Optimized Design of ECC Point Multiplication Algorithm Over GF(2m)

In order to improve the efficiency of the Elliptic Curve Cryptography (ECC) point multiplication algorithm, this paper presents a new high-efficient algorithm and architecture of ECC point multiplication. Firstly, we analyze and optimize the designs of the modular addition, the modular multiplication, the modular square and the modular inversion. Then, we propose an integral serial and partial parallel structure of point multiplication over GF(2m), and design the overall hardware circuit using 2 modular multiplication units. Over GF (2233), the experimental results using FPGA show that our approach can reduce time required for point multiplication to 5.87us, while the resource cost is kept a reasonable amount to 8682 slices.