Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: great cipher

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.

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.

 

 

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.

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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