Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: The Great Cipher

Not Your Average Monoalphabetic Cipher

The Great Cipher used by Louis XIV remained unbroken for 200 years.  What were the factors that led to such a secure cipher?

The father-son team of Antoine and Bonaventure Rossignol invented The Great Cipher while working closely with Louis XIV as his cryptanalysts. Initially, they were mainly code breakers, but their skill gave them the idea to create a much stronger way to encrypt messages. This idea turned into the Great Cipher. This cipher was very useful for the French and no enemy cryptanalysts were able to crack it. Unfortunately, the Rossignols’s death also meant that the Great Cipher’s secrets were lost and any archives encoded using it could no longer be read. Although this was inconvenient for the French, the real struggle would be experienced by future generations of code breakers. Eventually letters encrypted by the Great Cipher were passed on to Étienne Bazeries who worked tirelessly to decipher the letters. The high security of the cipher made it nearly impossible to decode.

The first factor that led to this secure cipher was the amount of characters included. 587 different characters immediately made it clear that the it was not a substitution cipher and later, Étienne also discovered it was not a homophonic cipher (a cipher that replaces letters with a proportional number of symbols to how often that letter is used). Later he would also try to decipher it as a digraph (one number represents a pair of letters), but this also was not correct. The grunt work that decoding the Great Cipher must have required is astonishing because the text says each idea could take Étienne multiple months to prove wrong. Eventually, Étienne was struck with the idea that each number represented a whole syllable. After tirelessly working on this idea, he was able to decode 124-22-125-46-345 as meaning “les ennemis”. This crucial breakthrough led to Étienne’s eventual success despite variations in the cipher and traps laid by the Rossignols. This elaborate cipher truly deserved its name as “The Great Cipher”.

Bazeries’ Quest Against The Great Cipher

The Great Cipher used by Louis XIV implemented a different method of cryptography and ciphering than ever before. The monoalphabetic substitution cipher was too easy to break while the polyalphabetic cipher created by Vigenère took too long to encipher and decode which was not efficient for military operations. The Great Cipher, created by the Rossingols and later cracked by Bazeries, utilized not only letters, but also numbers in the cipher. And the different numbers did not represent letters; they mostly represented syllables. This cipher also included traps. For example, some numbers initiated the deletion of the previous number. Some of the numbers did not represent syllables but single letters. The sophisticated nature of this cipher contributed to its dormancy for two centuries. Yet the ease of deciphering a message ciphered using the Great Cipher was quick enough to be used for military purposes, if the cipher was known. Another characteristic of the Great Cipher that was impressive was that it almost completely paralyzed the use of frequency analysis. Although frequency analysis actually lead to Bazeries cracking of the cipher when he noticed a repeated sequence of numbers. But he then completely guessed what those numbers could mean and he happened to be spot on.

Étienne Bazeries: Ahead of His Time

The Great Cipher, used by Louis XIV, was far more complex than any cipher used in the 17th century. It was not simply a substitution cipher nor a homophone cipher. Étienne Bazeries considered that the Great Cipher could be a digraph, which meant that each number represented a pair of letters instead of a single letter. After months of work, Bazeries came to the conclusion that the cipher was not a digraph. He stuck with the concept that each number represented multiple letters, considering that they could possibly represent syllables. After deciphering two words, les ennemis, Bazeries was able to decipher the rest of the text. Another factor that made the Great Cipher so complex was that some of the numbers did not represent single letters nor syllables. Instead these numbers simply deleted the number before them. The Great Cipher was so far beyond its time period that it took centuries for cryptanalysts to catch up and approach the cipher from a different angle.

Syllable Substitution

The Great Cipher of Louis XIV was truly a remarkable cipher, and its longevity only attests to its success. Antoine and Bonaventure Rossignol were the masterminds behind its brilliance, and with their death brought the end of its effective use. During the time of its use, the Rossignols lived adjacent to Louis XIV, since they were the only ones who could effectively use it. The fact that it took two centuries to crack is beyond remarkable, and it deserves praise.

The key to its success and difficulty was that the plain text was not explicitly the 26 letters of the alphabet. Most monoalphabetic and polyalphabetic substitutions start with the initial 26 letters (a, b, c, … z) as the original plain text and substitute each letter with another letter (or in the case of polyalphabetic ciphers) or maybe a couple letters. But the fact is that the plain text and the cipher text will be limited to the 26 letters of the alphabet, no matter the method of cipher used. This cipher was unique compared to others because the original plain text consisted of all of the individual sounds or syllable used, hence there were many, many more original plain text “letters” compared to an ordinary substitution ciphers. Therefore numbers had to be used rather than letters because there was no alphabet large enough to contain all of the syllables in the language.

Additionally, the Rossignols added traps within the cipher, such as numbers that adjusted adjacent numbers (like removing them entirely). Numbers also often translated to single letters rather than syllables which threw off people who attempted to decipher it. These key differences made the code inefficient since there were so many different “letters” that a person needed to keep track of, but at the same time made it virtually uncrackable to even the most scholarly people. If it were not for the sheer size of the pool of the total numbers used, people would have undoubtedly continued to use it.

The Durability of the Rossignols’ Great Cipher

The fact that the Rossignols’ Great Cipher remained invincible to decryption for over 200 years can be linked to both the complexity of the cipher and its novelty. The 587 different numbers used in the cipher creates thousands of possibilities; with hundreds of substitutions, any combination of multiple letters can be represented by a variety of numbers, and multiple letters or combinations of letters can have more than one number assigned to them. In Simon Singh’s The Code Book, he says that Bazeries spent months testing theories, only to find that they were incorrect (56). Immense time and effort were required to test simple possible theories, and traps were laid by the Rossignol to derail decryption efforts.

Another important factor in the Great Cipher was its ability to render frequency analysis obsolete. The cryptanalysts’ most useful tool was useless against this cipher. In order to decrypt the cipher, cryptanalysts needed to develop a completely new method, not just adapt an old one. In addition, the use of the cipher slowly faded after the death of the Rossignols, so no new messages could be created and examined. The urgency to decrypt the cipher also lessened after the cipher was no longer being used; the value of the messages became purely historical and held no political, military, or strategic value. The industrialization of cryptanalysis occurred after the Great Cipher and focused on monoalphabetic ciphers and messages in circulations, so the Great Cipher remained relevant to historians, but not to those with power and resources.

The Great Headache

The Great Cipher used by King Louis XIV was an extremely strong cipher for several reasons. First, the cipher text included 587 different numbers. This magnitude of possible decipherments was the first line of defense. Additionally, because multiple cipher types had been created by the time the Great Cipher was implemented, there were many more possibilities for the encryption than just the simple monoalphabetic cipher. However, the Rossignols chose not to use any previously created ciphers, vouching instead to devise their own. This creativity further complicated the matter of decipherment. Because the Great Cipher substituted numbers for syllables, any letter-based frequency analysis was useless. This major difference was probably the biggest reason why the cipher stayed unbroken for so long. Once discovering the substitution for syllables, the hard work of decipherment was still far from completion. The next stumbling block came in the form of inconsistency. Some of the numbers stood not for syllables, but for individual letters. Finally, the Rossignols laid “traps”, as Singh refers to them, within the cipher itself. One such example is a number which deletes the previous number. Combining all the individual parts of the Great Cipher results in a code which is devilishly difficult to decipher. Considering all the intricacies of the Great Cipher, it is little wonder that it remained a mystery for two centuries.

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