Some Remarks on the Computation of Multiplicative Inverses in GF(2^n)

초록

This paper study an effectiveness of irreducible polynomials in Galois field GF(2n). It is widely accepted that the efficiency of arithmetic algorithms depends on the basis and will depend on the irreducible polynomials when we choose polynomial basis. And it is presumed that the trinomial type is effective in multiplicative inversion problems considering less computational cost. Since the irreducible polynomial is used only one time in the extended Euclidean algorithm, the other extreme all-one-polynomial is tested and compared with trinomial counterparts. The all-one-polynomial is shown to be effective in multiplicative inversion problems between 140 and 210 bits.