High-speed and low power unified dual-field multiplier in GF (P) and GF (2m)

This paper presents a new hardware architecture for a unified multiplier, which operates in two types of finite field: GF (P) and GF (2m). We present a simple but highly useful modification of the conventional hardware implementation of accumulation in finite field over GF (P) and GF (2m). This new design uses parallel one's counters to accumulate the binary partial product bit in GF (P) and further uses a T flip-flop for binary extension field. The proposed multiplier in GF (2m) achieves 11.76% and 30.23% gain in speed for (8, 16, 32) and (64, 128) bit operands respectively and an average 3.92% reduction in power consumption. The unified dual field multiplier achieves 19.3% and 14.3% gain in speed and reduction in power consumption respectively for 8 bits operand. The proposed multiplier is scalable for operands of any size. The multiplier uses the LSB-first bit serial architecture for multiplication in GF (P) and GF (2m), other than Montgomery multiplication algorithm, which mostly employs existing dual field multipliers.