Hardware Implementation of Elliptic Curve Point Multiplication over GF (2) for ECC protocols

The Elliptic Curve Cryptography covers all relevant asymmetric cryptographic primitives like digital signatures and key agreement algorithms. In the present work, we develop a design of elliptic curve operations over binary Fields GF (2). The function used for this purpose is the scalar multiplication kP which is the core operation of ECCs. Where k is an integer and P is a point on an elliptic curve. The EC Point multiplication processor defined in affine coordinates is achieved by using a dedicated Galois Field arithmetic implemented on FPGA using VHDL language.