A formula for point addition in elliptic curves using a±ne representation and its implementation in FPGA is presented. The use of this new formula in hardware implementations of scalar multiplications for elliptic curve cryptography has the main advantages of: (i) reducing area for the implementations of elliptic curve point addition, and (ii) increasing the resistance to side channel attacks of the hardware implementation itself. Hardware implementation of scalar multiplication for elliptic curve cryptography using this new formulation requires low area resources while keeping high performance compared to implementations using projective coordinates, which are usually considered faster than the a±ne coordinates.