Efficient Algorithms and Architectures for Double Point Multiplication on Elliptic Curves

Efficient implementation of double point multiplication is crucial for elliptic curve cryptographic systems. We propose efficient algorithms and architectures for the computation of double point multiplication on binary elliptic curves and provide a comparative analysis of their performance for 112-bit security level. To the best of our knowledge, this is the first work in the literature which considers the design and implementation of simultaneous computation of double point multiplication. We first provide algorithmics for the three main double point multiplication methods. Then, we perform data-flow analysis and propose hardware architectures for the presented algorithms. Finally, we implement the proposed state-of-the-art architectures on FPGA platform for the comparison purposes and report the area and timing results. Our results indicate that differential addition chain based algorithms are better suited to compute double point multiplication over binary elliptic curves for high performance applications.