Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: King Louis XIV

The Cipher That Survived for 200 Years

The Great Cipher of King Louis XIV was an enhanced monoalphabetic substitution cipher that managed to remain unsolved for over two centuries.  It was developed by the father-and-son team of Antoine and Bonaventure Rossignol, two of the best cryptanalysts in France.  King Louis XIV used it to securely encrypt sensitive information regarding his political plans.  The first characteristic of the Great Cipher that made it so strong was that it used 587 different numbers to encode messages rather than just 26 symbols, like a standard monoalphabetic substitution cipher.  This meant that there were multiple possibilities for the significance of each number.  Cryptanalysts initially thought that each number corresponded to a single letter, with several ways to represent each letter.  A cipher like this would be quite effective in that it would be immune to frequency analysis, but the Great Cipher was actually even more complicated.  Rather than a single letter, each number represented a full syllable in the French language.  Since there are so many possible syllables, this method is several times more secure, requiring a cryptanalyst to match up far more than just 26 pairs of meanings.  In addition, the Rossignols made the cipher extra deceiving to potential codebreakers by making some of the numbers delete the previous syllable instead of signifying a unique one.  All of these strong encryption techniques contributed to the longevity of the Great Cipher, and it remained unsolved until expert cryptanalyst Commandant Étienne Bazeries finally broke through 200 years later.

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 Greatest Cipher

Louis XIV's Great Cipher was unique in its complexity, far far beyond the other ciphers used during the time period. Indeed at the time, by far the most popular type of cipher was the mono alphabetic substitution cipher, yet that is easily deciphered by a good cryptanalyst through the use of frequency analysis.  The Great Cipher was much more than a simple mono alphabetic substitution cipher in that it utilized numbers to represent letters, but on top of this, the numbers didn't just stand for letters they also stood for syallables. Since there was not a 1 to 1 relationship between letters and the cipher alphabet, it was nearly impossible to perform traditional frequency analysis on the cipher text. Furthermore, the cipher was brilliantly created with cipher text indicating to ignore the previous syllable or letter, making it tricky for any decoder to figure out what was part of the cipher and what was simply nonsense.

Perhaps the deciphering of the Great Cipher is even more impressive than the creation of such a complex cipher. The amazing creativity and brilliant thinking that Bazeries had to even consider looking at syllables has to be commended. Furthermore, for him to harp on a repeated phrase and be able to figure out what it meant is incredibly impressive. This also illustrates how amazing the cipher was in that it took Bazeries over three ears to crack it even with his uncanny ability to recognize that it is comprised of syllables.

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.

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