Cryptology: Tools for Polyalphabetic Substitution

In the »pre-machine« age people used three simple tools for ease of polyalphabetic substitution:

There is an even simpler version that doesn't need any tool—except the fingers for counting: the GRONSFELD cipher, called after the count of GRONSFELD who allegedly explained this cipher to the author Gaspar Schott during a voyage from Mainz to Frankfurt in the 17th Century. Its key consists of decimal digits, and each letter is shifted in the alphabet by as many positions as the current digit indicates. An example using the key 3857:

Alphabet Tables

The workflow of the BELLASO cipher using the TRITHEMIUS (»VIGENÈRE«) table was described in the last section.

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
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Q W E R T Z U I O P A S D F G H J K L Y X C V B N M
W E R T Z U I O P A S D F G H J K L Y X C V B N M Q
E R T Z U I O P A S D F G H J K L Y X C V B N M Q W
R T Z U I O P A S D F G H J K L Y X C V B N M Q W E
T Z U I O P A S D F G H J K L Y X C V B N M Q W E R
Z U I O P A S D F G H J K L Y X C V B N M Q W E R T
U I O P A S D F G H J K L Y X C V B N M Q W E R T Z
I O P A S D F G H J K L Y X C V B N M Q W E R T Z U
O P A S D F G H J K L Y X C V B N M Q W E R T Z U I
P A S D F G H J K L Y X C V B N M Q W E R T Z U I O
A S D F G H J K L Y X C V B N M Q W E R T Z U I O P
S D F G H J K L Y X C V B N M Q W E R T Z U I O P A
D F G H J K L Y X C V B N M Q W E R T Z U I O P A S
F G H J K L Y X C V B N M Q W E R T Z U I O P A S D
G H J K L Y X C V B N M Q W E R T Z U I O P A S D F
H J K L Y X C V B N M Q W E R T Z U I O P A S D F G
J K L Y X C V B N M Q W E R T Z U I O P A S D F G H
K L Y X C V B N M Q W E R T Z U I O P A S D F G H J
L Y X C V B N M Q W E R T Z U I O P A S D F G H J K
Y X C V B N M Q W E R T Z U I O P A S D F G H J K L
X C V B N M Q W E R T Z U I O P A S D F G H J K L Y
C V B N M Q W E R T Z U I O P A S D F G H J K L Y X
V B N M Q W E R T Z U I O P A S D F G H J K L Y X C
B N M Q W E R T Z U I O P A S D F G H J K L Y X C V
N M Q W E R T Z U I O P A S D F G H J K L Y X C V B
M Q W E R T Z U I O P A S D F G H J K L Y X C V B N

Writing the standard alphabet in an extra line above the primary alphabet is useful. The use of such a table (with another primary alphabet) was demonstrated before. In that section only the relevant part of the table was given. But it really was a disk cipher.

Attention: What is called »PORTA cipher« in the literature is a special polyalphabetic cipher with some fixed alphabets that are generated in some other way.

Exercise: For deciphering one could use a table that has the primary alphabet as its »headline«. Where lies the charme of this idea?

Cipher Disks

Compiling an alphabet table by hand is a bit tedious. PORTA picked up ALBERTI's and SILVESTRI's idea of a cipher disk. ALBERTI used it with a slightly different background and less systematically. PORTA saw its application for the general disk cipher that uses a primary alphabet and shifted secondary alphabets. Such a disk for example carries the standard alphabet on its outer ring, and the (permuted) primary alphabet on a movable inner ring. The shifted secondary alphabets arise by turning the inner ring: position the current key letter opposite to the plaintext »a« (or more generally to the first letter of the standard alphabet in use). Some pictures:

Compared with the alphabet table the cipher disk has the advantage of easy handling. On the other hand the usage is somewaht more error-prone—the operator easily makes a mistake in not exactly turning the disk.

Who wants to tinker with cipher disks and other simple cipher tools may use a template like this with 26 sectors.

Exercise. Make a cipher disk for use with the BELLASO cipher, and use it for decrypting the ciphertext from I.3.2.

Cipher Slides

Equivalent with a cipher disk, less elegant, but more easily made up, is the cipher slide. It consists of two rows that may be moved alongside each other on paper strips or wooden slats. The first row contains the standard alphabet, the second one the primary alphabet, doubled except the last letter. Example:

This tool is traceable to old England around 1600. In the 19th Century it was routinely used by the French army (»Règle St. Cyr«). The US Army introduced it in 1914 following a proposal by Parker HITT (1877 – 1971). Picture:

An example from 20th Century—although with a slightly more complicated algorithm—are the commercially exceedingly successful Kryha cipher devices. Insufficient cryptographic technique was wrapped in a fancy box and sold in huge quantities.