# Number - Gf(2) - Galois Field 2

> (Data|State) Management and Processing > (Data Type|Data Structure) > Number, Numeric, Quantity

### Table of Contents

## 1 - About

Galois Field 2 has just two elements: 0 and 1

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

## 2 - Articles Related

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## 3 - Operation

### 3.1 - Addition

### 3.2 - Subtraction

Adding is the same than subtracting in gf2.

### 3.3 - Multiplication

Multiplication is like ordinary multiplication

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

0 | 0 | 0 |

1 | 0 | 1 |

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## 4 - 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