Applying Pell Numbers for Efficient Elliptic Curve Large Scalar Multiplication

One of the most effective techniques of cryptography is the Elliptic Curve Cryptography (ECC) which is currently used widely. The ECC provides a high level of security with a smaller key size and faster calculation. The scalar multiplication using points on a curve is the main process to generate the key in the ECC. However, the computation time to generate the key significantly increases with a number of arithmetic operations for a large scalar multiplication. Therefore, a new method applying with Pell numbers is presented. This proposed method outperforms traditional binary representation method regarding the computational efficiency for the large scalar multiplication.