Why is XOR used in cryptography?

XOR is a mathematical calculation in cryptography. It is a logical operation. There are other logical operations: AND, OR, NOT, Modulo Function etc. XOR is the most important and the most used.

If it's the same, it's 0.

If it's different, it's 1.

Example:

Message : Hello

Binary Version of Hello : 01001000 01100101 01101100 01101100 01101111

Key-stream : 110001101010001101011010110011010010010111

Cipher text using XOR : 10001110 11000110 00110110 10100001 01001010

Applications : The one-time pad/Vern-am Cipher uses the Exclusive or function in which the receiver has the same key-stream and receives the ciphertext over a covert transport channel. The receiver then Xor the ciphertext with the key-stream in order to reveal the plaintext of Hello. In One Time Pad, the key-stream should be at-least as long as the message.

Fact : The One Time Pad is the only truly unbreakable encryption.

Exclusive Or used in Feistel structure which is used in the block cipher DES algo.

Note : XOR operation has a 50% chance of outputting 0 or 1.