Cryptography

The History and Mathematics of Codes and Code Breaking

Tag: Unbreakable cipher

The Struggle of being a Cryptography Student

In a student's first week in MATH 1111, they are asked a question about whether the ability to decrypt a code depends on intuition, creativity, or luck. At least in this year's class, the majority of students picked either intuition or creativity for various reasons. None of us anticipated that luck would be the key to any of this.

I have quickly learned that luck is the key to breaking any cipher, and that is the very reason why in practice, breaking cipher texts are so much harder than they seem. The common tests we use such as frequency analysis and the Kasiski test are effective in giving us hints and clues, but they fail to give the cryptanalyst any concrete or definitive pieces to move forward with. The hints and clues we receive lead us in the right path, but we still are forced to test and guess our way towards the answer. There is only so much that intuition that take us in terms of completely cracking the code. This is why there are codes and ciphers in the world today that are deemed "unbreakable", no matter how much time the world's best mathematicians spend on them, let alone a group of first-year college students.

Because the fundamental purpose of a cipher is to hide the message from any in the way of the message's delivery, its natural intention is to make sure it is as close to uncrackable as humanly possible. This inherently means that there will be intended twists to make deciphering even more difficult.

Breaking (Almost) Unbreakable Ciphers

The strength of the Vigenère Cipher depends largely on the length of the keyword. If the keyword is just one letter, then it is nothing more than a simple shift cipher; if the keyword is the same length as the plain text, there will be little to no discernable pattern. However, Singh clearly demonstrates that even with a keyword as long as the text, breaking the Vigenère is doable by guessing common words like "the."

Even though it is relatively straightforward to break even these more secure ciphers, doing so in practice is often much harder. Primarily, this is because of the amount of guessing and checking required and the creative insights necessary to realize the best way to break the code. During the process of deciphering the message, and essential step is guessing words either in the plain text or in the keyword, and if your guess is wrong, you have to backtrack until you are confident that all of your work is correct and start from there again. This makes the process of cryptanalysis tedious and time-consuming.

Once you know what method to use to break the cipher, deciphering the message is only a matter of time, but often, figuring out how to approach a complicated cipher takes even the smartest cryptanalysts years to figure out on their own. For example, breaking the simple Vigenère cipher was not difficult; once Charles Babbage figured out how to break it, the Vigenère went from being an unbreakable cipher to extremely insecure overnight. This demonstrates that breaking the cipher itself is often not the most difficult part; the hardest part of breaking complex ciphers is coming up with a foolproof method which exploits weaknesses in the cipher.

The Allure of an Undecipherable Cipher

The Beale Ciphers, despite the attempts of hundreds if not thousands of cryptanalysts, have never been broken before, and might never be broken in the future. Two of the three pages that Beale left behind are still shrouded in complete mystery, and likely will remain a mystery unless someone manages to find the key that Beale used to encode the ciphers. In all likelihood, all the cryptanalysts working on the cipher are wasting their time while hoping for an outcome that will never come. So why are so many people so interested in cracking the Beale Cipher?

The first and most obvious, though perhaps not the primary answer is the promise of wealth. Allegedly, the rest of the Beale Ciphers will lead the one who cracks the code to the treasure trove that Beale hid somewhere within 4 miles of Buford's Tavern. This was the primary motivation of the cryptanalysts during and immediately after Beale's time, because everyone wanted to be the first to solve it and get Beale's fortune. However, as time went on, hope of getting the money slowly faded, but people still actively try to crack the Beale Cipher. For them, the pursuit of fame, glory, and the unknown is enough to keep them going. Being the first person to solve a 200 year old, perviously unbreakable cipher would certainly be neat, even if the papers didn't actually lead to a $20 million grand prize. Their name would go down in history along with Babbage, Kasinki, and Bazeries as the people who finally cracked ciphers that completely baffled everyone else. It's a similar story with the Zodiac letters. Two of the letters have been decoded, but the remaining two are still completely undecipherable. Despite the many failed attempts by amateurs and professionals alike, many people still actively try to solve both ciphers, though not as much for practical purposes as for the thrill of the hunt.

The Appeal of an Unbreakable Cipher

The unbroken Beale ciphers, likely enciphered using a book cipher, will remain nearly impossible to break until we figure out what key text was used to encipher them. Despite this, cryptanalysts have been trying to decipher the messages using various key texts, essentially guessing and checking in the hopes that they stumble upon the correct one. At this point, a reasonable guess is that the key text was a letter written by Beale himself, and without that letter, the ciphers will remain unbroken.

Nevertheless, people continue to try to break the ciphers with various different methods. Some test new key texts and hope to crack the cipher by pure luck; others try cracking the cipher in new ways in hopes that the messages were encoded with something other than a book cipher. Either way, these efforts require large amounts of time and creativity for even a minuscule chance of cracking either one of the ciphers.

The people who try to break these ciphers today are likely aware that they are nearly impossible to crack, and their motivation is probably not the wealth; there are many other ways to get wealthy if you are willing to put in that much time and effort. Rather, the reward they chase after is an intellectual one; they are hoping that, even by pure chance, in cracking the Beale cipher, they will be the first one to read his note, knowing that the knowledge it contains is entirely theirs until they decide to share it with the world. Even though the contents of the note are probably all related to the buried treasure which is of secondary importance, there is a unique appeal to being the first one to break a supposedly unbreakable cipher. The opportunity to become known as the person who did the impossible is tantalizing, and apparently to some, that satisfaction is worth chasing after no matter how unlikely it is that you will achieve it.

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