How XOR Encryption Works
Explore the fascinating world of XOR encryption! Learn how this simple logical operator creates perfectly balanced output, making it a powerful tool for secure data encryption. Discover why XOR outperforms AND and OR in cryptography, and experiment with an interactive demonstration to see these operators in action.
XOR is a logical operator that returns True (or 1) if two values are different, and False (or 0) if they're the same. Contrast AND, which returns True (1) only if both values are True (1), and OR, which returns True (1) if either value is True (1).
XOR has an interesting property that makes it useful for encryption. Given some binary input string and some randomly generated binary encryption key, using the XOR operator to map each input digit to the corresponding key digit will produce 'perfectly balanced' output. That is, an input 0 will be encoded as 1 exactly half of the time, and as 0 the other half of the time. Since the encoding is a simple, parallelizable logical operation, it can be executed very fast.
In contrast, using the AND and OR operators produces biased output, as illustrated in the interactive table below. AND always encodes a 0 input as 0. Similarly, OR always encodes a 1 as 1. That means these operators would leak half the input data, making it relatively trivial to reconstruct the rest. XOR, however, doesn't leak any information. If the key is as long as the input data and the key is never re-used, XOR encryption is theoretically unbreakable. Click the buttons at the top of the interactive table to toggle between operators and see for yourself how each works.
| Plaintext | Key | Ciphertext | ||
|---|---|---|---|---|
| 0 | XOR | 0 | = | 0 |
| 0 | XOR | 1 | = | 1 |
| 1 | XOR | 0 | = | 1 |
| 1 | XOR | 1 | = | 0 |
Balance: Perfectly balanced. Equal 0s and 1s, regardless of input.
In practice, of course, these conditions are rarely met. XOR encryption in the real world typically uses a repeating key, and/or the key is reused over multiple inputs. That's why XOR is considered a fairly weak encryption algorithm and is not used very much. But under ideal conditions, XOR encryption is a fast and powerful thing.
