Abstract: In recent years, the communications field has achieved tremendous development.Applications such as online banking and mobile communications have increased the security requirements in resource-constrained environments.Compared with traditional cryptographic algorithms, elliptic curve cryptosystem(ECC) provides better security standards and more space for optimizing performance parameters.Therefore, an efficient elliptic curve cipher hardware design scheme is proposed.Based on the exis-ting research, the proposed scheme uses the projected coordinate system LD Montgomery ladder algorithm to study the core scalar multiplication operation in ECC, and uses parallel scheduling to reduce delay in the group operation layer.For finite field ope-rations, the bit-parallel multiplication algorithm and improved Euclidean inverse algorithm are adopted.Based on Xilinx Virtex-5 and Virtex-7 FPGA device, the architecture is implemented on the binary domains with lengths of 163, 233 and 283 respectively.The experimental results show that the proposed scheme requires less FPGA resource consumption and faster calculation speed.Compared with other methods, the hardware resource consumption is reduced by 52.9% and the scalar multiplication operation speed is increased by 3.7times, so it is better suitable for the application of resource-constrained devices.

Key words: Binary extension field, Elliptic curve cryptography, Field-programmable gate array, Inversion, Scalar multiplication