Cryptography

The History and Mathematics of Codes and Code Breaking

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The Great Cipher Was a Really Great Cipher

The 1600's were a strange time in the history of cryptography. Monoalphabetic ciphers had run their course, with cryptanalysts having the resources and know-how to crack any monoalphabetic cipher quickly. On the other hand, the newly developed polyalphabetic cipher, a cipher that uses multiple cipher alphabets, was effective but too tedious to be embraced by codemakers. People needed a method of encryption that was unbreakable and also not so difficult to use. That's when the Rossingols, cryptanalysts employed by the French government, developed the Great Cipher of Louis XIV. It is important to wonder why this particular cipher, which is just an enhanced monoalphabetic cipher, took 200 years to decipher.

The first reason why the Great cipher took so long to decipher was its complexity compared to ciphers cryptanalysis had seen in the past. The Great Cipher was a monoalphabetic cipher, meaning each symbol in the “cipher alphabet” mapped to one and only one thing in the plaintext alphabet. Still, it was extremely different from all other monoalphabetic ciphers. First, it used numbers. The use of numbers to map to letters had been a relatively new development in cryptography, and cryptanalysts still didn’t know the best method to decipher numeric codes. More importantly, however, the Great Cipher included 576 numbers: many more letters than there are in the alphabet. This great of a mismatch between the quantity of symbols and the quantity of letters had never been seen before, so there was initially a huge gap between the experience of the cryptallaists and the complexity of this cipher.

The second reason the Great Cipher took so long to decipher was the technologies available at the time. This was a cipher of 576 numbers. If it were 26 numbers, it would be somewhat obvious that each number matches a letter. However, with 576 numbers, each number could mean anything. So, many possibilities needed to be tested out. However, due to the fact that everything had to be written out, testing a possibility was extremely tedious, time consuming, and daunting. Bazeries, the man who eventually deciphered the Great Cipher 200 years later, spent months testing if it was a homophone and then spent months testing whether the numbers represented pairs of words. In short, no one wanted to do the herculean task of testing failing decriptions over and over again with pen and paper, so it took a long time before someone took up the task.

Lastly, the Great Cipher took so long to decipher because of the creativity and effectiveness of the cipher itself. Each cipher in the past had been based off of letters, but the Rossingols based their cipher off of syllables, matching each number to a syllable in the english language. This system made it just as easy to send messages and decode them with a key, but made the cipher extremely difficult to crack, given that there are so many potential syllables. The creativity put into this cipher showed, as no one thought to look at the syllables for 200 years. The Great Cipher took so long to crack because it was everything a great cipher is: complex, daunting, and way before its time. 

 

Why The Great Cipher Remained Great

The Great Cipher used by Louis XIV encoded syllables and single letters using 587 different numbers and remained unbroken for 200 years. One factor contributing to the strength of this cipher could be that during the time period in which the cipher was in use, the most well known ciphers included the monoalphabetic substitution cipher, the polyalphabetic substitution cipher, and the homophonic substitution cipher. People had commonly being encoding their message one letter at a time. Consequently, many trying to break The Great Cipher may have not considered syllables, consisting of a varying series of letters, were being encoded as one number. To further increase the strength the cipher, some single letters did correspond to a single number which would further confuse the cryptanalyst as to which numbers represented single letters and which represented syllables. To add to the confusion there were numbers that were traps which did not represent a syllable or a letter. Trap numbers deleted the previous number in the ciphertext. This cipher incorporated three layers of complexity which could attribute to why it remain unbroken for two centuries.

Furthermore, Louis XIV’s plaintext was in French meaning that enemies who potentially intercepted the messages would be unlikely to known common French syllables unless they were literate in French. It was probably more likely for a French-speaking people to loyal to his or her king than to Spain or other enemy countries during Louis XIV’s reign.

Lastly, after some time passed after Louis XIV’s reign the group of people interested in decoding his secret messages shifted from enemies to historians. Historians acknowledged the value of decoding the king’s secret messages to gain insight regarding the 17th century however, the urgency was nowhere near that of the enemies. Enemies need to decode his messages of his political scheming and planned attacks within days for the information to be of any benefit to them. A century later, the details of the dead king’s plans did not need to be deciphered within days considering they were events of the past. The lack urgency may have also contributed to the long lasting unbreakability of the cipher.

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.

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.

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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