A long long train of thought led me here. 
Mainly, my math textbook introduced the Hill cipher as an example of where invertible matrices are used. I searched around a bit and started wondering: how are attacks done? Do the attackers have to know what algorithm the cipher text used to attack it? Or is there some magical way to decrypt stuff? XD
How do people figure out what a particular cipher text means? And how do I tell how secure an encryption is?
Basically, encryption is a method to get a message to another person without people reading the letter to understand it. Generally, this is possible because only the receiver knows the encryption method and the key. You can attack encryptions either by guessing the encryption method and finding the key, or simply by listening in when the method and key are passed. An encryption is secure when both attack methods are really hard to do.
If it's possible to decode your text just by knowing the method of encryption you chose the wrong method. Modern cryptography operates under the assumption the the attacker knows everything except the (unencrypted) plaintext and the key. Kerckhoffs's principle
That's probably because all modern cryptography methods can be counted on two hands.
If you only count those that are widely used and known, yes, but that's not the reasoning behind the principle. The point is that keeping secret your method is a hard problem to just keeping secret a short key that can be changed as often as needed. The AES competition made that one of the major points: if an algorithm is insecure when known it's not a good one.
Actually, qualification for a good encryption algorithm goes even further. Given a portion of the plaintext, of any size, you should be unable to increase your chances of decrypting the rest of the plaintext or figure out the key. The reason for this is obvious: say you have an e-mail; at the start and end of all emails, there is protocol data; the headers and such. Any time you send an e-mail, I can know a large portion of the plaintext being sent simply by reading up on e-mail protocols. If by knowing these I can increase my ability to decode the key and plaintext, that encryption system is broken.
Beyond that, some number theory comes into play. If I can take the algorithm and use specified text to generate a key-value pair, that key-value pair should have no statistical relationship with the input data. It should be indistinguishable from a uniform random number sequence under statistical analysis. Otherwise heuristic crackers could give weights to different values, reducing average brute-force cracking time by an order of magnitude or more.
Additionally, the key should be kept as short as possible while maintaining the above parameters. A simple XOR operation fits all the above parameters, but neglects this one. This makes it not useful. After all, in order to send a key, you need some sort of basically secure communication method to ensure the key isn't intercepted. If your key is as long as your message, you obviously have access to a secure channel of communication capable of sending a message as long as the message itself as plaintext, invalidating the entire reason for using encryption in the first place.
Of course, that's just the basic gist of it; if you want to learn more, I suggest Coursera and/or Udacity courses on the topic, which is where I got my info from.
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Topic: How is cryptography done? o_O (Read 2093 times)