XOR Encryption

Exclusive-OR encryption, while not a public-key system such as RSA, is almost unbreakable through brute force methods. It is susceptible to patterns, but this weakness can be avoided through first compressing the file (so as to remove patterns). Exclusive-or encryption requires that both encryptor and decryptor have access to the encryption key, but the encryption algorithm, while extremely simple, is nearly unbreakable.



Exclusive-OR encryption works by using the boolean algebra function exclusive-OR (XOR). XOR is a binary operator (meaning that it takes two arguments - similar to the addition sign, for example). By its name, exclusive-OR, it is easy to infer (correctly, no less) that it will return true if one, and only one, of the two operators is true. The truth table is as follows:
A   B    A XOR B
T   T       F
T   F       T  
F   T       T 
F   F       F
(A truth table works like a multiplication or addition table: the top row is one list of possible inputs, the side column is one list of possible inputs. The intersection of the rows and columns contains the result of the operation when done performed with the inputs from each row and column)

The idea behind exclusive-OR encryption is that it is impossible to reverse the operation without knowing the initial value of one of the two arguments. For example, if you XOR two variables of unknown values, you cannot tell from the output what the values of those variables are. For example, if you take the operation A XOR B, and it returns TRUE, you cannot know whether A is FALSE and B is TRUE, or whether B is FALSE and A is TRUE. Furthermore, even if it returns FALSE, you cannot be certain if both were TRUE or if both were FALSE.

If, however, you know either A or B it is entirely reversible, unlike logical-AND and logical-OR. For exclusive-OR, if you perform the operation A XOR TRUE and it returns a value of TRUE you know A is FALSE, and if it returns FALSE, you know A is true. Exclusive-OR encryption works on the principle that if you have the encrypted string and the encryption key you can always decrypt correctly. If you don't have the key, it is impossible to decrypt it without making entirely random keys and attempting each one of them until the decryption program's output is something akin to readable text. The longer you make the encryption key, the more difficult it becomes to break it.

The actual way exclusive-OR encryption is used is to take the key and encrypt a file by repeatedly applying the key to successive segments of the file and storing the output. The output will be the equivalent of an entirely random program, as the key is generated randomly. Once a second person has access to the key, that person is able to decrypt the files, but without it, decryption is almost impossible. For every bit added to the length of the key, you double the number of tries it will take to break the encryption through brute force.

C++ uses ^ for bit-level exclusive-OR. To encrypt a single character you can use char x=x^key; if you have a key of one byte. To encrypt a string of characters with a longer key, you can use something akin to the following code:
#include <iostream.h>
int main()
{
  char string[11]="A nice cat";
  char key[11]="ABCDEFGHIJ";
  for(int x=0; x<10; x++)
  {
    string[x]=string[x]^key[x];
    cout<<string[x];
  }
  return 0;
}
The program encrypts each character in the string using the ^ bit operator to exclusive-OR the string value with the key value for each character.