Novel structures for serial multiplication over the finite field GF(2m)

Two novel uni-directional systolic structures for serial multiplication over the finite field GF(2^m) are presented. The architecture of the new structures posses features of regularity, modularity, and uni-directional data flow. One of the new structures is a serial-parallel structure, whereas the other structure is a fully serial one. Both structures consist of (m/2) novel cells. Due to the novel cells architectures of the new structures, the initial delay (i.e. the number of cycles required to obtain the first output) and the latency (i.e. the number of cycles required to complete the multiplication process) are decreased by 25% and 17% respectively. Also, the number of latches of the new structures are reduced by more than 20% when compared to existing uni-directional serial-parallel structures