A novel systolic GF(2k) field Multiplication-Inversion arithmetic unit

In this paper a systolic Multiplication-Inversion architecture is proposed that can be extended to perform all GF(2^k) field operations. This architecture is based on a proposed Modified version of the Extended Euclidean Algorithm that through appropriate reusability and initialization it can perform multiplication and inversion. Therefore, while other known designs need two hardware components for multiplication and inversion, in the proposed design only one hardware module for both operations is used that give very interesting results in terms of Area complexity, critical path delay, latency and throughput.