Hardware implementation of double basis multiplier using TMVP approach over GF (2m)

Finite field multiplication plays a important roles in the applications of elliptic curve cryptography. In this paper, we use PB and modified polynomial basis(MPB) define a double basis multiplication, where MPB is transformed by PB when F(x) = xm + xn + 1, n ≥. m/2 We find that the double multiplication can transformed into Toeplitz matrix vector produc-t(TMVP). To reduce time and space complexities, we recursively use two-way TMVP approach calculate the product of double basis multiplication. We respectively implement shifted addition algorithm and TMVP approach in hardware chip FPGA Kintex7-xc7k325T. The proposed structure can obtain significantly lower area-delay product.