Efficient Multi-bit Shifting Algorithm in Multiplicative Inversion Problems

This paper proposes an efficient inversion algorithm for Galois field GF(2n) by using a modified multi-bit shifting method. It is well known that the efficiency of arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. An inversion algorithm, which modifies a multi-bit shifting based on the Montgomery algorithm, is studied. Trinomials and AOPs (all-one polynomials) are tested to calculate the inverse. It is shown that the suggested inversion algorithm reduces the computation time 1 ~ 26% of the forgoing multi-bit shifting algorithm. The modified algorithm can be applied in various applications and is easy to implement.