J K L M N
P P Q R S T U V W X Y Z A B C D E F G H I J K L M N O
Q Q R S T U V W X Y Z A B C D E F G H I J K L M N O P
R R S T U V W X Y Z A B C D E F G H I J K L M N O P Q
S S T U V W X Y Z A B C D E F G H I J K L M N O P Q R
T T U V W X Y Z A B C D E F G H I J K L M N O P Q R S
U U V W X Y Z A B C D E F G H I J K L M N O P Q R S T
v V W X Y Z A B C D E F G H I J K L M N O P Q R S T U
W W X Y Z A B C D E F G H I J K L M N O P Q R S T U V
X X Y Z A B C D E F G H I J K L M N O P Q R S T U V W
Y Y Z A B C D E F G H I J K L M N O P Q R S T U V W X
Z Z A B C D E F G H I J K L M N O P Q R S T U V W X Y
The letter of the key word is located in the first row and the plain text letter is located in the first column. To find the substitution letter, trace the column of the key letter down to the row of the plain text letter and use the letter found in this cell.

For decryption, the same table may be used in a different way: From the key letter in the first row trace down until you find the cipher text letter. The plain text letter is then found at the first column of that row.

There are three possibilities to use the keyword. CipherClerk's Applet offers a choice for these Operation Modes:

Beaufort cipher

The only difference to the Vigenere cipher is the use of the table: Locate the plain text letter in the first column and trace in the row to the key letter. The substitution letter is found in the first row of this column. Note that enciphering and deciphering a text doesn't differ!

Beaufort / Vigenere Variant Cipher

For this variant of the Beaufort cipher, the role of the key and plain text letters are exchanged. Note that enciphering by Beaufort Variant cipher and deciphering by Vigenere cipher (and vice versa) are identical operations!


Gronsfeld Cipher

The Gronsfeld cipher is just a Vigenere variant using numbers as key. The numbers may form a running key: When the chosen key consists of N digits, the key stream is obtained from a Fibonacci series: K(X) = K(X-N)+ K(X-N+1). CipherClerk's Applet allows you to specify the numeric key by an alphabetic one.


V + I = D ??

Beside the use of a table as given above, there is another way to achieve. If you write the alphabet on two strips of paper you may obtain each line of the Vigenere table by sliding one so that the first letter in the Vigenere table is found under the letter 'A'. By doing so you get a slide rule for doing calculations with characters. This way you will find that V+I is D, not 6! Cryptographers call such a device a St.Cry slide.

Once we've made it down to basic math, we can now describe the ciphers above mathematically. Let P (C) denote a letter of the plain (cipher) text while K denotes the letter of the key word for P (C). Using this, we find:
 

Cipher Enciphering Deciphering
Vigenere C = P + K P = C - K
Beaufort C = K - P P = K - C
Variant C = P - K P = C+ K

Polyalphabetic Substitution Cipher

This cipher uses a Vigenere table built using mixed alphabets. You may choose the operation modes and the substitution schemes as described above. Additionally, you may choose how the mixed alphabets are generated. You may specify under which letter of the plain text alphabet the letters of the "sliding" key shall be written. By default, the 1. letter of the plain text alphabet is used.

You may choose different mixes and keys for generating mixed alphabets for plain text - the first line of the Vigenere table - and cipher text - the rest of the table.

If you choose the PT / CP Interrupted operation mode must enter at least one character into the text field in the "Operation Mode:" line.


GROMARK Cipher

This is a Gronsfeld cipher using a mixed alphabet and a running key. A keyword mixed sequence is used as ciphertext alphabet.


Della Porta Cipher

This cipher the following table for encryption and decryption:
 
KEY A B C D E F G H I J K L M
A, B N O P Q R S T U V W X Y Z
C, D O P Q R S T U V W X Y Z A
E, F P Q R S T U V W X Y Z A B
G, H Q R S T U V W X Y Z A B C
I, J R S T U V W X X Z A B C D
K, L S T U V W X Y Z A B C D E
M, N T U V W X Y Z A B C D E F
O, P U V W X Y Z A B C D E F G
Q, R V W X Y Z A B C D E F G H
S, T W X Y Z A B C D E F G H I
U, V X Y Z A B C D E F G H I J
W, X Y Z A B C D E F G H I J K
Y, Z Z A B C D E F G H I J K L
Enciphering and deciphering are done by the same procedure: The key letter is located in the first column of the table. Then the letter to process (either plain text ot cipher text) is searched in that row. It is substituted by the letter found above - or below - in the row. Obviously, this cipher requires alphabets with an even number of letters.

Origionally, a 22 letter alphabet was used: J was replaced by I, K by Q, V and W by U. ChipherClerk lets you use this alphabet as well.

As for the other polyalphabetic substitution ciphers you may choose one of the operation modes.


Transpositeur à permutations secrètes

This cipher device uses twenty strips containing mixed alphabets: Ten of them hold the plain tex alphabets, the others those of the cipher text. Each of the plain text alphabet strips is linked to one of the cipher text alphabet strips and than entered into the device where the two connected strips may slide freely. There are indicators for plaintext and ciphertext letters. To encrypt a message, the strips are adjust so that the first ten letters of the message apear at the indicator rof the plain text. Then the cipher letters are read from thier indicator.
There are 13 168 189 440 000 possible arangements of the strips, so it may seem pretty secure. However, a competent cryptanalysist will eliminate 13 168 189 439 999 of them wihtin a few hours and read what he is not supposed to be able to read....


To proceed, you may