## About

Galois Field 2 has just two elements: 0 and 1

Usual algebraic laws still hold, e.g. multiplication distributes over addition

a * (b + c) = a * b + a * c## Articles Related

## Operation

### Addition

Addition is like exclusive-or:

+ | 0 | 1 |
---|---|---|

0 | 0 | 1 |

1 | 1 | 0 |

vector addition

```
1 1 1 1 1
+ 1 0 1 0 1
= 0 1 0 1 0
```

### Subtraction

Adding is the same than subtracting in gf2.

### Multiplication

Multiplication is like ordinary multiplication

x | 0 | 1 |
---|---|---|

0 | 0 | 0 |

1 | 0 | 1 |

## cryptosystem

The probability distribution of the cyphertext does not depend on the plaintext.

Idea is the basis for cryptosystem: the one-time pad. If each bit is encrypted with its own one-bit key, the cryptosystem is unbreakable