A Comparison of Double Point Multiplication Algorithms and their Implementation over Binary Elliptic Curves

Efficient implementation of double point multiplication is crucial for elliptic curve cryptographic systems. We revisit three recently proposed simultaneous double point multiplication algorithms. We propose hardware architectures for these algorithms, and provide a comparative analysis of their performance. We implement the proposed architectures on Xilinx Virtex-4 FPGA, and report on the area and time results . Our results indicate that differential addition chain based algorithms are better suited to compute double point multiplication over binary elliptic curves for both high performance and resource constrained applications. Index Terms Elliptic curve cryptography (ECC), differential addition chains, binary fields, double point multiplication, Field Programmable Gate Array (FPGA).