# XOR

The XOR (Exclusive OR) operator is a logical operation that takes two binary inputs and returns a single binary output.

In cryptography, XOR is often used as a simple method for combining two values into a single value or for separating a single value into two parts.

## How it works ?

XOR is a bitwise operator which returns **`0`** if the bits are the same, and **`1`** otherwise. In textbooks the XOR operator is denoted by **`⊕`**, but in most programming languages you will see the char`^` used instead.

| A | B | Result |
| - | - | ------ |
| 0 | 0 | 0      |
| 0 | 1 | 1      |
| 1 | 1 | 0      |
| 1 | 0 | 1      |

For longer binary inputs, the XOR operation is done bit by bit : `1010 ^ 0111 = 1101` . If the two operand haven't the same size, then the shorter padded with non-significant `0` :

```
1010 ^ 01 = 1010 ^ 0001 = 1011
```

## Properties

Like other standard mathematical objects, xor has some specific properties :

```
Commutative  : A ⊕ B = B ⊕ A
Associative  : A ⊕ B ⊕ C = A ⊕ (B ⊕  C) = (A ⊕ B) ⊕ C
Identity     : A ⊕ 0 = A
Self-Inverse : A ⊕ A = 0
```

These properties are very interesting cause it permit the following :

$$
D = A \oplus B \ A \oplus D = A \oplus ( A \oplus B) = A \oplus A \oplus B = (A \oplus A) \oplus B = 0 \oplus B = B
$$

## Python

```python
from pwn import *

A = "someData"
B = "OtherData"

xored = xor(A,B)
```

## Resources

{% embed url="<https://gchq.github.io/CyberChef/#recipe=XOR(%7B>" %}