Raymond Toy <toy@rtp.ericsson.se> wrote:
+---------------
| Doing GF(2) arithmetic is easy as Duane's code shows. In fact rather
| than doing the mods, you could just use logxor and logand to implement
| + and *.
|
| GF(256) arithmetic is quite a bit different. You can't use modulo
| arithmetic on integers. You have to manipulate polynomials whose
| coefficients are from GF(2). You can, represent the polynomials as
| bit-vectors or integers, however.
+---------------
If you represent them as integers, then you can use table-lookups for
multiplication & division [to multiply, look up the "logs" of the numbers,
add them mod 256, then look up the anti-log of the sum -- and you can even
avoid the "mod 256" if you make the anti-log table be 512 entries long],
and addition/subtraction is still just XOR.
So GF(256) can be done reasonably fast, even without 64 KB lookup tables...
-Rob
-----
Rob Warnock, 8L-855 rpw3@sgi.com
Applied Networking http://reality.sgi.com/rpw3/
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