On Inversion Algorithms over Optimal Extension Fields Using Lagrange Representation
We present, illustrate and analyze some basic notions of the Lagrange Representation (LR) over finite fields, and elementary theory of Optimal Extension Fields. In combining the Lagrange Representation theory and the Frobenius mapping theorem, we could establish an inversion algorithm in the LR version. Our contribution is of adapting an addition-chain-like method over an Optimal Extension Field to the Lagrange Representation.
M. L. Qi et al., "On Inversion Algorithms over Optimal Extension Fields Using Lagrange Representation ", Applied Mechanics and Materials, Vols. 20-23, pp. 277-282, 2010