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

Advertising

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

Adding is the same than subtracting in gf2.

Multiplication is like ordinary multiplication

x	0	1
0	0	0
1	0	1

Advertising

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