Polyalphabetic cipher
Encyclopedia
A polyalphabetic cipher is any cipher based on substitution
, using multiple substitution alphabets. The Vigenère cipher
is probably the best-known example of a polyalphabetic cipher, though it is a simplified special case. The Enigma machine
is more complex but still fundamentally a polyalphabetic substitution cipher.
by Leon Battista Alberti around 1467 was believed to be the first polyalphabetic cipher. Alberti used a mixed alphabet to encrypt a message, but whenever he wanted to, he would switch to a different alphabet, indicating that he had done so by including an uppercase letter or a number in the cryptogram. For this encipherment Alberti used a decoder device, his cipher disk
, which implemented a polyalphabetic substitution with mixed alphabets.
Although Alberti is usually considered the father of polyalphabetic cipher, it has been claimed that polyalphabetic ciphers may have been developed by the Arab cryptologist Al Kindi 600 years before Alberti http://waprogramming.com/papers/vol1-no1/(03-08)%20An%20overview%20of%20modern%20cryptography.pdf.
Johannes Trithemius
, in a book published after his death, invented a progressive key polyalphabetic cipher called the Trithemius cipher
. Unlike Alberti's cipher, which switched alphabets at random intervals, Trithemius switched alphabets for each letter of the message. He started with a tabula recta
, a square with 26 alphabets in it (although Trithemius, writing in Latin
, used 24 alphabets). Each alphabet was shifted one letter to the left from the one above it, and started again with A after reaching Z (see image).
Trithemius's idea was to encipher the first letter of the message using the first shifted alphabet, so A became B, B became C, etc. The second letter of the message was enciphered using the second shifted alphabet, etc. Alberti's cipher disk implemented the same scheme. It had two alphabets, one on a fixed outer ring, and the other on the rotating disk. A letter is enciphered by looking for that letter on the outer ring, and encoding it as the letter underneath it on the disk. The disk started with A underneath B, and the user rotated the disk by one letter after encrypting each letter.
The cipher was trivial to break, and Alberti's machine implementation not much more difficult. Key progression in both cases was poorly concealed from attackers. Even Alberti's implementation of his polyalphabetic cipher was rather easy to break (the capitalized letter is a major clue to the cryptanalyst). For most of the next several hundred years, the significance of using multiple substitution alphabets was missed by almost everyone. Polyalphabetic substitution cipher designers seem to have concentrated on obscuring the choice of a few such alphabets (repeating as needed), not on the increased security possible by using many and never repeating any.
The principle (particularly Alberti's unlimited additional substitution alphabets) was a major advance—the most significant in the several hundred years since frequency analysis
had been developed. A reasonable implementation would have been (and, when finally achieved, was) vastly harder to break. It was not until the mid-19th century (in Babbage
's secret work during the Crimean War
and Friedrich Kasiski
's generally equivalent public disclosure some years later), that cryptanalysis
of well-implemented polyalphabetic ciphers got anywhere at all.
Substitution cipher
In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth...
, using multiple substitution alphabets. The 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....
is probably the best-known example of a polyalphabetic cipher, though it is a simplified special case. The Enigma machine
Enigma machine
An Enigma machine is any of a family of related electro-mechanical rotor cipher machines used for the encryption and decryption of secret messages. Enigma was invented by German engineer Arthur Scherbius at the end of World War I...
is more complex but still fundamentally a polyalphabetic substitution cipher.
History
The Alberti cipherAlberti cipher
- Leon Battista Alberti :Created in the 15th century , it was the peak of cryptography at that time. Its inventor was Leon Battista Alberti, an illegitimate son of an Italian nobleman. He was also interested in painting and writing, though he is probably best known for his architecture...
by Leon Battista Alberti around 1467 was believed to be the first polyalphabetic cipher. Alberti used a mixed alphabet to encrypt a message, but whenever he wanted to, he would switch to a different alphabet, indicating that he had done so by including an uppercase letter or a number in the cryptogram. For this encipherment Alberti used a decoder device, his cipher disk
Cipher disk
A cipher disk is an enciphering and deciphering tool developed in 1470 by the Italian architect and author Leon Battista Alberti. He constructed a device, consisting of two concentric circular plates mounted one on top of the other...
, which implemented a polyalphabetic substitution with mixed alphabets.
Although Alberti is usually considered the father of polyalphabetic cipher, it has been claimed that polyalphabetic ciphers may have been developed by the Arab cryptologist Al Kindi 600 years before Alberti http://waprogramming.com/papers/vol1-no1/(03-08)%20An%20overview%20of%20modern%20cryptography.pdf.
Johannes Trithemius
Johannes Trithemius
Johannes Trithemius , born Johann Heidenberg, was a German abbot, lexicographer, historian, cryptographer, polymath and occultist who had an influence on later occultism. The name by which he is more commonly known is derived from his native town of Trittenheim on the Mosel in Germany.-Life:He...
, in a book published after his death, invented a progressive key polyalphabetic cipher called the Trithemius cipher
Trithemius cipher
The Trithemius cipher is a polyalphabetic cipher invented by the German author and monk Johannes Trithemius in the 15th century. The cipher was published in his book Polygraphia, which is credited with being the first published work on cryptology. It uses a letter square with the 26 letters of the...
. Unlike Alberti's cipher, which switched alphabets at random intervals, Trithemius switched alphabets for each letter of the message. He started with a tabula recta
Tabula recta
In cryptography, the tabula recta is a square table of alphabets, each row of which is made by shifting the previous one to the left...
, a square with 26 alphabets in it (although Trithemius, writing in Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
, used 24 alphabets). Each alphabet was shifted one letter to the left from the one above it, and started again with A after reaching Z (see image).
Trithemius's idea was to encipher the first letter of the message using the first shifted alphabet, so A became B, B became C, etc. The second letter of the message was enciphered using the second shifted alphabet, etc. Alberti's cipher disk implemented the same scheme. It had two alphabets, one on a fixed outer ring, and the other on the rotating disk. A letter is enciphered by looking for that letter on the outer ring, and encoding it as the letter underneath it on the disk. The disk started with A underneath B, and the user rotated the disk by one letter after encrypting each letter.
The cipher was trivial to break, and Alberti's machine implementation not much more difficult. Key progression in both cases was poorly concealed from attackers. Even Alberti's implementation of his polyalphabetic cipher was rather easy to break (the capitalized letter is a major clue to the cryptanalyst). For most of the next several hundred years, the significance of using multiple substitution alphabets was missed by almost everyone. Polyalphabetic substitution cipher designers seem to have concentrated on obscuring the choice of a few such alphabets (repeating as needed), not on the increased security possible by using many and never repeating any.
The principle (particularly Alberti's unlimited additional substitution alphabets) was a major advance—the most significant in the several hundred years since frequency analysis
Frequency analysis
In cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers....
had been developed. A reasonable implementation would have been (and, when finally achieved, was) vastly harder to break. It was not until the mid-19th century (in Babbage
Charles Babbage
Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer...
's secret work during the Crimean War
Crimean War
The Crimean War was a conflict fought between the Russian Empire and an alliance of the French Empire, the British Empire, the Ottoman Empire, and the Kingdom of Sardinia. The war was part of a long-running contest between the major European powers for influence over territories of the declining...
and Friedrich Kasiski
Friedrich Kasiski
Major Friedrich Wilhelm Kasiski was a Prussian infantry officer, cryptographer and archeologist. Kasiski was born in Schlochau, West Prussia .-Military service:...
's generally equivalent public disclosure some years later), that cryptanalysis
Cryptanalysis
Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...
of well-implemented polyalphabetic ciphers got anywhere at all.
See also
- Topics in cryptography