Efficient Hardware Multiplicative Inverters

Abstract

We propose two hardware inverters for calculating the multiplicative inverses in finite fields GF(2^m): one produces a result in every O(m) time using O(m) area; and the other produces a result in every O(1) time using O(m²) area. While existing O(m)-time inverters require at least two shift registers in the datapath, the proposed O(m)-time implementation uses onlyon e, thus costing less hardware. By exploiting the idea used in the O(m)-time inverter and developing a new wayof controlling the dataflow, we also design a new O(1)-time inverter that works faster but costs less hardware than the best previouslypro posed O(1)-time implementation with the same area-time complexity.