LFSR Based Low Complexity Montgomery Multiplier in GF(2m) for A Class of Fields

Montgomery multiplication (MM) in GF(2(m)) is a popular technique to speedup network security protocols such like digital signature provided by elliptic curve cryptography (ECC) and key distribution supported by ECC or Diffie-Hellman. MM in GF(2(m)) is defined as ABr(-1) mod f(x), where f(x) is the irreducible polynomial of degree m and r is a fixed element in the field. In this paper, a low complexity Montgomery multiplier in GF(2(m)) using Linear Feedback Shift Registers (LFSR) is proposed for the class of fields generated with an irreducible all-one polynomial. The latency of the proposed architecture is shown to be lower than the best among existing works found in the literature. Furthermore, highly regular architecture in LFSR and available LFSR based low power techniques make our proposal more attractive than non-LFSR architectures. On the other hand, the constraint of the new multiplier is that it will not have speed advantage when the system clock rate is higher than 2GHz.