Re: Computing Rijndael's S-Box?

From: Björn Fay (mail_at_bfay.de)
Date: 08/30/05

```Date: Tue, 30 Aug 2005 12:04:25 +0200

```

cobussteyn@absamail.co.za wrote:
> I'm a newbie when it comes to cryptography and currently I'm hooked on
> Rijndael. I know most of the implementations of it have the S-box
> hard-coded into the app for speed gain, but I would like to compute
> that s-box myself.
>
> You probably know it is defined by the finite field mapping in GF(2^8)
> onto its inverse, and then it is transformed by a certain matrix (i
> have that one) and then 0x63 is added.
>
> Can someone help me to compute that first mapping of GF(2^8) onto its
> inverse? How do you compute the inverse?
>
> Thanx !

You have to use the Extended Euclidean Algorithm an explanation can be found in books for discrete mthematics or in wikipedia:
http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm

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