The History and Mathematics of Codes and Code Breaking

Author: perezaa

Have Your Cake and Eat it Too

The National Security Agency (NSA) was responsible for establishing a standardized enciphering system for commercial use to update the previous obsolete system.  In doing so it chose the Lucifer Cipher, which was the strongest commercial cipher developed.  The primary reason it was chosen was because it was good enough, but only just.  The NSA wanted a system which was complex enough so that an average person would not be able to solve it, but not too strong that the NSA itself would not be able to break it.  As the Lucifer Cipher had only 56 bits of code (100,000,000,000,000,000 possibilities) an average person would not have access to enough computing power to solve it, but the NSA would have enough to test out every possibility and break it if necessary.

I feel that this is an invasion of privacy by the government as it should not have the right to break into a private message, when the sender intended it to be secure.  This choice of a cipher that the government could break came at a cost to security and longevity, as the exponential growth of commuters over the years since the 70’s now allows for this code to be broken much more easily today.

Image: "USA Flag" by freefotouk, Flickr (CC)

Looks Guilty, is Guilty

The brutal treatment of the protagonist, Marcus Yarrow, in Chapters 3 and 4, following the Bay Bridge bombing was something that suck out to me as I tried to put myself in the situation and how I would have reacted.  One less obvious theme related to cryptography which I noticed was the appearance of guilt that results from Marcus’ heavy defense of his privacy.  It is human nature to feel that someone who does not want to tell you everything would be hiding something bad from you.  Marcus’ actions in his first encounter with the Department of Homeland Security’s interrogation seemed to point to him trying to hide something.  Although Marcus only tried to resist for a short amount of time, and the treatment by the Department of Homeland Security was less than proper, he did show resistance which could have prompted some reaction by the DHS.

The concept of no cipher being better than a bad cipher was also present in this scene.  The idea of this is that a ciphered message which is broken could do more harm to the party enciphering than if the same message was discovered not enciphered.  Although there were no ciphers, the passwords and security precautions made by Marcus made him look guiltier just as an enciphered message could have done.  In this scene the passwords were not "broken" but instead were taken by force, which in the long run, has the same overall effect. Regardless of the means of discovering a secret, the fact that it was a secret makes it seem worse to the party discovering it.

Image: This is Secret by Trey Ratcliff

What is it all worth?

The Beale Ciphers have remained unsolved for over a hundred years, yet thousands of people have tried to interpret its hidden meaning.  The code has never been cracked due to a very complex number cipher as well as the possibility that the cipher text has been altered, making it forever impossible to crack.  The main reason that people would persist in trying to solve the cipher was for the “pot of gold at the end of the rainbow.”  The “pot of gold” literally was a stockpile of gold worth over $20 million, found by Beale and his crew.  Even now, when there is almost no chance of the treasures remaining undisturbed, scholars continue to work on trying to break the Beale ciphers.  These people are not in search of monetary gain, but instead a challenge to attempt to complete.

Image: "Puzzle," Ryan Amos, Flickr (CC)

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 Ease of Encryption

Cryptanalysis has changed greatly over history in terms of difficulty and ability to be solved.  According to Simon Singh “Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship…” This is the case for two reasons: first, a civilization would need to have a very standardized written communication system before cyphering would even be necessary, as there is no practicality in encrypting a written language that no one understands to begin with.  Second, as written languages began to become standardized, the lack of popular education in reading and writing, left cryptography to the only greatest scholars.  Substitution cyphers could be relatively simple and still effectively conceal a message.


As education became more common, cyphers would need to be much more complex as more people could work on successfully decrypting.  More modernly, as education has hit new levels along with the emphasis on critical thinking, a simple substitution cypher could be analyzed for common frequency patterns easily broken by a group of college freshmen (THAT’S US!).


Additionally, with the development of computers, new heights of complexity are introduced to cryptography.  A simple common device such as a cell phone uses complex encryption that can ensure privacy for simple text messages, to creating secure lines for bank transactions.  Not only have the creation of codes been revolutionized by computers, but the decryption of them have been improved just as much.  Even complex substitution cyphers that would have left scholars thinking for days could be broken in seconds.


It is amazing how we take the complexity and convenience of encryption for granted as others in the past labored greatly to make a fraction of that security possible.

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