Some Remarks on E cient Inversion in Finite FieldsChristof

This contribution is concerned with bit parallel inverters over nite elds. Two alternative approaches for inversion with low complexity which were proposed in the late nineteen eighties will be reviewed. Previously they seem to have received relatively little attention in the scientiic community. Both methods are based on multiple eld extension of GF (2). We will try to restate the two algorithms in a clear fashion. It will be shown that one architecture is a generalization of the other's architecture core algorithm. As an impressive example of the advantage of inverters operating over extension elds, the optimized complexity of a bit parallel inverter in the important eld GF (2 8) will be computed, resulting in a surprisingly low gate count.