Fast Elliptic Curve Point Multiplication using Double-Base Chains

Among the various arithmetic operations required in implementing public key cryptographic algorithms, the elliptic curve point multiplication has probably received the maximum attention from the research community in the last decade. Many methods for e#cient and secure implementation of point multiplication have been proposed. The e#ciency of these methods mainly depends on the representation one uses for the scalar multiplier. In the current work we propose an e#cient algorithm based on the so-called double-base number system. We introduce the new concept of double-base chains which, if manipulated with care, can significantly reduce the complexity of scalar multiplication on elliptic curves. Besides we have adopted some other measures to further reduce the operation count. Our algorithm compares favorably against classical and other similar approaches