A novel polynomial basis multiplier for arbitrary elliptic curves over GF (2m)

Finite field GF (2^m) arithmetic plays a crucial role in applications like Computer algebra, Coding theory and Elliptic Curve Cryptography (ECC). The GF (2^m) multiplication is considered significant building block among the finite field arithmetic operations. A new shift and add polynomial basis multiplier over GF (2^m) is explained in this paper for irreducible GF (2^m) generating polynomials f (x) = x^m +x(k_t) + x(k_t-1) + ...... x(k₁) + 1. The multiplier which is proposed has less area and minimum number of gates. In this paper the RTL code is compiled and synthesized using Encounter RTL Compiler tool provided by the Cadence Design Systems. Synthesis is carried out using the TSMC 135nm, 65nm and 40nm technology files.