An extension of TYT inversion algorithm in polynomial basis

This letter is concerned with an extension of Takagi et al. algorithm (TYT) for inversion computation in GF(m2). Unlike the original algorithm, the method introduced here uses a polynomial basis representation. As the main contribution, the proposed method reduces both the number of required multiplications and squaring operations by applying a modified decomposition for m−1. When the field is generated with an irreducible trinomial, our proposal shows almost the same practical complexity as the TYT algorithm using normal basis.