Cryptography

The History and Mathematics of Codes and Code Breaking

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Unbreakable 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 Great Cipher, invented by Antoine and Bonaventure Rossignol, was one of the toughest codes to decipher. There are some very important factors to consider when trying to understand why it may have taken so long for someone to crack it. First of all, Antoine got his recognition for deciphering the letter that resulted in a victory for the French. With his work in cryptanalysis he and his son were appointed to the senior positions in the court, so by this time he has already established his reputation as being one of the best cryptanalysts in Europe. His expertise gives him an advantage because he can recognize the weaknesses in ciphers, therefore when he has to create his own, he would know how to make it indecipherable. Of course, this is relative because ciphers can only stay indecipherable for so long before new methods are developed by cryptanalysts to break them. Second, it is usually a weakness to have a long cipher text because it gives the other person a better chance to recognize patterns, however, this cipher had thousands of symbols with only 587 of them being different. This only makes it a lot more difficult for someone to decipher it because it gives them too much information to work with which instead of showing a pattern, creates confusion. Finally, the more time that passes, the harder it is for someone to decipher a text because of lack of contextual clues. When it is the same time period, there is a better chance to crack a cipher text because you would be fully immersed in the linguistics of that society. Since language evolves over time it is best to try to decipher a code as soon as possible. Because of the complexity of the Great Cipher it did take a lot of dedication and persistence for Bazeries to finally crack it after 200 years.

Deciphering the Great Cipher

For an impressive two-hundred years, the Great Cipher of Louis XIV thwarted several generations of accomplished cryptanalysts – a surprising feat, given that it did so through the manipulation of a substitution cipher. The cipher was created by the son-and-father pair of Antoine and Bonaventure Rossignal, who were recognized by King Louis XIV for their cryptological prowess. Their cipher was so secure that upon their deaths, decipherment of the French archives became impossible for the following two centuries. In 1890, however, Commandant  Etienne Bazeries, a distinguished expert of the French Army’s Cryptographic Department, began a successful three year endeavor of cracking the 17th-century code.

Despite Commandant Bazeries’ success in deciphering the Great Cipher of Louis XIV, the cipher can be termed “secure,” for it served its purpose well over its intended lifespan. Its success can be attributed to several ingenious cryptographic techniques that the Rossignal’s implemented into the cipher. The superficial level of complexity in the cipher is found in its range of representative numbers, of which there were 587, altogether representing only 26 letters. The wide range of numbers thus circumvented the technique of frequency analysis in its most basic application, for each letter would be represented by more than a single number. Realizing this, Bazeries applied frequency analysis in search of French diagraphs, with which he had no success. Frequency analysis proved effective only in the search of syllabic combinations, meaning that the cipher was constructed entirely from syllables. This characteristic probably grants the cipher most of its security. Because syllables exist in such variety, can be composed of one, two, or three letters of the English alphabet, and have less obvious patterns, it is considerably difficult to identify an applicable permutation of the assumed cipher. Moreover, the Rossignal’s integrated traps within the cipher to mislead a cryptanalyst from deducing the cipher-text. One trap, for example, included numbers that would essentially remove the number prior to it.

The use of syllabic substitution as well as the traps employed by the Rossignal’s certainly attributed to the considerable success of the Great Cipher of Louis XIV. However, as history has demonstrated time and time again, decipherment is only a matter of time.

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What's So "Great" About the Great Cipher?

The Great Cipher was created by the Rossignols in the 17th century and remained unbroken for the next two centuries due to a number of security features that made it nearly unbreakable. When an expert French cryptographer Bazeries got his hands on letters that were enciphered using the Great Cipher, he spent the next three years trying to break the code. Through his efforts we learned just how secure the cipher really was. The pages of the letter he was trying to decipher contained thousands of numbers but only 587 unique ones were used. At first, Bazzaries assumed that the extra numbers were just homophones, meaning that multiple numbers represented the same letter. After months of trying this method, he decided that the Great Cipher was not a homophonic cipher and moved onto the next idea. He tried to break the code as if it was a digraph, meaning that each number corresponded to a pair of letters. He tried to use frequency analysis on pairs of letters but this failed as well. He then tried a different form of the digraph idea in which each number represented a syllable. After he used frequency analysis on the syllables most used in the French language he found that the phrase "les ennemis" appeared many times on each page. When he replaced every number that corresponded with these syllables he was able to complete the partially completed words and solve the message. While he was solving the message, he was stumped many times because the Rossingols had placed traps in the cipher that were meant to trip up any people trying to break the code. For example, some numbers represented single letters instead of a syllable and to make the cipher even more complicated one of the numbers represented neither a letter nor a syllable, but actually deleted the previous number. It is easy to see why the Great Cipher went unsolved for 200 years because it was so revolutionary in the techniques it used to keep out prying eyes seeking the information held within the cipher.

The Great Cipher: 200 Years of Security

Louis XIV used the Great Cipher, invented by Antoine and Bonaventure Rossignol, throughout the seventeenth century. Following the death of the Rossignols, The Great Cipher remained an unsolved mystery until the nineteenth century, when new texts encrypted by The Great Cipher were discovered and passed on to a French cryptographer Bazeries. Bazeries struggled with the cipher for years, but eventually was able to successfully decipher several key historical messages and crack The Great Cipher.

The Great Cipher utilized 587 different numbers and was not a homophonic cipher, as Bazeries found after many failed attempts. Bazeries then explored the idea that the Great Cipher was based off of digraphs, or pairs of letters. Although this idea was wrong, it ultimately led him to his discovery that The Great Cipher paired numbers to syllables. The cipher proved to be even more complicated as certain numbers stood for single letters only while others stood for syllables. There were also tricks embedded in the cipher; for example, certain numbers meant that the number before it should be deleted.

The Great Cipher was protected for 200 years due to its great complexity and ingenuity for the time period. The manipulation of syllables as opposed to letters was revolutionary in the cryptography world. The added complexity through the use of single letters and nulls made Bazeries’s task even more difficult. The Great Cipher was a remarkably secure cipher that stumped the finest cryptographers for 200 years.

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.

The "Unbreakable" Code

Louis XIV’s code was one that was not deciphered for over 200 years. It used 587 number codes which represented letters and syllables, among other things. The cypher was created by Antoine and Bonaventure Rossignol as a means to keep military, economic, and other personal information hidden.
The cypher however did not use a standard substitution alphabet, as could be discovered by the fact that there were 587 number codes. Commandant Etienne Bakeries, who was an expert in military code breaking, devoted himself to trying to break Louis XIV’s cypher in the 1890’s. He first discovered that the codes did not represent a homophone alphabet, which would use multiple symbols for the same letter to remove the use for frequency analysis. Next he discovered that the cypher did not use a digraph, or each symbol representing a pair of letters. Bakeries’ first major breakthrough came in recognizing a cluster of numbers that was repeated often. He found this to mean “les ennemis”, with the numbers representing syllables in the French language. Little by little he was able to begin solving for more letters, followed by some words, which lead to eventually solving the entire code.
It may seem that the cypher in fact failed, but one has to remember, a cypher’s effectiveness doesn’t come from if it can be solved, but actually on if it can’t be solved in time to be able to use the knowledge against the author. 200 years later, the cypher had done its job and was already obsolete.

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 Cipher Eludes Great Minds

The Great Cipher was elusive to even the greatest scholars for more than two centuries, creating a whole span of encrypted letters containing enigmatic answers to some of the biggest speculations in history. When the breakthrough in the pattern of the cipher came in 1983 at the hands of Bazeries, the reasons the cipher was exponentially difficult to crack were revealed.

Not only did Bazeries discover that there were 587 different numbers in total, but he also learned after painstaking exploration that the numbers were not homophones. The simple fact that the Great Cipher did not follow the common practice of substituting one or multiples numbers for a single letter further complicated the ability for cryptanalysts to crack it. Furthermore, the Great Cipher was additionally not combinations of double letters indicated by numbers, but instead contained numbers that represented the syllables in the French language.

The Rossingols were not secure in simply allowing numbers to represent syllables. To further complicate the cipher, the number of digits in the numbers representing each syllable did not correspond to the number of letters in each syllable. For example, in the first word Bazeries decrypted, "les ennemis," while the three digit number 124 represents the syllable "les", three digit numbers also represent "ne" and "s", 125 and 345, respectively. The Rossingols additionally created numbers that represented not a syllable, but deletion of the previously stated syllable.

Together with the death of the Rossingols before the secrets of the cipher could be revealed, these factors created an entirely secure cipher. One so secure it would take the human race an additional two hundred years of discovery to crack.

 

 

Cipher Complexity of the Great Cipher

The Great Cipher, created by Antoine and Bonaventure Rossignol was, at its time, one of the greatest ciphers ever made. Cryptanalysists for 200 years worked to break the secrets hidden in the Rossignol's cipher, but it was only until Étienne Bazeries, a French expert in cryptography, spent three years tirelessly working on this cipher that it was finally broken. At that time, cryptanalysists had discovered the secret of frequency analysis to crack monoalphabetic substitution ciphers and had even discovered how to decipher homophonic substitution ciphers by looking at the unique character each letter in the English alphabet has.

The Rossignols' cipher built on these techniques but made cryptanalysis exponentially harder by making a few adjustments to the old techniques. The Rossignols, instead of assigning multiple numbers to the most common letters as in homophonic substitution, assigned multiple three digit numbers to the most common syllables. This made frequency analysis, though not impossible, much harder and more complex.

Bazeries, who finally cracked the cipher, was only able to discover their methods after three years of many trials and errors. Bazeries first thought the cipher might be a regular homophonic cipher, then perhaps a similar cipher with pairs of letters represented by numbers. After many months of educated guesses, Bazeries finally was able to discover one word, "les enemis," by using advanced frequency analysis but with French syllables instead of words.

This cipher was much harder to crack than its predecessors because of the use of syllables instead of letters. The Rossignols complicated their system even more by adding some numbers as syllables and some as single letters. They also made their cipher harder to crack by adding "traps" such as a number that represented no syllable or letter at all, but rather the deletion of the previous number. By increasing the layering of their cipher, the Rossignols were able to create a very complex cipher that effectively kept secret the information for over 200 years. Though even the Great Cipher was not impervious to the scrutiny of cryptanalysists, and all ciphers will eventually be figured out, the strength of a cipher is not measured by if it is able to be broken but how long it keeps the information safe.

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