The password-based key derivation function Scrypt has been employed for many services and applications due to its protection ability. It has also been employed as a proof-of-work algorithm in blockchain implementations. Although this cryptographic hash function provides very high security, the processing speed and power consumption to generate a hashed block for the blockchain network are low-performance. In this paper, a high-speed and low-power hardware architecture of the Scrypt function is proposed to generate blocks for the Scrypt-based blockchain network. This architecture minimizes the number of main computational blocks to reduce the power consumption of the system. In addition, the proposed sharing resources and pipelined architectures make the calculation speed increase significantly while the hardware cost is reduced by half compared to the parallel non-pipelined architecture. The full hardware system is designed and implemented on Xilinx Virtex-7 and Aveo U280 FPGA platforms. The hash rate of the proposed system reaches 229.1 kHash/s. Its hash rate, hardware and energy efficiencies are much higher than those of the other works implemented on FPGA and GPU hardware platforms. The proposed hardware architecture is also successfully implemented in an ASIC design using ROHM 180 nm CMOS technology.