Efficient Bit-Serial Finite Field Montgomery Multiplier in GF(2m)

Montgomery multiplication in finite fields has been paid more and more attention recently since it shows advantageous over regular multiplication in speeding up elliptic curve cryptography based network security protocols. In this paper, a most-significant-bit first bit-serial Montgomery multiplication algorithm in GF(2(m)) using weakly dual bases is proposed for the first time. Then a new bit-serial Montgomery multiplier architecture is proposed using a linear feedback shift register (LFSR). Complexity comparison has shown that the proposed multiplier is comparable to or has certain advantage over the best among the existing similar works found in the literature.