Number - Gf(2) - Galois Field 2

Data System Architecture


Evariste Galois

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



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


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

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