The mathematics of RAID-6
First version 20 January 2004
Last updated 21 May 2009
RAID-6 supports losing any two drives. The way this is done is by computing
two syndromes, generally referred P and Q.
1 A quick summary of Galois field algebra
The algebra used for this is the algebra of a Galois field, GF(2
8
). A smaller or
larger field could also be used, however, a smaller field would limit the number
of drives possible, and a larger field would require extremely large tables.
GF(2
8
) allows for a maximum of 257 drives, 255 (2
8
− 1) of which can be
data drives; the reason for this is shown below.
The representation of GF(2
8
) used is the same one as used by the Rijndael
(AES) cryptosystem. It has the following properties; this is not, however, an
exhaustive list nor a formal derivation of these properties; for more in-depth
coverage see any textbook on group and ring theory.
Note: A number in {} is a Galois field element (i.e. a byte) in hexadecimal
representation; a number without {} is a conventional integer.
1. The addition field operator (+) is represented by bitwise XOR.
2. As a result, addition and subtraction are the same operation: A + B =
A − B.
3. The additive identity element (0) is represented by {00}.
4. Thus, A + A = A − A = {00}.
5. Multiplication (·) by {02} is implemented by the following bitwise rela-
tions:
1
