Number - Gf(2) - Galois Field 2

1 - 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

3 - Operation

3.1 - 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

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

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

data/type/number/gf2.txt · Last modified: 2017/09/13 16:04 by gerardnico