Speeding up scalar multiplication using a new signed binary representation for integers

Abstract

Scalar multiplication dP and gP+hQ are important in encryption, decryption and signature in information security and wireless network. The speed of computation of scalar multiplication is significant for related applications. In this paper, a new signed binary representation (SBR) for integers called complementary code method (CC) is proposed, which has minimum weight and needs less memory. An efficient algorithm using CC method for computing dP is shown also. According to analyzing and comparing to the other methods, this algorithm is the better one in window methods and is the simplest for applying in software and hardware. By applying joint representation in computing gP+hQ, new algorithm using CC method has the least joint weight compared to other methods mentioned in this paper. So, the new SBR can efficiently speed up the computation of scalar multiplication dP and gP+hQ and can be widely used in secure communication for improving the speed of encryption and signature. © Springer-Verlag Berlin Heidelberg 2007.