Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: syllables

The Great Cipher: Coding in a primitive form

Great Cipher used by Louis XIV was such a successful cipher because it incorporated many types of cryptography, but also "foolproofed" itself by creating almost a ciphertext keyboard. For example, certain numbers created sounds, similar to how computer code can prompt a computer to emit audio. Similarly, certain groups of numbers deleted the previous letter/cluster, like the backspace key of a computer, and how a computer is coded to understand that deleting is the function of the key. I would argue that the Great Cipher was a form of computer code before its time, with the Rossignols being the coders and Louis XIV or any recipient being the computer. Before the Great Cipher, many cryptanalysts were accustomed to assigning one letter with a singular symbol, or group of numbers, but this cipher was so successful because it prompted the reader to emit a syllable, as computer code prompts a computer to perform a very specific behavior rather than reword the code given. It is remarkable to imagine that such a complicated form of cryptography was developed so long ago, because we in some ways still utilize it today. Again, this method connects back to the argument of monarchs controlling the most developed forms of cryptography because of their resources and the content of their messages (Louis XIV could afford to house the Rossingnols). If records were kept, it would be interesting to research whether Antoine and Bonaventure were the first people to develop such a code, and how it relates to modern day technology programming.

The Greatness of the Great Cipher

I see The Great Cipher is synonymous to the simple monoalphabetic substitution cipher, just on steroids. The concept is the same—one cipher letter or multiple cipher numbers represent a number of plaintext letters. However, what makes the two so different in their difficulty to be cracked lies in the sheer possibility of combinations that could be created from each cipher.

The cipher key was not limited to just one letter replacing another; instead, a few numbers represented syllables. Thus, this opened up a lot more possibilities to stump cryptanalysts.

Before, it was clear in monoalphabetic substitutions that one cipher letter represented one letter of the plaintext. Therefore, we were only faced with a certain amount of different cipher keys to deal with. Even though a completely random monoalphabetic cipher would yield so many possibilities, frequency analysis could easily help decipher it. But now with a cipher with undeterminable characteristics (does "1" represent a letter or does "123" represent one letter? Or a syllable? I'm guessing they did not know how many numbers represented how many letters), patterns that lead to the cracking The Great Cipher become less obvious. There is a multitude of syllables that exist in the French language, making combinations all the greater in amount. This increases the difficulty because although we might see a string of numbers or other patterns, the specific plaintext it refers to—whether it be just one letter or two or three—has much more holes and traps. 

In addition, many people might still be familiar with only the mono alphabetic substitution (since cryptology was still developing), so people might have not thought in a “numbers now represents syllables” way just yet. A reason for the people's unfamiliarity would be that since the Great Cipher was made by two people (the Rossignols) who already knew how to crack extremely hard ciphers, their knowledge of the weakness of strong ciphers bolstered their knowledge to build something knew that didn’t fall into the traps of the simple mono alphabetic substitution cipher. As such, because they thought five steps ahead of everyone else. In addition to their death, the Great Cipher remained unsolved for 200 years because the only people smart enough to crack hard ciphers and used the weakness of those to create a new super hard to crack cipher had died. In short, their knowledge of the Great Cipher died along with them until it was unearthed 200 years later.

Power of The Great Cipher

There exists a never ending battle in the field of cryptography between those coming up with encryption methods and encrypting messages to those trying to break these ciphers. This back and forth is an ongoing and fairly quick process with each side constantly making advancements. However, the 2nd chapter of Singh discussed "The Great Cipher" which was the cipher used by Louis XIV, which remained unbroken for 200 years. The obvious question is then, what made this particular cipher so difficult and take so long to crack?

There are multiple reasons for this, starting with the complexity of the code itself. The code was comprised of 587 unique numbers with thousands of numbers altogether. This alone makes it very difficult to decipher as if you were assuming these numbers corresponded to letters or a set number of letters, as there would have to be repeated elements of the cipher text corresponding to the same thing in the plain text, which would render frequency analysis practically useless. This leads into the next reason why the cipher was so secure, which is that the numbers corresponded to syllables instead of letters or groups of letters. The majority of the ciphers up till this point revolved around changing something into individual letters, so this not being the case probably threw off many would be deciphers of the text.

Lastly, one of the main reasons this code was so secure is the technology that was available at the time. Nowadays with our computers, excel files, other programs and whatnot it is fairly simple and straightforward to do things such as frequency analysis or substituting in sequences in the cipher text for what we assume it to be in plain text. However, back in the 17th and 18th centuries performing these tasks by hand (especially with a text thousands of characters long) would be an incredibly daunting task. The sheer time commitment it would take to decipher a text of this length would be enormous and this probably discouraged many people from attempting to decipher it.

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A Great Deal of Creativity

As cryptographers attempted to improve the security of ciphers, while maintaining their practicality, more complex ciphers were being created.  The monoalphabetic substitution cipher was becoming less secure, leading to the advent of the polyalphabetic cipher and the homophonic cipher.  Yet, these ciphers required much more time to encipher, and were too complex for everyday use.  Cryptographers were on a mission to develop a cipher that was less complex than a polyalphabetic cipher and just as secure.  By the 17th century Antoine and Bonaventure Rossignol met that goal by creating the Great Cipher of Louis XIV.  The Great Cipher was simply an enhanced version of a monoalphabetic cipher, yet it remained unbroken for over two hundred years.  How was the Great Cipher so secure?

The Rossignol's were both excellent cryptographers and cryptanalysts.  As cryptanalysts, they had much more insight when creating the Great Cipher.  The Rossignol’s knew that this new cipher had to be very different from ciphers in the past.  This would ensure the security of Louis XIV’s messages and French secrets.  By acknowledging this idea, and using their past experiences as cryptanalysts, the Rossignol’s created a cipher that used numbers to encode syllables.  In the past, no cryptographer attempted to encipher a plaintext according to anything but letters.  By using syllables, it would take years for any cryptanalysts to decipher their codes.  Cryptanalysts rely on past information in order to solve a cipher.  Because the Great Cipher utilized a new method, cryptanalysts found it very difficult to solve.  Another factor that led to such a secure cipher was that the probability of solving the Great Cipher was so low.  The Great Cipher utilized 578 numbers, whereas typical monoalphabetic substitution ciphers featured 26 letters.  The Rossignol’s didn’t rely on just the use of syllables as their only method of security.  They also included traps in their ciphers to confuse cryptanalysts.  Sometimes numbers represented a single letter instead of a syllable, while other times a number represented nothing at all.  Ultimately, the Great Cipher represented a significant change in cryptography.  It utilized creativity and several lines of defense to keep the French secrets safe.

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.

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 Complexity of the Great Cipher

Antoine and Bonaventure Rossignol created the Great Cipher of Louis XIV and made it so complex that it took over 200 years to decipher. Generation after generation attempted to crack the cipher, yet no progress was made. The Rossignol’s both died, which terminated the ciphers use, as well as cutting off any potential collaboration with the creators and knowledge of exact details that could have been useful to the hundreds of codebreakers that tried to uncover the mystery. It was not until Commandant Etienne Bazeries came along and spent three years of his life working on deciphering letters of Louis XIV that the code was finally solved. Bazeries knew that it was not a substitution cipher, as there were 587 different numbers instead of the usual 26 different numbers. To Bazeries’ dismay, the cipher was also not a homophonic cipher, which was a possibility he entertained for months.

His final attempt proved to be worth it after all. The main factor that made this cipher so secure was the fact that each number represented a whole syllable, not a pair of letters. Bazeries finally got on a roll, guessing the remaining letters of an unfinished word, which enabled him to recognize other syllables. Another major deceiving factor in the Great Cipher was the traps that the Rossignols inserted; some numbers occasionally deleted previous numbers instead of standing for another syllable. The combination of the traps, the vague numbers, and the inability to collaborate with the Rossignols created an extremely secure and virtually unbreakable cipher.

 

 

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The Great Decipherment

The Great Cipher, invented by the Rossignol family, was such a difficult cipher to crack because of two important factors. First the details and use of it was lost one the Rossignols died, which meant hat cryptanalyst had to start from scratch without knowing anything about how the cipher was created besides what they assume based on what other ciphers looked like during the same time period as Louis XIV.  The other significant factor that made the Great Cipher so powerful is the fact that it was not a simple single letter substitution cipher but actually a double letter substitution with a twist: instead of substituting letters, it instead substituted syllables. This greatly complicated the cipher because there an incredibly large number of ways in which to rearrange and cipher syllables, and if there is now starting point at which to begin deciphering the Great Cipher, then it becomes infinitely harder to crack the Great Cipher as opposed to a simple single letter substitution cipher. While these things combine to make it difficult to crack the Great Cipher; the inclusion of traps, such as numbers to delete the previous syllables, made it difficult to tell whether or not a postulated key to the cipher is correct until the traps are detected and accounted for. The combination of having no information about the formation of the Great Cipher as well as the unique substitution it uses as well as traps to trick cryptanalysts all combined to make it unbroken for 200 years after it was created despite the effort of many intelligent cryptologists.

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