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Intro to Cryptosystems

Cryptanalysis

The Zimmermann Telegram

Edgar Allan Poe

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Cryptanalysis

Cryptanalysis is probably the thing most people first think of when they think of Cryptology. Most of the time when the subject is broached, the first image is a Sherlock Holmes-type detective, sitting and diligently working on the cipher text left behind from the last encounter he had with his arch nemeses. This idea of attempting to break a code we do not already know is fascinating. Of course, one can see how this can be a very useful skill for a military to posses. If One encodes information to hide it from prying eyes, through Cryptanalysis we can still get to the information we are attempting to obtain. As far as military this could be vital strategic information or plans, the knowledge of which may allow us to be able to prevent an enemy from gaining the upper hand. However Cryptanalysis also can be a very dangerous weapon. If a person is very adapt at breaking codes, then no information is safe from them. Things like encoded credit card numbers or personal digital information is all encoded in databases and throughout the internet. A person could, in cryptanalical theory, break into all of this and have access to these very vital pieces of information.
Cryptanalysis has naturally been around as long as Cryptography, however its first major breakthrough historically came with World War II. In this war, the German's used a very infamous code, Enigma, which allowed them to communicate without fear of anyone else being able to access the information. The Allied forces did eventually break this code, and this truly became the first major victory for Cryptanalysis. Since Enigma was a private-key crypto-system, and was based on an Affine Shift, it had a finite number of keys able to exist. With this information, and the help of a one of the first true computers designed especially for this, the Allied forces used an exhaustive key search to crack the German code, and thus allowing the Allied forces access to top secret German military information. It is believed without this cryptanalyical effort, the Allied forces may have not been able to win the war.
Even though there are many different ways to encrypt something, decryption has by far less methods than does cryptography. There are in fact only two true ways to crack a code. An Exhaustive Key Search is probably the most effective way, and works on the theory if one encrypts text using a cipher such as Affine or a Caesar Cipher they had to have encrypted the text by using a function F(x). Then we can theoretically use F-1(x) to decrypt it. We do not, however, know what F(x) is. We do know there are a finite possibilities for what F(x) could be, and if we run through them all systematically then we should be able to decrypt the code. Here is where computers play a major role. Let us say there are 1,000 different possible keys, or 10,000 or 1,000,000? We would need to run through all of them to get the correct key, since a computer can try many keys in a very short amount of time or even sometimes simultaneously, we could crack codes with a large number of keys in a relatively short amount of time.
The other type of cryptanalsys is called Frequency Analysis, and can be a very powerful cyptanalical tool against such things as a Random Cipher, or any cipher where there is an exact one to one mapping from regular alphabet to cipher alphabet, or where F(x) is a one to one function. It works on the principle certain letters appear more in natural text than others. Of course this is subject to what language the text is written, however for a regular English paragraph it is safe to assume the letter "e" will appear more than any other. If we had a piece of cipher text we are trying to crack, and it was at least a paragraph long, we could count to find which letter appears most often. Then we could say whatever letter that is, it probably corresponds to the letter "e."
One question always coming up is, "Is there an unbreakable code?" The answer to this is no. Every code is theoretically breakable, however some may be so complex or have so many keys it is essentially unbreakable. Cryptologists, when developing their encryption schemes, think about this, and will put in little traps to help through Cryptanalysists off, such as encoding each group of ten letters using a different key. This way a simple frequency analysis, or even an exhaustive key search would prove useless if the text is taken as a whole. Even such crypto-systems as RSA and other public key systems are breakable, however cryptanalysis for these crypto-systems can be very complex and frustratingly tedious.
Cryptanalsysis, as a whole much like cryptology, is becoming more and more digital and high-tech. Computers can run though keys and count faster than any human, however the programs and algorithms used are still the same techniques used throughout the ages.