<s>
The	O
MixColumns	O
operation	O
performed	O
by	O
the	O
Rijndael	B-Algorithm
cipher	I-Algorithm
,	O
along	O
with	O
the	O
ShiftRows	O
step	O
,	O
is	O
the	O
primary	O
source	O
of	O
diffusion	O
in	O
Rijndael	B-Algorithm
.	O
</s>
<s>
This	O
demonstrates	O
that	O
the	O
operation	O
itself	O
is	O
similar	O
to	O
a	O
Hill	B-Algorithm
cipher	I-Algorithm
.	O
</s>
<s>
It	O
can	O
be	O
performed	O
by	O
multiplying	O
a	O
coordinate	O
vector	O
of	O
four	O
numbers	O
in	O
Rijndael	B-Algorithm
's	O
Galois	O
field	O
by	O
the	O
following	O
circulant	O
MDS	B-General_Concept
matrix	I-General_Concept
:	O
</s>
<s>
A	O
C	B-Language
example	O
of	O
such	O
an	O
implementation	O
follows	O
:	O
</s>
<s>
Commonly	O
,	O
rather	O
than	O
implementing	O
Galois	O
multiplication	O
,	O
Rijndael	B-Algorithm
implementations	O
simply	O
use	O
pre-calculated	O
lookup	O
tables	O
to	O
perform	O
the	O
byte	O
multiplication	O
by	O
2	O
,	O
3	O
,	O
9	O
,	O
11	O
,	O
13	O
,	O
and	O
14	O
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
C#	O
these	O
tables	O
can	O
be	O
stored	O
in	O
Byte[256]	O
arrays	O
.	O
</s>
