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I think it's worth pointing out that this algorithm (as stated, anyway) is useless over any field of characteristic 2, i.e. the field GF(2^m) for any m.
The reason is that, if x is an element of GF(2^m), then x^(-1) = x^(2^m - 2), and the right hand side of this equation is exactly what is being computed in step 2. So, essentially, this algorithm computes inverses by assuming it has access to a subroutine that computes inverses!
This is the first time I've seen this algorithm, so I don't know what's going on here, but this should be addressed somehow since the article states "It was [...] first used over GF(2^m)".
