New low complexity bidirectional systolic structures for serial multiplication over the finite field GF(qm)

Abstract

Two low complexity bidirectional systolic structures for serial multiplication over the finite field GF(qm) are presented. The first structure is based on generalising the GF(2m) multiplication algorithm and the semi-systolic multiplication structure for general q, and on a novel cell architecture which is equivalent to two conventional cells used in existing structures and has a new fast mod-q multi operand adder. The second proposed structure is a modified version of the first structure where a twin-pipe is used to double the throughput rate and the hardware utilisation. Owing to the use of bidirectional data flow in both structures, the initial delay of the proposed systolic structures is reduced by 50% when compared to related systolic structures based on unidirectional data flow. The area requirements of the new systolic structures are also reduced considerably when compared to related structures. This is illustrated by a remarkable reduction of more than 45% in the area–time requirements of the proposed structures when compared to existing GF(2m) structures based on unidirectional data flow.