Exclusive OR is a mathematical calculation in cryptography. It is a logical operation.
There are other logical operations in our CISSP study guides: AND, OR, NOT, Modulo Function etc. etc.
XOR though, is the most important and the most used.
And it's really easy to understand.
It consists of the multiplication of 1 and 0, that's it.
If it's 1 times 1, the result is 0.
If it's 0 times 0, the result is 0.
If it's a combination of 1 and a 0, the result is 1.
If it's the same, it's 0.
If it's different, it's 1.
Example
Our message:
Hello
Regular binary version of Hello:
01001000 01100101 01101100 01101100 01101111
Our secret keystream:
110001101010001101011010110011010010010111
To get the ciphertext, you multiple the binary version of the message with the random keystream.
Hello 01001000 01100101 01101100 01101100 01101111
Keystream 11000110 10100011 01011010 11001101 00100101
Cipertext 10001110 11000110 00110110 10100001 01001010
Real Life Usages
The onetime pad uses the Exclusive Or function. The receiver has a copy of the keystream, and receives the ciphertext over a covert transport channel. The receiver then XORs the ciphertext with the keystream in order to reveal the plaintext of Hello.
Fun fact: The onetime pad is considered the only truly unbreakable encryption algorithm.
The block cipher DES uses Exclusive Or.
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