Hastening point multiplication in the ECC

The demanding of the lightweight algorithms to produce efficient techniques used for security, is paving the way toward the exploiting of elliptic curve for cryptography. Therefore, there has a trend for substituting the traditional public key cryptography by the Elliptic Curve Cryptography (ECC) due to its efficiency for providing a high security with smaller keys in the comparison with other algorithms. The main problem in elliptic curve cryptography is the complexity of executing the operation of multiplying a point on the elliptic curve by the scalar value which is mainly fulfilled by the doubling and addition operations and is called scalar multiplication or point multiplication. This scalar can be represented by zeros and ones in terms of binary system. In double-and-add method, the number of ones (hamming weight) determines the number of addition operations, while the number of bits that represents the scalar determines the number of doubling operations. This paper produces the encoding method for reducing the hamming weight of the scalar and thereby diminishing the complexity of the scalar multiplication. The proposed method is compared with the one's complement method and the simulation analysis showed that it gives lower hamming weight than the one's complement method.