A New Double Point Multiplication Method and its Implementation on Binary Elliptic Curves with Endomorphisms

Efficient and high-performance implementation of point multiplication is crucial for elliptic curve cryptosystems. In this paper, we present a new double point multiplication algorithm based on differential addition chains. We use our scheme to implement single point multiplication on binary elliptic curves with efficiently computable endomorphisms. Our proposed scheme has a uniform structure and has some degree of built-in resistance against side channel analysis attacks. We design a crypto-processor based on the proposed algorithm for double point multiplication and evaluate its area and time efficiency on FPGA. To the best of the authors’ knowledge, this is the first hardware implementation of single point multiplication (using double point multiplication) on elliptic curves with efficiently computable endomorphisms. Our analysis and timing results show that the expected acceleration in point multiplication is considerable. Prototypes of the proposed architectures are implemented and experimental results are presented.