Unified dual-field multiplier in GF(P) and GF(2k)

A scalable unified multiplier for both prime fields GF(P) and binary extension fields GF(2^k), where P=2^m-1 and GF(2^k) is generated by an irreducible all one polynomial. The proposed unified dual-field multiplier uses the LSB-first bit-serial architecture for multiplication in GF(P) and GF(2^k) other than the Montgomery multiplication algorithm, which has been employed by most existing dual-field multipliers. The proposed unified dual-field multiplier costs little space and time complexities. The new multiplier is scalable for operands of any size while other existing dual-field multipliers are only scalable for operands with multiples of m. Furthermore, the proposed multiplier has simplicity, regularity, modularity and concurrency and is very suitable to be implement in VLSI.