Fast simultaneous scalar multiplication

Scalar multiplication is a very expensive operation in elliptic curve based cryptographic protocol. In this paper, we propose a modified simultaneous elliptic curve scalar multiplication algorithm using complementary recoding. The signed binary representation of an integer is obtained by simple arithmetic operations such as complement and bitwise subtraction. This is an efficient method to obtain the signed binary representation of scalar when compared to other standard methods such as NAF, MOF and JSF.