Polygraphic substitution
Encyclopedia
A polygraphic substitution is a cipher in which a uniform substitution is performed on blocks of letters. When the length of the block is specifically known, more precise terms are used: for instance, a cipher in which pairs of letters are substituted is bigraphic.
As a concept, polygraphic substitution contrasts with monoalphabetic (or simple) substitutions in which individual letters are uniformly substituted, or polyalphabetic substitutions in which individual letters are substituted in different ways depending on their position in the text. In theory, there is some overlap in these definitions; one could conceivably consider a Vigenère cipher
with an eight-letter key to be an octographic substitution. In practice, this is not a useful observation since it is far more fruitful to consider it to be a family of eight monoalphabetic substitutions.
devised the first bigraphic substitution. However, it was nothing more than a matrix of symbols. In practice, it would have been all but impossible to memorize, and carrying around the table would lead to risks of falling into enemy hands.
In 1854, Charles Wheatstone
came up with the Playfair cipher
, a keyword-based system that could be performed on paper in the field. This was followed up over the next fifty years with the closely related four-square
and two-square
ciphers, which are slightly more cumbersome but offer slightly better security.
In 1929, Lester S. Hill
developed the Hill cipher
, which uses matrix algebra to encrypt blocks of any desired length. However, encryption is very difficult to perform by hand for any sufficiently large block size, although it has been implemented by machine or computer. This is therefore on the frontier between classical and modern cryptography.
As a concept, polygraphic substitution contrasts with monoalphabetic (or simple) substitutions in which individual letters are uniformly substituted, or polyalphabetic substitutions in which individual letters are substituted in different ways depending on their position in the text. In theory, there is some overlap in these definitions; one could conceivably consider a Vigenère cipher
Vigenère cipher
The Vigenère cipher is a method of encrypting alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword. It is a simple form of polyalphabetic substitution....
with an eight-letter key to be an octographic substitution. In practice, this is not a useful observation since it is far more fruitful to consider it to be a family of eight monoalphabetic substitutions.
Specific ciphers
In 1563, Giambattista della PortaGiambattista della Porta
Giambattista della Porta , also known as Giovanni Battista Della Porta and John Baptist Porta, was an Italian scholar, polymath and playwright who lived in Naples at the time of the Scientific Revolution and Reformation....
devised the first bigraphic substitution. However, it was nothing more than a matrix of symbols. In practice, it would have been all but impossible to memorize, and carrying around the table would lead to risks of falling into enemy hands.
In 1854, Charles Wheatstone
Charles Wheatstone
Sir Charles Wheatstone FRS , was an English scientist and inventor of many scientific breakthroughs of the Victorian era, including the English concertina, the stereoscope , and the Playfair cipher...
came up with the Playfair cipher
Playfair cipher
The Playfair cipher or Playfair square is a manual symmetric encryption technique and was the first literal digraph substitution cipher. The scheme was invented in 1854 by Charles Wheatstone, but bears the name of Lord Playfair who promoted the use of the cipher.The technique encrypts pairs of...
, a keyword-based system that could be performed on paper in the field. This was followed up over the next fifty years with the closely related four-square
Four-square cipher
The four-square cipher is a manual symmetric encryption technique. It was invented by famous French cryptographer Felix Delastelle.The technique encrypts pairs of letters , and thus falls into a category of ciphers known as polygraphic substitution ciphers...
and two-square
Two-square cipher
The Two-square cipher, also called double Playfair, is a manual symmetric encryption technique. It was developed to ease the cumbersome nature of the large encryption/decryption matrix used in the four-square cipher while still being slightly stronger than the Playfair cipher.The technique...
ciphers, which are slightly more cumbersome but offer slightly better security.
In 1929, Lester S. Hill
Lester S. Hill
Lester S. Hill was an American mathematician and educator who was interested in applications of mathematics to communications. He received a Bachelor's degree from Columbia College and a Ph.D. from Yale University . He taught at the University of Montana, Princeton University, the University of...
developed the Hill cipher
Hill cipher
In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical to operate on more than three symbols at once. The following discussion assumes an elementary...
, which uses matrix algebra to encrypt blocks of any desired length. However, encryption is very difficult to perform by hand for any sufficiently large block size, although it has been implemented by machine or computer. This is therefore on the frontier between classical and modern cryptography.